Verification - Input Commands

Activation and deactivation of elements in *ACTIVATE_ELEMENTS are verified in this test.

Tested parameters: $t_{birth}$ and $t_{death}$.

Four CHEX elements are positioned along the X-axis as displayed in Figure 1. The activation and deactivation of each element is presented in Table 1.

An initial velocity in the X-direction is imposed on element 1. Once element 1 has passed the position of element 2, element 2 and 4 are activated and element 3 deactivated. Element 1 continues to translate along the X-axis and then collides with element 4, bounces back, and eventually collides with element 2.

The positions of the elements at initiation and termination are checked.

Tests

This benchmark is associated with 1 tests.

Deleting elements created by *COMPONENT_REBAR with *ACTIVATE_ELEMENTS are verified with this test.

One rebar grid is created using *COMPONENT_REBAR. The grid is given an initial velocity in x-direction. A function is set so that when the center of gravity of all rebar elements which are > 0 in X-direction, the rebar elements will be deactivated, see Figure 1.

The mass of the rebars at initiaton and termination is checked.

Tests

This benchmark is associated with 1 tests.

Strength prior to element activation in *ACTIVATE_ELEMENTS is verified in this test.

Tested parameters: $\xi$.

Four CHEX elements are positioned as displayed in Figure 1.

Element 1 and 3 are merged to element 2 and 4 respectively. Element 2 and 4 are given an initial velocity in the X-direction and element 1 and 3 are not activated until half the simulation time has passed. Before activation, element 1 has full strength while element 3 has no strength. Once the elements are activated, there should be no gap between element 1 and 2.

The positions of the elements at initiation and termination are checked.

Tests

This benchmark is associated with 1 tests.

The different mass distribution options available in *ADD_MASS are verified in this test.

Tested parameters: m_add and distribution.

Three discs are spinning around their central axes. In the first disc, the added mass is distributed over the nodes (option 0). In the second and third disc, the added mass is distributed over the area (option 1 and 2). An added mass equal to the actual mass of the disc is used.

The kinetic energy due to the added mass for each disc is calculated as:

$$ E_k = \frac{1}{2} \cdot I \cdot \omega^2 $$

$\omega$ is the angular velocity and $I$ is the moment of inertia, defined as:

$$ I = \frac{1}{2} \cdot m \cdot r^2 $$

$m$ is the mass and $r$ is the radius of the disc.

The kinetic energy of each disc at termination is checked.

Tests

This benchmark is associated with 1 tests.

Activation and deactivation of *BC_MOTION are verified in this test.

Tested parameters: t_beg and t_end.

Two CHEX elements are subjected to a constant force. The first element is fixed in XYZ at initiation and released after half the termination time. The second element is free at initiation and fixed in XYZ after half the termination time. The displacement at termination, $d$, should therefore be the same in both elements:

$$ d = \frac{a \cdot (t_{end}/2)^2}{2} $$

The displacements of the elements are checked at termination.

Tests

This benchmark is associated with 1 tests.

The options for prescribed rotational motions in *BC_MOTION are verified in this test.

Tested parameter: $pmeth$.

A rotational motion is imposed on three CHEX elements. In the first element, the rotation is defined as:

$$ \theta = \frac{\pi}{4}\cdot\frac{t^2}{t_{end}^2} $$

$t$ is the current time in the simulation and $t_{end}$ is the termination time.

In the second element, the angular velocity is defined as:

$$ \dot{\theta}= \frac{\pi}{2}\cdot\frac{t}{t_{end}^2} $$

In the third element, the angular acceleration is defined as:

$$ \ddot{\theta} = \frac{\pi}{2}\cdot\frac{1}{t_{end}^2} $$

The rotation of the elements at termination should therefore be $\pi/4$ rad.

The rotations of the elements are checked at termination.

Tests

This benchmark is associated with 1 tests.

The options for prescribed translational motions in *BC_MOTION are verified in this test.

Tested parameters: $pmeth$, $direc$, $cid$ and $sf$.

The test consists of 27 CHEX elements in a grid of 3 x 3 x 3, as displayed in Figure 1.

Each element in the grid has unique settings in *BC_MOTION:

1, 1:3, 1:3 - prescribed motions in the X-direction
2, 1:3, 1:3 - prescribed motions in the Y-direction
3, 1:3, 1:3 - prescribed motions in the Z-direction

1:3, 1, 1:3 - prescribed accelerations
1:3, 2, 1:3 - prescribed velocities
1:3, 3, 1:3 - prescribed displacements

1:3, 1:3, 1 - motions defined using a curve
1:3, 1:3, 2 - motions defined using a function
1:3, 1:3, 3 - motions defined using either a curve or a function, with a scale factor defined

For example, the element in position 2, 2, 2 has a prescribed velocity in the Y-direction defined by a function.

The displacement, $d$, velocity, $v$, and acceleration, $a$, are defined so that the displacements of the elements are the same at termination:

$$ d = v \cdot t_{end} = \frac{1}{2} \cdot a \cdot t_{end}^2 $$

The displacements of the elements are checked at termination.

Tests

This benchmark is associated with 1 tests.

This test is similair to the test "*BC_MOTION - Rotational constraints in the global coordinate system". In the current test, the rotational constraints are defined in local coordinate systems instead.

Tests

This benchmark is associated with 1 tests.

Rotational constraints defined in the global coordinate system are verifed in this test.

Tested parameters: bc_rot and csysid_rot.

The test consists of 24 CHEX elements positioned as displayed in Figure 1. The three elements in each column has the same rotational constraint. From left to right: 0, X, Y, Z, YZ, ZX, XY, XYZ.

A spin is applied to all elements. The eight elements in each row spin around the same axis but each about its own center of gravity. The rotation point is set in the center of gravity by setting $csysid_{rot} = 0$.

The top row rotates around the Z-axis, the middle row around the Y-axis and the bottom row around the X-axis. At termination the elements that are free to rotate should have rotated $\pi/4$ rad.

The rotations of the elements are checked at termination.

Tests

This benchmark is associated with 1 tests.

This test is similair to the test "*BC_MOTION - Translational constraints in the global coordinate system". In the current test, the translational constraints are defined in local coordinate systems instead.

Tests

This benchmark is associated with 1 tests.

Translational constraints defined in the global coordinate system are verified in this test.

Tested parameter: bc_tr.

Eight CHEX elements are aligned along the global X-axis as displayed in Figure 1.

A unique translational constraints are imposed on each element. From left to right: 0, X, Y, Z, XY, YZ, ZX, XYZ. A pressure is applied, causing deformation of all elements except the one fixed in XYZ.

At termination, the displacement should be zero in the constrained directions. Displacements in the free directions are calculated based on the applied pressure and bulk modulus of the material.

The displacements of the elements are checked at termination.

Tests

This benchmark is associated with 1 tests.

Tested parameters: coid, entype₁, enid₁, entype₂, enid₂.

This model tests the command *BC_PERIODIC. Two rigid elements inside a box component is given a prescribed motion in X & Y-direction. The box component consists of a mesh of 5x5x2 elements. Motion in Z-direction is restricted for the entire model. The bottom surface is completely fixed. To apply cyclic symmetry to the model, periodic boundary conditions are used to couple surface 1 & 2, and surface 3 & 4. The corresponding nodes for the coupled surfaces experience equivalent displacements. See Figure 1.

A larger model displaying the repetitive pattern is illustrated in Figure 2.

Node displacements are checked for version control.

Tests

This benchmark is associated with 1 tests.

This model tests the command *BC_SYMMETRY. The test consists of six CHEX elements, all located at a distance from the symmetry planes defined in the global coordinate system. The elements are given a prescribed velocity in the -Z, +Z, -Y, +Y, -X, +X directions. None of the elements should pass through any of the axes of the symmetry planes. See Figure 1.

X, Y and Z coordinates of the elements are checked for version control.

Tests

This benchmark is associated with 1 tests.

Symmetry and tolerance defined in local coordinate systems are verified in this test.

Tested parameters: csysid₁, csysid₂, csysid₃, tol

An element is defined by the coordinates ($d$, $d$, $d$) and ($L+d$, $L+d$, $L+d$), where $L$ is the element side length and $d$ is an offset distance. Three local coordinate systems are defined as displayed in Figure 1. and described in Table 1. Symmetry conditions are defined in these local coordinate systems.

Prescribed motions are imposed on the three surfaces opposite the surfaces affected by the symmetry.

Two tests are done. In the first test, the tolerance is greater than $d$, meaning that symmetry will be active, and the element expands because of the prescribed motions. In the second test, the tolerace is smallar than $d$, meaning that symmetry conditions are not active, and the cube will translate instead of expanding.

The displacements of the nodes initially located at ($d$, $d$, $d$) and ($L+d$, $L+d$, $L+d$) are checked at termination.

Tests

This benchmark is associated with 2 tests.

Symmetry options and tolerance defined in the global coordinate system are verified in this test.

Tested parameters: $plane$ and $tol$.

The test consists of a CHEX element defined by the coordinates ($d$, $d$, $d$) and ($L+d$, $L+d$, $L+d$), where $L$ is the element side length and $d$ is an offset distance. Prescribed displacements are imposed on the surfaces opposite the symmetry surfaces. The displacements are in the normal directions of the surfaces.

A total of 16 configurations of the model are run and these can be divided into two sets. All symmetry options (0, X, Y, Z, XY, YZ, ZX, XYZ) are tested for both sets. In one of the sets, the tolerance is greater than the offset distance and in the other set it is not, meaning that the symmetry is not activated.

At termination, the displacement of the surfaces affected by the symmetry should be equal to zero. The displacement of free surfaces should be equal to the prescribed displacement.

The displacements of the nodes initially located at ($d$, $d$, $d$) and ($L+d$, $L+d$, $L+d$) are checked at termination.

Tests

This benchmark is associated with 16 tests.

Teleportation displacements and velocities in the global coordinate system are verfied in this test.

Tested parameters: trig, $\Delta_x$, $\Delta_y$, $\Delta_z$, $\Delta v_x$, $\Delta v_y$, $\Delta v_z$.

A CHEX element is given the initial velocity $v_{0,x}$, $v_{0,y} = 2 v_{0,x}$ and $v_{0,z} = 3 v_{0,x}$.

Teleportation displacements are defined in the global coordinate system as:

$\Delta_x = -v_{0,x}\cdot trig$, $\Delta_y = -v_{0,y}\cdot trig$, $\Delta_z = -v_{0,z}\cdot trig$

Parameter $trig$ is set to half the termination time.

Teleportation velocities are defined as:

$\Delta v_x = -v_{0,x}$, $\Delta v_y = -v_{0,y}$ and $\Delta v_z = -v_{0,z}$.

A sensor is located in the center of the element, which coincides with the origin of the global coordinate system at initiation.

Coordinates of the sensor at teleportation should be:

$v_{0,x}\cdot trig$, $v_{0,y}\cdot trig$ and $v_{0,z}\cdot trig$ in the X-, Y- and Z-direction.

Coordinates of the sensor at termination should be:

$-\Delta v_x\cdot (term-trig)$, $-\Delta v_y\cdot (term-trig)$ and $-\Delta v_z\cdot (term-trig)$ in X-, Y- and Z-direction.

Parameter $term$ is the termination time.

Sensor coordinates vs. time is presented in Figure 1. together with target curves.

Max, min and average values of sensor coordinates are checked.

Tests

This benchmark is associated with 1 tests.

Multiple teleportations using a trigger function is verfied in this test.

Tested parameters: $trig$, $\Delta_x$, $\Delta_y$, $\Delta_z$, $multiple$ and $velocity$.

A CHEX element is given the initial velocity $v_{0,x}$, $v_{0,y} = 2 v_{0,x}$ and $v_{0,z} = 3 v_{0,x}$.

A sensor (with id = 1) is defined at the center of the element, which coincides with the origin of the global coordinate system at initiation.

A trigger function is defiend as:

$$ \sqrt{xs(1)^2 + ys(1)^2 + zs(1)^2} - disp_{max} $$

The first term corresponds to the sensor displacement and $disp_{max}$ is the displacement at which teleportation is to occur, defined as:

$$ disp_{max} = trig\cdot \sqrt{v_{0,x}^2+v_{0,y}^2+v_{0,z}^2} $$

Parameter $trig$ is set to a third of the termination time.

Teleportation displacements are defined as $\Delta_x = -v_{0,x} \cdot trig$, $\Delta_y = -v_{0,y} \cdot trig$, $\Delta_z = -v_{0,z} \cdot trig$, meaning that the element is teleported to its initial position, and the velocities are defined to continue after teleportation.

This configuration should generate two teleportations, and the sensor coordinates at termination should be:

$trig\cdot v_{0,x}$, $trig\cdot v_{0,y}$ and $trig\cdot v_{0,z}$ in the X-, Y- and Z-direction.

Sensor coordinates vs. time is presented in Figure 1. together with target curves.

Max, min and average values of sensor coordinates are checked.

Tests

This benchmark is associated with 1 tests.

Teleportation rotations in a local coordinate system are verified in this test.

Tested parameters: $trig$ and $\theta_z$.

Two CHEX elements are defined in a local coordinate system, which at initiation coincides with the global coordinate system. A sensor (id = 1) is defined at the origin of the local coordinate system. The elements are given an initial velocity $v_0$ in the local X-direction.

A trigger function for teleportation is defined as:

$$ abs(xs(1)) - X_{max} $$

$abs(xs(1))$ corresponds to the absolute value of the sensor X-coordinate and $X_{max}$ is the displacement at which teleportation should occur.

Teleportation rotation is defined as $\theta_z = \pi$, and the velocity is defined to continue after the teleportation. This means that after rotation, the local X-direction (which is the elements velocity vector) changes direction and is now opposite the global X-direction.

A second teleportation occurs once the sensor X-displacement reaches $-X_{max}$. After this teleportation, the local X-axis coincides with the global X-axis again.

Sensor X-coordinate vs. time is presented in Figure 1. together with a target curve.

Max, min and average value of sensor X-coordinate is checked.

Tests

This benchmark is associated with 1 tests.

All features of *BC_TEMPERATURE are verified in this test.

Tested parameters: $cid$, $sf$, $t_{beg}$ and $t_{end}$.

Eight CHEX elements are positioned as displayed in Figure 1. The temperature of the four elements in the left column is controlled by a curve while the temperature of the elements in the right column is controlled by a function.

The curve is defined as:

The function is defined as:

$$ T(X, t) = \left(\frac{X - X_{min}}{X_{max} - X_{min}}\right) \cdot \left(\frac{t}{t_{end}}\right) \cdot T_{max} $$

$t_{end}$ is the termination time and $T_{max}$ is the maximum temperature. $X$ corresponds to the X-coordinate and $t$ the current time in the simulation. $X_{min}$ and $X_{max}$ are minimum and maximum X-coordinates of the elements in the right column.

The temperatures in the two elements at the top row are just controlled by the curve and function. In the second row, a scale factor of 0.5 is used. Activation and deactivation times are used in the third and forth row respectively.

Maximum and average temperature are checked in the elements.

Tests

This benchmark is associated with 1 tests.

One-dimensional heat conduction is verified in this test.

Tested parameters: $entype$, $enid$ and $cid$.

Prescribed temperatures are imposed at the ends of a rod with an initial uniform temperature, causing the temperature along the rod to change due to conduction. The initial and final temperature in a sensor located at the blue mark in Figure 1. is compared to analytical results.

Temperature at initiation and termination is checked.

Tests

This benchmark is associated with 1 tests.

This tests the *BOLT_FAILURE command. In this benchmark, the bolt failure functionality is tested for two bolts. The bolts are modelled by *COMPONENT_BOLT and the test model is presented in Figure 1.

The bolts are prestressed up until failure. The test is done twice with different parameters set for $T_{fail}$, $S_{fail}$ and $W_{fail}$. This is to ensure that the criteria for the damage parameter, $D$, is fulfilled both by reaching the force limit and the energy absorbed limit. Once $D = 1$ the bolts are eroded, see Figure 2.

For both the tests the maximum value of the damage parameter is checked. For the test were the minimum abosorbed energy prior to failure is checked, the maximum absorbed energy is also checked.

Tests

This benchmark is associated with 2 tests.

Tested parameters: $R$.

This model tests the parameter $R$ in *CFD_DETONATION, which is used to limit the distance the detonation front is allowed to propagate through programmed burn. The test consists of two spherical CFD HE subdomains both with an inner radius of 10 mm and outer radius of 20 mm. A detonation point is set in the centre of each sphere. One of the subdomain's detonation radius is limited to its inner radius by setting $R = 0.01$. It is tested that only the subdomain without the radius limitation is triggered from the detonation.

The test setup can be seen in Figure 1.

Undetonated energy vs. time can be seen in Figure 2.

First and last value of undetonated energy is checked for version control.

Tests

This benchmark is associated with 1 tests.

This model tests airblast propagation for the CFD solver. A hemi-spherical blast modeled with quarter symmetry is detonated. To determine sphericity of the charge at close range, sensors are placed at 0° and 45° angle, measuring the time the blast wave arrives. This is done at two distances, 0.5 and 1.0 meters from the detonation point. Also, incident pressure is being measured. The test setup can be seen in Figure 1.

The configuration is a 0.853493 g TNT charge. Considering half shape and quarter symmerty, the size of the charge would be equal to a charge in free air of:

$$ m_{free \ air} = 0.853493 \cdot 8 = 6.827944 \ kg $$

And due to energy absorbed by the ground, a correction factor of 1.8 is being used:

$$ m_{hemisphere} = \frac{m_{free \ air}}{1.8} $$

Which for this configuration will be a charge of:

$$ m_{hemisphere} = \frac{6.827944}{1.8} = 3.8 \ kg $$

The results are compared with analytical values from Kingery-Bulmash.

Incident pressure vs. time can be seen in Figure 2.

Maximum value of incident pressure and time of arrival at the sensors is checked for version control.

Tests

This benchmark is associated with 1 tests.

This test is similar to the test "*CFD_DOMAIN - Airblast propagation". The difference is that it is being run in two steps.

In step 1, Time and incident pressure is being measured for the closest sensors at $0.5 \ m$ range. The simulation is then stopped.

In step 2, the simulation continues from the output of step 1. Time and incident pressure is beging measured for the sensors at $1.0 \ m$ range.

The expected outcome is to get the same results as the test "*CFD_DOMAIN - Airblast propagation".

Tests

This benchmark is associated with 2 tests.

This model tests that the CFD coupling correctly handles the interaction with Finite Elements and SPH particles at the same time.

The test setup consists of two geometrically identical plates on each side of a spherical charge in the CFD-Domain. Quarter symmetry is used. One is modeled with Finite Elements and the other with SPH Particles. The response should be the same for both methods.

The test setup can be seen in Figure 1.

The velocity of the plates in Z-direction is measured.

Velocity vs. time can be seen in Figure 2.

Last and average velocity is checked for version control.

Tests

This benchmark is associated with 1 tests.

This test shows that higher order elements are superior to linear elements in the case of bending.

Tested parameters: $entype$, $enid$ and $order$.

Two cantilever beams are subjected to a transverse point load at the unconstrained end. One of the beams is modeled with five LHEX elements and the other with five CHEX elements, as visible in Figure 1.

The displacements of the ends vs. time from the simulation are plotted in Figure 2 together with an analytical value of max deflection obtained from Euler-Bernoulli beam theory.

Tests

This benchmark is associated with 1 tests.

Conversion to higher order elements within a specified geometry is verified in this test.

Tested parameters: $entype$, $enid$, $order$ and $gid$.

Three square plates modeled with LHEX elements are positioned as displayed in Figure 1. A geometry (*GEOMETRY_PIPE) is defined with its axial direction aligned with the center of the plates. The diameter of the geometry is smaller than the side length of the plates, meaning that only a part of the plates is inside the geometry. Elements within the geometry are converted to the higher order elements in two of the plates.

The coordinates of a node in each plate are checked.

Tests

This benchmark is associated with 1 tests.

Conversion from linear elements to higher order elements with *CHANGE_P-ORDER is verified in this test.

Tested parameters: $entype$, $enid$ and $order$.

Three plates meshed with LHEX elements are used in this test. Each plate is assigned a unique polynomial order (1,2 or 3) in *CHANGE_P-ORDER. The elements in two of the plates are therefore converted into higher order elements as visible in Figure 1.

The coordinates of a node in each plate are checked.

Tests

This benchmark is associated with 1 tests.

Tested parameters: coid, pid_from, pid_to, gid.

The model tests the command *CHANGE_PART_ID. The test consists of two parts and a geometry. With the use of the command *CHANGE_PART_ID the elements of Part 10 that are inside Geometry 123 will be moved to Part 20. See Figure 1.

The physical mass of part 10, 11 & 20 is checked for version control.

Tests

This benchmark is associated with 1 tests.

Tested parameters: coid, pid_from, pid_to, gid

The model tests that the command *CHANGE_PART_ID is functioning within included files when using offsets to part ID:s. The test is similar to the test "*INCLUDE - Offset" and should give the same result.

Targets:
-First cube should rotate 1 lap about X-axis.
-Second cube should move downwards 1 m in Z-direction.

Tests

This benchmark is associated with 1 tests.

Dimensions and positioning of bolts defined with *COMPONENT_BOLT are verified in this test.

Tested parameters: $pid_1$, $pid_2$, $pid_3$, $pid_4$, $csysid$, $D$, $L$, $h$ and $t$.

Two bolts are created using *COMPONENT_BOLT. One is created in the global coordinate system and the other in a local coordinate system. Both the origin and the axes in the local coordinate system differs from the global system, as visible in Figure 1.

Coordinates for a number of nodes are checked.

Tests

This benchmark is associated with 1 tests.

Positioning of bolts with the command *TABLE is verified in this test.

Tested parameters: $pid_1$, $pid_2$, $pid_3$, $pid_4$, $tid$, $D$, $L$, $h$ and $t$.

A number of bolts are positioned as displayed in Figure 1. by using the command *TABLE.

Coordinates for some of the nodes are checked.

Tests

This benchmark is associated with 1 tests.

Dimensions and positioning of boxes defined with *COMPONENT_BOX are verified in this test.

Tested parameters: $pid$, $N_x$, $N_y$, $N_z$, $csysid$, $x_1$, $y_1$, $z_1$, $x_2$, $y_2$ and $z_2$.

Two boxes are created using *COMPONENT_BOX. One is created in the global coordinate system and the other one in a local coordinate system. Both the origin and the axes in the local coordinate system differs from the global system, as visible in Figure 1.

Coordinates for a number of nodes are checked.

Tests

This benchmark is associated with 1 tests.

Dimensions and positioning of boxes defined with *COMPONENT_BOX_IRREGULAR are verified in this test.

Tested parameters: $pid$, $N_1$, $N_2$, $N_3$, $csysid$, $x_{1-8}$, $y_{1-8}$, $z_{1-8}$, $id_{1-n}$, $x_{id,1-n}$, $y_{id,1-n}$ and $z_{id,1-n}$.

Two boxes are created using *COMPONENT_BOX_IRREGULAR. One is created in the global coordinate system and the other one in a local coordinate system. Both the origin and the axes in the local coordinate system differs from the global system, as visible in Figure 1.

Coordinates for a number of nodes are checked.

Tests

This benchmark is associated with 1 tests.

Dimensions and positioning of cylinders defined with *COMPONENT_CYLINDER are verified in this test.

Tested parameters: $pid$, $N_1$, $N_2$, $csysid$, $x_1$, $y_1$, $z_1$, $x_2$, $y_2$, $z_2$, $R_1$ and $R_2$.

Two cylinders are created using *COMPONENT_CYLIDNER. One is created in the global coordinate system and the other one in a local coordinate system. Both the origin and the axes in the local coordinate system differs from the global system, as visible in Figure 1. The cylinder in the local coordinate system is tapered, verifying that parameters $R_1$ and $R_2$ works.

Coordinates for a number of nodes are checked.

Tests

This benchmark is associated with 1 tests.

Dimensions and positioning of pipes defined with *COMPONENT_PIPE are verified in this test.

Tested parameters: $pid$, $N_1$, $N_2$, $N_3$, $csysid$, $\alpha_c$, $x_1$, $y_1$, $z_1$, $x_2$, $y_2$, $z_2$, $R_1$, $R_2$, $R_3$ and $R_4$.

Two pipes are created using *COMPONENT_PIPE. One is created in the global coordinate system and the other one in a local coordinate system. Both the origin and the axes in the local coordinate system differs from the global system, as visible in Figure 1.

Parameter $\alpha_c$ is set to 180 deg. for the pipe defined in the global coordinate system. Parameter $R_1$, $R_2$, $R_3$ and $R_4$ are set so that the pipe in the local coordinate system is tapered and hollow.

Coordinates for a number of nodes are checked.

Tests

This benchmark is associated with 1 tests.

A rebar element with length $L$, diameter $D$ ($L$ >> $D$) and Young's modulus $E$ is fixed at both ends. A transverse displacement, $disp$ ($disp$ < $D$), is defined at the center of the element, causing the element to bend.

The load required to deflect the element to the defined displacement is calculated as:

$$ P = 48EI\cdot \frac{disp}{L^3} $$

$I$ is the second moment of area, defined as:

$$ I = \pi\cdot\frac{D^4}{64} $$

The reaction force in each support should therefore be $P/2$. The reaction forces at termination are checked.

Tests

This benchmark is associated with 1 tests.

Dimensions and positioning of rebar grids defined with *COMPONENT_REBAR are verified in this test.

Two rebar grids are created using *COMPONENT_REBAR. One is created in the global coordinate system and the other one in a local coordinate system. Both the origin and the axes in the local coordinate system differs from the global system. The rebar grids consist of one cell in the X-direction, two cells in the Y-direction and three cells in the Z-diretion, as visible in Figure 1.

Coordinates for a number of nodes are checked.

Tests

This benchmark is associated with 1 tests.

Dimensions and positioning of spheres defined with *COMPONENT_SPHERE are verified in this test.

Tested parameters: $pid$, $N$, $N_c$, $csysid$, $\alpha_c$, $x_0$, $y_0$, $z_0$, $R_1$, $R_2$.

A sphere and a slice of a sphere are created using *COMPONENT_SPHERE. The sphere is defined in the global coordinate system and the slice in a local coordinate system. Both the origin and the axes in the local coordinate system differs from the global system, as visible in Figure 1. Parameter $\alpha_c$ is set to 180°. in the slice.

Coordinates for a number of nodes are checked.

Tests

This benchmark is associated with 1 tests.

Tested parameters: coid, pid₁, pid₂, csysid, R, h, m, η, k_max, cid_axial, cid_shear, cid_bend, cid_rate.

This model tests the command *CONNECTOR_DAMPER. It consists of two tests, one with quasi-static and one with a dynamic response.

An axially loaded damper is positioned between two plates with the command *CONNECTOR_DAMPER. It is first compressed and then loaded in tension. The base plate is restricted in all directions while the top plate is assigned a motion in the negative and positive Z-direction.

See Figure 1.

The damper properties are the same for both tests but the prescribed velocity of the top plate differs.
-Velocity (Quasi-static) = $0.01 \ m/s$
-Velocity (Dynamic) = $1 \ m/s$

The quasi-static as well as the dynamic response of the dampers can be seen in Figure 2.

Maximum and minimum normal force and displacement in Z direction is checked for version control.

Tests

This benchmark is associated with 2 tests.

This test is similair to the test "*CONNECTOR_GLUE_LINE - Normal stress". In the current test, the glue is subjected to a combination of normal and shear stress instead.

Tested parameters: $w$, $h$, $E$, $\nu$, $\sigma_f$, $\tau_f$, $G_I$ and $G_{II}$.

Forces vs. displacements are presented in Figure 1 and 2 together with target curves of the analytical solutions.

Maximum and average value of the forces, delamination energy and area are checked.

Tests

This benchmark is associated with 1 tests.

The glue properties of *CONNECTOR_GLUE_LINE in a state of normal stress is verified in this test.

Tested parameters: $w$, $h$, $E$, $\nu$, $\sigma_f$ and $G_I$.

Two quadratic plates with length 100 mm and thickness 10 mm are glued together with *CONNECTOR_GLUE_LINE. The glue line has a width of 5 mm and a thickness of 1 mm. The glue line runs 10 mm from the edges around the plate, as illustrated in Figure 1.

Prescribed motions causing a state of normal stress in the glue are imposed on the plates. Force vs. displacement from the simulation is presented in Figure 2 together with a target curve of the analytical solution.

Maximum and average value of the force, delamination energy and area are checked.

Tests

This benchmark is associated with 1 tests.

This test is similair to the test "*CONNECTOR_GLUE_LINE - Normal stress". In the current test, the glue is subjected to a state of shear stress instead.

Tested parameters: $w$, $h$, $E$, $\nu$, $\tau_f$ and $G_{II}$.

Force vs. displacement from the simulation is presented in Figure 1 together with a target curve of the analytical solution.

Maximum and average value of the force, delamination energy and area are checked.

Tests

This benchmark is associated with 1 tests.

This test is similair to the test "*CONNECTOR_GLUE_SURFACE - Normal stress". In the current test, the glue is subjected to a combination of normal and shear stress instead.

Tested parameters: $h$, $E$, $\nu$, $\sigma_f$, $\tau_f$, $G_I$ and $G_{II}$.

Forces vs. displacements are presented in Figure 1 and 2 together with target curves of the analytical solutions.

Maximum and average value of the forces, delamination energy and area are checked.

Tests

This benchmark is associated with 1 tests.

The glue properties of *CONNECTOR_GLUE_SURFACE in a state of normal stress is verified in this test.

Tested parameters: $h$, $E$, $\nu$, $\sigma_f$ and $G_I$.

Two quadratic plates with length 100 mm and thickness 10 mm are glued together with *CONNECTOR_GLUE_SURFACE. Prescribed motions causing a state of normal stress in the glue are imposed on the plates.

Force vs. displacement from the simulation is presented in Figure 1 together with a target curve of the analytical solution.

Maximum and average value of the force, delamination energy and area are checked.

Tests

This benchmark is associated with 1 tests.

This test is similair to the test "*CONNECTOR_GLUE_SURFACE - Normal stress". In the current test, the glue is subjected to a state of shear stress instead.

Tested parameters: $h$, $E$, $\nu$, $\tau_f$ and $G_{II}$.

Force vs. displacement from the simulation is presented in Figure 1 together with a target curve of the analytical solution.

Maximum and average value of the force, delamination energy and area are checked.

Tests

This benchmark is associated with 1 tests.

*CONNECTOR_RIGID is verified in this test.

Tested parameters: $entype$ and $enid$.

Two rigid elements are connected with a rigid connection. One of the elements is set in motion. The displacement and velocity in the other element is checked at termination.

Tests

This benchmark is associated with 1 tests.

This test is similair to the test "*CONNECTOR_SPOT_WELD - Normal stress". In the current test, the spot welds are subjected to a combination of normal and shear stress instead.

Tested parameters: $R$, $h$, $k$, $F_t$, $F_s$, $W_t$ and $W_s$.

The resultant force vs. displacement from the simulation is presented in Figure 1 together with a target curve of the analytical solution.

Maximum and average value of the force and dissipated energy are checked.

Tests

This benchmark is associated with 1 tests.

The spot weld properties of *CONNECTOR_SPOT_WELD in a state of normal stress is verified in this test.

Tested parameters: $R$, $h$, $k$, $F_t$ and $W_t$.

Two quadratic plates with length 200 mm and thickness 10 mm are connected to each other by four spot welds defined with *CONNECTOR_SPOT_WELD as illustrated in Figure 1.

Prescribed motions causing a state of normal stress in the spot welds are imposed on the plates. Force vs. displacement from the simulation is presented in Figure 2 together with a target curve of the analytical solution.

Maximum and average value of the force and dissipated energy are checked.

Tests

This benchmark is associated with 1 tests.

This test is similair to the test "*CONNECTOR_SPOT_WELD - Normal stress". In the current test, the spot welds are subjected to a state of shear stress instead.

Tested parameters: $R$, $h$, $k$, $F_s$ and $W_s$.

Force vs. displacement from the simulation is presented in Figure 1 together with a target curve of the analytical solution.

Maximum and average value of the force and dissipated energy are checked.

Tests

This benchmark is associated with 1 tests.

This test is equivalent to the test "*CONNECTOR_SPOT_WELD - Normal stress". The only difference is the input format, in which *CONNECTOR_SPOT_WELD_NODE is used to define the connector location of the spot welds from Node ID. The command is used in combination with *PROP_SPOT_WELD.

All parameters used are the same as in the test "*CONNECTOR_SPOT_WELD - Normal stress", which means that the same result is expected.

Tests

This benchmark is associated with 1 tests.

This test is similair to the test "*CONNECTOR_SPR - Normal stress". In the current test, the rivet is subjected to a combination of normal and shear stress instead.

Tested parameters: $R$, $h$, $f_n^{max}$, $f_t^{max}$, $d_n^{max}$, $d_t^{max}$, $\xi_n$, $\xi_t$, $a_1$, $a_2$ and $a_3$.

Forces vs. time and damage vs. time from the simulation are presented in Figure 1, 2 and 3 together with target curves from a verification script.

Maximum and average forces and damage in the rivet are checked in spr.out. The dissipated energy is also checked for version control.

Tests

This benchmark is associated with 1 tests.

The rivet properties of *CONNECTOR_SPR in a state of normal stress is verified in this test.

Tested parameters: $R$, $h$, $f_n^{max}$, $d_n^{max}$, $\xi_n$, $a_1$, $a_2$ and $a_3$.

Two plates are connected to each other by a self-piercing rivet. Prescribed motions causing a state of normal stress in the rivet are imposed on the plates. Force vs. time and damage vs. time from the simulation are presented in Figure 1 and 2 together with target curves from a verification script.

Maximum and average force and damage in the rivet are checked in spr.out. The dissipated energy is also checked for version control.

Tests

This benchmark is associated with 1 tests.

This test is similair to the test "*CONNECTOR_SPR - Normal stress". In the current test, the rivet is subjected to a state of shear stress instead.

Tested parameters: $R$, $h$, $f_t^{max}$, $d_t^{max}$, $\xi_t$, $a_1$, $a_2$ and $a_3$.

Force vs. time and damage vs. time from the simulation are presented in Figure 1 and 2 together with target curves from a verification script.

Maximum and average force and damage in the rivet are checked in spr.out. The dissipated energy is also checked for version control.

Tests

This benchmark is associated with 1 tests.

Intrinsic operations (dnorm, dnorm_min, dnorm_max) are verified in this test.

Tested parameters: coid, N₁, N₂, m, k

The model contains three springs with different functions defining elastic force versus elongation. The springs are clamped at one end and are given a prescribed displacement at the other end.

The springs have the following properties:

Spring 1:
$$ F_1(t) = dnorm $$

Spring 2:

$$ F_2(t) = dnorm\_min $$

Spring 3:

$$ F_3(t) = dnorm\_max $$

The prescribed displacement of the free nodes is presented in Table 1.

Force vs. time for the springs is presented in Figure 1.

The spring forces are checked at termination.

Tests

This benchmark is associated with 1 tests.

Linear stiffness and damping in *CONNECTOR_SPRING are verified in this test.

Tested parameters: $N_1$, $N_2$, $m$, $k$ and $\xi$.

The model contains two springs with constant stiffness $k$ and mass $m$. The node mass is $m/2$. The springs are clamped at one end and are given an initial velocity $v_0$ at the other end. Spring 1 is undamped and spring 2 is damped. The absolute damping $c$ is defined as a fraction $\xi$ of the critical damping of the springs highest eigenfrequency $\omega_{max}$.

Analytical displacement, spring 1 (undamped):

$$ \omega_0 = \sqrt{\frac{2k}{m}} %= 4.47214 rad/s $$

$$ x_1 (t) = \frac{v_0}{\omega_0}\cdot sin (\omega_0 t) $$

Displacement at time $t = 1$, spring 1:

$$ x_1 (1) = \frac{v_0}{\omega_0}\cdot sin (\omega_0) %= -0.21718 $$

Analytical displacement, spring 2 (damped):

$$ \xi_2 = \frac{c}{\sqrt{2mk}} = \sqrt{2}\cdot \xi %= 0.14142 $$

$$ \omega_d = \omega_0\cdot \sqrt{1-{\xi_2}^2} %= 4.42719 rad/s $$

$$ x_2 (t) = \frac{v_0}{\omega_d}\cdot sin(\omega_d t)\cdot exp(-\xi_2\cdot \omega_0 t) $$

Displacement at time $t = 1$, spring 2:

$$ x_2 (1) = \frac{v_0}{\omega_d}\cdot sin(\omega_d)\cdot exp(-\xi_2\cdot \omega_0) %= -0.11516 $$

The spring displacements are checked at termination.

Tests

This benchmark is associated with 1 tests.

Non-linear stiffness and damping in *CONNECTOR_SPRING are verified in this test.

Tested parameters: $N_1$, $N_2$, $m$, $k$ and $\xi$.

The model contains two springs with non-linear force-displacement and damping properties. The springs are clamped at one end and given a prescribed velocity $v=1$ at the other end. Velocity and displacement at a given moment $t$ takes trivial values.

$$ v_{norm} = v = 1 $$

$$ d_{norm} = \int v_{norm}dt = v_{norm}t = t $$

The force at $t = 1$, spring 1:

$$ F_1(1) = \exp(d_{norm}) = \exp(t) = e %\approx 2.718 $$

The force at $t = 1$, spring 2:

$$ F_2(1) = d_{norm} + \exp(v_{norm}) = t + \exp(t) = 1 + e %\approx 3.718 $$

The spring forces are checked at termination.

Tests

This benchmark is associated with 1 tests.

This model tests the unloaded spring length, parameter $l_{0}$ in *CONNECTOR_SPRING , which is used when importing results in subsequent simulations. The test consists of 2 steps. The *CONNECTOR_SPRING command with parameter $l_{0}$ is automatically generated by the solver engine in the state file impetus_state_spring1.k at termination.

The model contains two springs with constant stiffness $k$ and mass $m$. The node mass is $m/2$. The springs are clamped at one end and are given an initial velocity $v_0$ at the other end. Spring 1 is undamped and spring 2 is damped. The absolute damping $c$ is defined as a fraction $\xi$ of the critical damping of the springs highest eigenfrequency $\omega_{max}$.

Analytical displacement, spring 1 (undamped):

$$ \omega_0 = \sqrt{\frac{2k}{m}} $$

$$ x_1 (t) = \frac{v_0}{\omega_0}\cdot sin (\omega_0 t) $$

Displacement at time $t = 1$, spring 1:

$$ x_1 (1) = \frac{v_0}{\omega_0}\cdot sin (\omega_0) $$

Analytical displacement, spring 2 (damped):

$$ \xi_2 = \frac{c}{\sqrt{2mk}} = \sqrt{2}\cdot \xi $$

$$ \omega_d = \omega_0\cdot \sqrt{1-{\xi_2}^2} $$

$$ x_2 (t) = \frac{v_0}{\omega_d}\cdot sin(\omega_d t)\cdot exp(-\xi_2\cdot \omega_0 t) $$

Displacement at time $t = 1$, spring 2:

$$ x_2 (1) = \frac{v_0}{\omega_d}\cdot sin(\omega_d)\cdot exp(-\xi_2\cdot \omega_0) $$

The test setup can be seen in Figure 1.

Spring elongation vs. time for step 1 can be seen in Figure 2 together with a target curve from a verification script.

Spring elongation vs. time for step 2 can be seen in Figure 3 together with a target curve from a verification script.

The spring displacements are checked for version control.

Tests

This benchmark is associated with 2 tests.

Contact and friction forces between all element types are verified in this test.

Tested parameters: $pfac$ (automatic calculation of penalty stiffness) and $\mu$.

The test consists of 81 plate-pairs divided into nine models with nine plate-pairs in each model. One of the nine models is presented in Figure 1. The nine bottom plates in each model are of the same element type, but the type differs between the nine models. Each of the nine top plates consists of a unique type of elements and are the same in all models.

The type of elements used in the bottom plates in each model is presented in Table 1. Each row of top plates consists of a certain element type and each column of elements of a certain polynomial order. Top to bottom: tetrahedrons, pentahedron, hexahedron. Left to right: linear, quadratic, cubic.

The plates are first pressed together by a prescribed pressure (*LOAD_PRESSURE) and then a prescribed motion (*BC_MOTION) is causing the top plates to slide against the fixed bottom plates.

The contact force in the direction of the applied pressure vs. time for all plate-pairs and all models are presented in Figure 2 - 10 while the contact force in the sliding direction vs. time for all plate-pairs and all models are presented in Figure 11 - 19. Contour plots of the contact pressure for all models are presented in Figure 20 - 28

The contact forces are checked at termination.

Tests

This benchmark is associated with 9 tests.

The contact force in a simulation based on a state-file is verified in this test.

Tested parameter: $pfac$ (automatic calculation of penalty stiffness).

The model consists of nine pairs of plates. Each pair consists of a certain type of solid elements: LTET, LPEN, LHEX, QTET, QPEN, QHEX, CTET, CPEN or CHEX.

The process is divided into two steps. In step 1, the two plates in each pair are pressed together by a prescribed motion. At termination, the results are exported to a state-filek. The model at initiation and termination is displayed in Figure 1.

In step 2, the state-file is imported. The plates are fixed and a contact with the same configuration as in step 1 is defined. The contact force should therefore be of the same magnitude at termination of step 1, initiation of step 2 and at termination of step 2.

Contact forces in the direction of loading from step 1 and and step 2 are presented in Figure 2 and 3. The discrepancy in contact force between the different element types is mainly due to the coarse mesh that has been used. With a refined mesh, the discrepancy is reduced.

The contact forces are checked at initiation and termination in both steps.

Tests

This benchmark is associated with 2 tests.

Contact between multiple parts by using the "all-to-all"-option in *CONTACT is verified in this test.

Tested parameters: $entype_1$, $entype_2$ and $pfac$ (automatic calculation of penalty stiffness).

The model consists of 500 deformable spheres inside a rigid casing. There is no initial contact between the spheres, but the spheres are expanding during the course of the simulation, and contact emerges between the spheres. See Figure 1.

Maximum contact penetration, contact area at termination and energy balance are checked for version control.

Tests

This benchmark is associated with 1 tests.

Tested parameters: fric_heat.

This is a general test for *CONTACT. The model tests friction to heat conversion which is generated when a block is sliding against a plate.

The test setup is displayed in Figure 1

Targets:
The friction energy generated should be equal to the thermal energy that is added to the block and the plate.

First, average and last values for thermal energy and friction energy is checked for version control.

Tests

This benchmark is associated with 1 tests.

This is a general test for *CONTACT.

Tested parameter: $pfac$ (automatic calculation of penalty stiffness).

A Newton's cradle containing three balls is simulated in this test. The model is displayed in Figure 1. The collisons are elastic and no energy loss occurs in the system.

The energy balance, and maximum and minimum kinetic energy of the balls are checked.

Tests

This benchmark is associated with 1 tests.

This is a general test for *CONTACT.

Tested parameters: $pfac$ (automatic calculation of penalty stiffness).

This is a model of a Vickers hardness test. The test is done with nine specimens, each modeled with a unique type of solid elements. The indenter is modeled with LHEX-elements in all cases, since negligible deformations are expected in the indenter. The specimen configuration is presented in Figure 1 and the maximum contact pressure is presented in Figure 2.

Contact forces vs. time are presented in Figure 3. Similar response is obtained from all specimens except for the linear tetrahedron specimen, which shows a significantly stiffer response.

Maximum contact force, maximum contact penetration and energy balance are checked.

Tests

This benchmark is associated with 1 tests.

Accuracy edge in *CONTACT_ACCURACY is verified in this test.

Tested parameters: accuracy_edge.

Two identical sets consisting of a cube and a cylinder are used in this test. The cylinders are linearly tapered, and the inner radius at one end equals the cubes face diagonal, $D_c/2$, while the radius on the other end equals $0.97\cdot D_c/2$.

The cubes are positioned inside the cylinders, so that only edges are in contact, and given an initial velocity so that they move towards the other sides of the cylinders. The test setup is displayed in Figure 1.

Contact forces between the cubes and the cylinders increases gradually as the cubes are moving down the cylinders. The smoothness of the contact forces are controlled with contact accuracy. The accuracy level used is 10 for both sets but the flag to activate increased accuracy at sharp edges (Accuracy_edge) is activated for the second set (right) but not for the first set(left). The initial and final state of the model is displayed in Figure 2.

Contact force vs time for both sets is presented in Figure 3.

As seen in Figure 3, Accuracy_edge when activated leads to increased contact force.

Maximum and average contact force is checked for both sets.

Tests

This benchmark is associated with 1 tests.

Contact accuracy level in *CONTACT_ACCURACY is verified in this test.

Tested parameters: accuracy_level.

Four identical sets consisting of a sphere and a cylinder are used in this test. The cylinders are linearly tapered, and the inner radius at one end equals the sphere radius, $R_s$, while the radius on the other end equals $0.97\cdot R_s$.

The spheres are positioned inside the cylinders, at the end with a radius $R_s$, and given an initial velocity so that they move towards the other end of the cylinder. The initial and final state of the model is displayed in Figure 1.

Contact forces between the spheres and the cylinders increase gradually as the spheres moves down the cylinder, and the smoothness of the contact forces are controlled by the contact accuracy. Investigated accuracy levels are 1, 2, 3 and 10 for set 1, 2, 3 and 4, respectively.

Contact force vs time for each set is presented in Figure 2.

Quantifying the "noise" of the contact force in set 1, 2 and 3 is done by integrating the absolute value of the difference between contact force in set 1, 2, 3 and the contact force of set 4, meaning that contact force in set 4 acts as reference curve. The accumulated noise of set 1, 2, 3 is presented in Figure 3.

As seen in Figure 3 , a higher contact accuracy leads to reduced level of noise.

Maximum and average contact force in set four is checked together with maximum and average accumulated noise in set 1, 2 and 3.

Tests

This benchmark is associated with 1 tests.

The command *CONTACT_REBAR is tested. The command is used to define contact between rebars and the "regular" FE-elements. Five boxes (*COMPONENT_BOX) and five rebars (*COMPONENT_REBAR) are used in the test, see Figure 1.

The rebars are at rest at initiation whereas a prescribed velocity of 10 m/s is imposed on the boxes (towards the rebars). The boxes impacts the rebars and the kinetic energy of each rebar at termination is checked for version control. The largest contact penetration is also checked.

Tests

This benchmark is associated with 1 tests.

This model tests the *COORDINATE_SYSTEM command. Three identical cubes are created with side length 1. Cube 1 is created with a fixed coordinate system while the other cubes are created with a tilted coordinate system with its origin located on the boundary between them. The coordinate system is given an optional part ID of 3 which ties it to cube 3. The cubes are set in motion and as cube 3 separates from cube 2, the coordinate system is forced to follow cube 3 while the fixed coordinate system remains at its initial location. See Figure 1.

The final positions of the coordinate systems are checked in the version control.

Tests

This benchmark is associated with 1 tests.

This tests the *COORDINATE_SYSTEM_CYLINDRICAL command. This command is used with *TRANSFORM_MESH_CYLINDRICAL to transform a mesh with defined cylindrical coordinates. The model is a pipe. In the transformation, inner and outer radius are decreased and the model is translated in the axial direction. Final coordinates of two nodes at opposite ends are checked for version control. One is at the inner radius, the other at the outer radius.

Tests

This benchmark is associated with 1 tests.

This model tests the *COORDINATE_SYSTEM_FIXED command. Two elements are created, one at the center of the global coordinate system and one at the center of a fixed, local coordinate system. The latter system is shifted one unit along all axis and the direction of the X-axis in the global coordinate system has the unit vector ($1,1,0$). It is therefore at a 45° angle in the XY-plane relative to the global system.

The center of the cubes are at origin of their respective coordinate systems, with side lengths of 1 unit. Node 1 of the first cube should thus have coordinates ($-0.5,-0.5,-0.5$). The corresponding node of the second cube, node 9, should have coordinates ($1,0.5,1-\sqrt {0.5}$). This is checked in the version control.

Tests

This benchmark is associated with 2 tests.

Tested parameters : csysid, $x_0$, $y_0$, $z_0$, $\hat{x}_x$, $\hat{x}_y$, $\hat{x}_z$, $\bar{y}_x$, $\bar{y}_y$, $\bar{y}_z$.

This model tests the command *COORDINATE_SYSTEM_FUNCTION. A local coordinate system with its origin following sensor ID=1 and with prescribed, time dependent, direction cosines. It is rotating 360° around its Z-axis for the time duration.

A cube with side length $1 \ m$ is given a prescribed displacement of $1 \ m$ in the global X-direction. The local coordinate system is used as a translational constraint for the cube, restricting its motion in the current local Y- and Z-axis. Hence, the cube will only translate in the local coordinate system's current X-direction. See Figure 1.

The displacement of the cube is displayed in Figure 2 together with target curves from a verification script.

Final translation should be $1 \ m$ in the global X-direction. The position of the cube is checked for version control.

Tests

This benchmark is associated with 1 tests.

This tests the *COORDINATE_SYSTEM_NODE command. A metal box has a rigid box merged to it at one end. A constant force is applied to the rigid body with *LOAD_FORCE. This force is defined in a node coordinate system so as to always act perpendicular to the length of the model. It thus acts as a torque on the box.

At the opposite end, in the plane of the applied force, the corner nodes are constrained in all directions such that the box can only rotate about the z-axis. The torque is parallel to the Z-axis, in the opposite direction ($\mathbf{-z} \parallel \textbf{r} \times \mathbf{F}$).

The spin of the rigid body about the Z-axis should therefore decrease linearly. See Figure 1. This is checked for version control.

Tests

This benchmark is associated with 1 tests.

This tests the *CURVE command. Three rigid elements are moved by the *BC_MOTION command. All motion is defined by displacement set by *CURVE inputs. One element follows a simple linear trajectory before returning to initial position, while the two other elements follows trajectories that have scaled abissa or ordinate values. Displacement of elements are checked for version control.

Tests

This benchmark is associated with 1 tests.

Tested parameters: coid, entype, enid, fid, padding.

This model tests the command *DEFINE_ELEMENT_SET. It consists of two steps.

A cylindrical impactor punches a hole in a plate. The model is first run with only linear elements (Step 1). The purpose of this step is to identify the region undergoing large deformations. This is done by formulating an inclusion criteria by setting a FUNCTION (here defined as elements with effective plastic strains larger than 0.5).

$$ epsp - 0.5 $$

The FUNCTION is evaluated for each element in the part. An element will be included in the part set if the function returns a positive value. At termination, the element set is written to the file element_set_X.k, (where X=coid) which will be used in step 2.

In subsequent simulations (Step 2) elements in the set are converted to 3rd order hexahedra (for increased accuracy). To test the paramater padding, two element sets are generated, one with and one without padding. See Figure 1.

The element sets generated are checked for version control.

Tests

This benchmark is associated with 3 tests.

This tests the contact interference of *ELEMENT_SHELL and other deformable bodies. *ELEMENT_SHELL can only be used to generate rigid bodies. The element thickness is specified in *PART, but this thickness is not active in contact situations.

The set-up is a rigid cone with an initial velocity impacting at the center of the open face of a pipe. The pipe has a lesser radius than the cone, bringing the cone to halt. The initial kinetic energy of the cone is $1585.5 \ kJ$ ($m = 317.1 \ kg$ , $v_{0} = 100 \ m/s$), and this value is checked against the final energy balance found in "energy.out".

Note that by using linear elements in the first test, the stiffness is artificially high. This offset is improved in the second and third run, in which quadratic and cubic elements are used.

Tests

This benchmark is associated with 3 tests.

This tests that *ELEMENT_SHELL and *PART generates elements correctly. Mass and volume of a $1 \ m$ square rigid shell with a thickness of $1 \ m$ is checked in part.out. The density of the material is $1000 \ kg/m^3$. The generated shell element can be seen in Figure 1.

Tests

This benchmark is associated with 1 tests.

This tests the higher order *ELEMENT commands. This includes quadratic and cubic hexahedron, pentahedron, and tetrahedron elements - six element types in total (Figure 1 to 6.). The pentrahedron elements can be oriented in two different ways, both are tested for both the quadratic and cubic element.

The element mesh has been created using *ELEMENT_SOLID and *CHANGE_P-ORDER and then exported to an input file that has the higher order *ELEMENT commands. In these tests, these input files are checked using *BC_MOTION. The geometry is a block with side length of $0.01 m$. It is stretched in Z-direction with a logarithmic strain of 1. Hardening of material is Ramberg Osgood ($n=1, K= 150e^{9}$). The yield strengh is $300 MPa$, Young's modulus is $210 GPa$, and Poisson's ratio is $0.33$.

Stress and strain at the end of the simulation is checked for version control.

Tests

This benchmark is associated with 8 tests.

This tests the *ELEMENT_SOLID command. This includes linear hexahedron, pentahedron and tetrahedron elements. In these tests, the elements are checked using *BC_MOTION. The geometry is a block with side length of $0.01 m$. It is stretched in Z-direction with a logarithmic strain of 1. Hardening of material is Ramberg-Osgood ($n = 1, K = 150e^{9}$). The yield strength is $300 MPa$, Young's modulus is $210 GPa$, and Poisson's ratio is $0.33$.

For version control, stress and strain is checked at the end of simulation.

Tests

This benchmark is associated with 4 tests.

This model tests the *END command. The test is identical to the test "*LOAD_GRAVITY - Gravity test", with the addition of an *INITIAL_VELOCITY command after the *END command. If the *END command doesn't end the input correctly, the elements will output different velocities and the checks will fail.

Tests

This benchmark is associated with 1 tests.

Tested parameters: eosid, $S$, $\Gamma$.

This model tests the *EOS_GRUNEISEN command.

An abrupt pressure is introduced on one side of a highly elongated rectangular cuboid with dimensions:
Length = 1 m
Width = 0.001 m
Height = 0.001 m

As the shock wave travels along its length, 10 equally-distanced sensors are measuring pressure. The Mie-Gruneisen equation of state is implemented with the command *EOS_GRUNEISEN. For comparison one cuboid with *EOS_GRUNEISEN and one without it is tested for.

The test setup is displayed in Figure 1 and 2.

The wave induced by the shock pulse takes the shape of a square wave. This can be seen in Figure 3, where the difference between the two test cases is visble. Only two sensors are displayed for clarity.

The noise is measured by integrating the absolute value of the pressure difference between the test cases at each sensor. See Figure 4.

The maximum value of the pressure difference at each sensor is checked for version control.

Tests

This benchmark is associated with 1 tests.

This test is similar to the test "*PART - Element erosion". In this test, the erosion criteria are instead defined with *EROSION_CRITERION.

Tests

This benchmark is associated with 1 tests.

This test is similar to the test "*EROSION_CRITERION - Element erosion". In this test, the erosion criteria are defined with *EROSION_CRITERION but also in *PART.

It is tested that the erosion parameters defined in *PART have higher priority.

Tests

This benchmark is associated with 1 tests.

Tested parameters: coid, entype, enid, $\Delta t_{target}$.

This model tests the *FREQUENCY_CUTOFF command for the already existing test, See "LOAD_DAMPING - Mass damping".

The objective of this test is to speed up the simulation time without compromising accuracy. This is done by suppressing angular frequencies $w > 2/\Delta t_{target}$ which allows for larger time steps.
The target time step size is set to $\Delta t_{target} = 1\mu s$.

Tip displacement of the beams from the original test (without *FREQUENCY_CUTOFF) compared with this test (with *FREQUENCY_CUTOFF) can be seen in Figure 1

First, average, min and last values of tip displacements are checked for version control.

Tests

This benchmark is associated with 1 tests.

Tested parameters: coid, entype, enid, $sf_{cap}$.

This model tests the *FREQUENCY_CUTOFF command for the already existing test, See "MAT_METAL - Quasi-static yield stress". The objective is to speed up the simulation time without compromising accuracy.

The primary purpose of the command is to allow for larger time steps in quasi-static processes. This is achieved by suppressing angular frequencies $\omega > 2/\Delta t_{target}$. The scale factor, $sf_{cap}$ which limits the maximum increase of time step size is set to 4.

Effective stress vs. effective plastic strain is presented in Figure 1 together with a target curve from a verification script.

Maximum and average effective stress and effective plastic strain are checked for version control.

Tests

This benchmark is associated with 1 tests.

This tests the *FUNCTION command and some of its supported functions and parameters. More specifically, these built-in functions are tested:

• Trigonometric sine function
• Trigonometric cosine function
• Absolute value
• Minimum value of $x_{1},x_2...$ $x_n$
• Maximum value of $x_{1},x_2...$ $x_n$
• Step function ($x<0\Rightarrow0$, $x>0\Rightarrow1$)
• Sign function ($x<0\Rightarrow-1$, $x>0\Rightarrow1$)
• Exponential function ($e^x$)
• $x_{1},x_2...$ $x_n$ & $\bullet$ Square root function
• $x_{1},x_2...$ $x_n$ & $\bullet$ Classical error function

Eight rigid single element bodies are displaced along the X-axis by the *BC_MOTION command. The analytic functions for the motions are shown in the Table 1.

Tests

This benchmark is associated with 1 tests.

This tests the *FUNCTION command and some of its supported functions and parameters. More specifically, these built-in functions are tested:

• Reaction force in X-direction from *BC_MOTION
• Reaction force in Y-direction from *BC_MOTION
• Reaction force in Z-direction from *BC_MOTION

The fxr-, fyr-, and fzr function returns the reaction force ($fr$) of *BC_MOTION command. This returned force level is then used to define a velocity value (see Equation below). In this specific case a tensile specimen is stretched until reaching the target force $10 kN$ ($F$) using the aforementioned reaction force and equation.

$$ v = erf(1 - \frac{fr}{F}) $$

Tests

This benchmark is associated with 3 tests.

This tests the *FUNCTION command and some of its supported functions and parameters. More specifically, it verifies calls from one function to another function in multiple functions commands.

For version control, it is checked that the highest function (the function that refers to all other sub-functions) returns the correct value in the end.

Tests

This benchmark is associated with 1 tests.

This tests the *FUNCTION command and some of its supported functions and parameters. More specifically, these built-in functions are tested:

• Smooth displacement function
• Smooth velocity function
• Smooth acceleration function

Three rigid single element bodies are displaced along the X-axis by using the *BC_MOTION command.

Tests

This benchmark is associated with 1 tests.

This tests the *GEOMETRY_BOX command. It allows the user to specify a geometry by defining two sets of coordinates. To test the command, *LOAD_PRESSURE is applied in the geometry. A hollow sphere occupies the same geometry, and the momentum of the sphere is checked for version control.

A $0.01 \ MPa$ pressure is applied to a $1x1 \ m$ area of the sphere. The mass of the sphere is a bit less than $1000 \ kg$, and final momentum is checked for version control.

Tests

This benchmark is associated with 1 tests.

This model tests the functionality of the *GEOMETRY_COMPOSITE command.

Tested parameters: gid, gid${}_1$, gid${}_2$.

Two component boxes are created, see the yellow and grey box in Figure 1. Also two box geometries are created.

*GEOMETRY_COMPOSITE is being used to remove the smaller box geometry from the larger box geometry. *BC_MOTION is used to prescribe a velocity to the remaining geometry. In this case this means that only the yellow box should move since it has elements that are bordering to the remaining geometry.

Coordinates of both boxes are checked for version control.

Tests

This benchmark is associated with 1 tests.

Tested parameters: gid, gid${}_1$, gid${}_2$.

This model tests the command *GEOMETRY_COMPOSITE. A square plate is subjected to a thermal surface load. The geometry defining the load pressure is created with *GEOMETRY_COMPOSITE. The composite geometry is created by combining two box geometries of side length $0.8 \ m$ and $0.4 \ m$ respectivly. The smaller box is referenced with a negative ID which removes it from the larger geometry. See Figure 1.

The area of the surface subjected to the thermal load is: $$ A_{Geometry 1} - A_{Geometry 2} = 0.8^2 - 0.4^2 = 0.48 \ m^2 $$

The thermal surface load applied is $1 \ MW/m^2$ giving a total energy supplied to the plate of: $$ 1,000,000 \cdot 0.48 = 480,000 \ J/s $$

The energy supplied from the thermal surface load is presented in Figure 2.

The energy from the thermal surface load and temperature at both sensors are checked for version control.

Tests

This benchmark is associated with 1 tests.

Tested parameters: gid, gid${}_1$, gid${}_2$.

This model tests the command *GEOMETRY_COMPOSITE. A square plate is subjected to a load pressure of $0.01 \ MPa$. The geometry defining the load pressure is created with *GEOMETRY_COMPOSITE. The composite geometry is created by combining two box geometries of side length $0.8 \ m$ and $0.4 \ m$ respectivly. The smaller box is referenced with a negative ID which removes it from the larger geometry. See Figure 1.

The area of the surface subjected to load pressure is: $$ A_{Geometry 1} - A_{Geometry 2} = 0.8^2 - 0.4^2 = 0.48 \ m^2 $$ The force generated is: $$ F = P \cdot A = 10000 \cdot 0.48 = 4800 \ N $$

The force generated from load_pressure.out is presented in Figure 2.

Tests

This benchmark is associated with 1 tests.

Tested parameters: gid, $x_1$, $y_1$, $z_1$, $x_2$, $y_2$, $z_2$, $R_1$, $R_2$, $R_3$.

This model tests the *GEOMETRY_EFP command. An Explosively Formed Projectile is constructed by the use of three geometries generated with *GEOMETRY_EFP. The three geometries will form the Casing, Explosive and Liner volumes that are filled with particles that make up the EFP. This is done with the help of *GEOMETRY_COMPOSITE. Additionaly the wave shaper is created with *GEOMETRY_PIPE.

The test setup is displayed in Figure 1.

In order to verify that the *GEOMETRY_EFP command is working properly the number of particles of the different geometries at time zero is checked.

The number of particles of the ingoing components of the EFP is presented in Figure 2.

Tests

This benchmark is associated with 1 tests.

This tests the *GEOMETRY_PART command. The model is a simplified version of that found in the *LOAD_PRESSURE benchmark. A pressure is applied to a surface of a structure by a geometry defined from a part. Final momentum of the structure is checked for version control.

Tests

This benchmark is associated with 1 tests.

This tests the *GEOMETRY_PIPE command. It is used to define a straight pipe or cylinder in space by its face center coordinates. To test the command, *LOAD_PRESSURE is applied in the geometry. A hollow sphere occupies the same geometry, and the momentum of the sphere is checked for version control.

Tests

This benchmark is associated with 1 tests.

This tests the *GEOMETRY_SEED_COORDINATE. The command is used to define a geometry from a coordinate. In this test, a geometry is defined on the surface of a structure and a pressure is applied in the geometry.

Final momentum of the structure is checked for version control.

Tests

This benchmark is associated with 1 tests.

This test is similair to the test of *GEOMETRY_SEED_COORDINATE, but in this test, the geometry is created from a seed node with command *GEOMETRY_SEED_NODE. Final momentum of the structure is checked for version control.

Tests

This benchmark is associated with 1 tests.

This tests the *GEOMETRY_SPHERE command. A sphere geometry with radius $4 \ m$ is defined in between two blocks. An pressure of $50 \ kPa$ is applied in the geometry to move the blocks apart. The center of the sphere is at the surface of one of the blocks. The force on this block should therefore be $16 \pi \cdot 50 \ kN$. The other block is at a distance of $2 \ m$ from the center of the sphere. Expected force on this block is $12\pi \cdot 50 \ kN$. These targets are used for version control by checking the final momentums of both blocks.

Tests

This benchmark is associated with 1 tests.

Tested parameters: nid_offset, eid_offset, pid_offset, mid_offset, gid_offset.

This model tests the offset parameters in the *INCLUDE command. In total three files are used, "main.k", "sub.k" and "element_offset.k". In the "main.k" file the file "sub.k" is included with an offset of 100, 200, 990, 995, 999 to nid_offset, eid_offset, pid_offset, mid_offset, gid_offset respectively.

To see that gid_offset works properly, functions are created within "sub.k" that returns the Y- and Z-coordinates of a sensor that is created in "main.k". The sensor ID should thus be 999+sensor ID.

In "sub.k, "element_offset.k" is included which defines a cube from 8 solid element. To see that mid_offset and pid_offset is working properly the material ID and part ID in the "main.k" file should be 995+material ID, 990+Part ID. Also the element ID's and Node ID's should be 200+Element ID and 100+Node ID. This is checked with Output node and Output element.

Targets:

• First cube should rotate 1 lap about X-axis
• Second cube should move downwards 1 m in Z-direction

Tests

This benchmark is associated with 1 tests.

This tests the *INCLUDE command. A mesh file is included, then transformed and scaled. The model is a single cubic element. Coordinates of two oppsite corners are checked in "node.out" for version control.

Tests

This benchmark is associated with 1 tests.

Tested functionality:
Import results from one simulation and use it to define the initial state in another model.

If running the model in one step the Z-coordinate of the back face is $Z=6.654e^{-3}$ at time $t=10 \ \mu s$. The simulation is split into two steps, the first from $t=0$ to $t=2 \ \mu s$ and the second from $t=2 \ \mu s$ to $t=10 \ \mu s$.

Step 1 ($0 - 2 \ \mu s$): Has already been completed and the state is stored in impetus_state1.k and impetus_state1.bin.
Step 2 ($2 - 10 \ \mu s$): Current model.

Target:
If the end result from Step 1 is correctly imported to Step 2, the back face should be at $Z=6.654e^{-3}$ at termination.

Tests

This benchmark is associated with 3 tests.

Randomly distributed initial damage is defined on a model consisting of $32 \times 32$ geometrically identical cubes, as presented in Figure 1. The number of cubes is assumed to be enough to consider the test valid from a statistical point of view. Each cube is constructed by a single linear hexahedral element.

The initial damage in each element is uniform throughout the entire element which is achieved by utilizing an imperfection radii (a built-in parameter in *INITIAL_DAMAGE_RANDOM).

A prescribed velocity is imposed at one of the cubes surfaces while the opposite surface of the cubes is fixed in the direction of the prescribed velocity, hence the cubes are uni-axially stretched. The plastic work that has been accomplished when the final cube/element is eroded due to fully developed damage is checked against the same quantity obtained from an alternative numerical approach.

Tests

This benchmark is associated with 1 tests.

Randomly distributed initial damage is defined on a model consisting of $100 \times 100$ geometrically identical cubes, as presented in Figure 1.

To ensure randomness, a new damage distribution is generated each time the solver starts with the command *RANDOM_NUMBER_GENERATOR_SEED. The number of cubes is assumed to be enough to consider the test valid from a statistical point of view. Each cube is constructed by a single linear hexahedral element.

The initial damage in each element is uniform throughout the entire element which is achieved by utilizing an imperfection radii (a built-in parameter in *INITIAL_DAMAGE_RANDOM).

The randomly distributed initial damage is defined to the model by assigning a Heaviside step function to the distribution function $f(D)$, which describes the number of defects $N$ per unit volume of matter. The initial damage is only allowed to be within the range of $0.49-0.51$. The probability $p$ that an element is assigned an initial damage is:

$$ p = 1-e^{-N \cdot v} $$

Where $v$ is the element volume and $N$ the number of defects per unit volume. With $N=500$ and $v=0.001$, $p$ is:

$$ p = 1-e^{-500 \cdot 0.001} = 0.39347 $$

The elements are uni-axially stretched to the point to which only the elements with an initial damage are eroded. The final volume of the model is then:

$$ V_{final} = V_{initial} \cdot (1-p) $$

Where $V_{final}$ is the final volume and $V_{initial}$ the initial volume of the model. With $V_{initial} =10$ The final volume should be:

$$ V_{final} = 10 \cdot (1-0.39347) = 6.0653 $$

This can be seen by tracking the total volume of the model. Volume vs. time can be seen in Figure 2.

First and last value of volume is checked for version control.

Tests

This benchmark is associated with 1 tests.

Tested parameters: entype, enid, $\Delta_0$, $m$, $D_{max}$, $R$.

The model tests the *INITIAL_DAMAGE_SURFACE_RANDOM command.

Randomly distributed initial damage is defined on the top surface of a plate consisting of $32 \times 32$ linear hexahedral element, as presented in Figure 1. The number of elements is assumed to be enough to consider the test valid from a statistical point of view.

A prescribed velocity is imposed at the top surface of the model while the opposite surface is fixed in the direction of the prescribed velocity, hence the model is uni-axially stretched. Failed elments are eroded. The plastic work that has been accomplished when the final element is eroded due to fully developed damage is checked against the same quantity obtained from an alternative numerical approach.

Tests

This benchmark is associated with 1 tests.

This model tests the command *INITIAL_DISPLACEMENT. The nodes of an element is repositioned at time zero.

The x-coordinate center of gravity of the part should go from $0 \ to \ 1$. The test is checked for version control.

Tests

This benchmark is associated with 1 tests.

The command *INITIAL_MATERIAL_DIRECTION is used to define material directions in anisotropic materials. In this command the material direction is defined by use of the element corner nodes.

The test consists of three hexahedron elements, one of each type (linear/quadratic/cubic). Each element is assigned a unique material direction. The fiber direction is defined in the X-direction for the linear element, in the Y-direction for the quadratic element and in the Z-direction for the cubic element.

The elements are then stretched, first in the X-direction, then in the Y-direction and lastly in the Z-direction. The elements restore the original geometry between the stretches and therefore the loading is uniaxial.

The material used have a stiffness of $10 \ GPa$ in the fiber direction and $5 \ GPa$ perpendicular to the fibers. The maximum stretch in each direction is 5% (nominal).

The maximum stress in the fiber direction should therefore be $10e9 \cdot ln(1+0.05) \approx 487.9 \ MPa$ and $5e9 \cdot ln(1+0.05) \approx 244.0 \ MPa$ perpendicular to the fiber direction. This is checked in the version control.

Figure 1 shows the results from the latest version control together with targets.

Tests

This benchmark is associated with 1 tests.

Tested parameters: coid, entype, enid, pathid.

This model tests functionality of the command *INITIAL_MATERIAL_DIRECTION_PATH. The model tests that material fiber directions are interpolated between paths that are split into two segments. For reference two components are used, one with the fiber directions along a single path and the other one with fiber directions interpolated between two paths. See Figure 1

Both components are modelled with one element in the thickness direction. One side of the components is fixed and the other side is given a prescribed velocity in the X-direction. To distinguish the effect that fiber direction has, output sensors are placed at given locations to measure displacements. Figure 2

Maximum X-displacements at the sensors are checked for version control.

Tests

This benchmark is associated with 1 tests.

The model tests initial material directions when using multiple elements in the thickness direction. This test is similar to the test "*INITIAL_MATERIAL_DIRECTION_PATH - Material fiber direction split".

Tests

This benchmark is associated with 1 tests.

The command *INITIAL_MATERIAL_DIRECTION_PATH is used to define material directions in anisotropic materials. In this command the material direction is defined by user defined paths.

The test consists of three hexahedron elements, one of each type (linear/quadratic/cubic). Each element is assigned a unique material direction. The fiber direction is defined in the X-direction for the linear element, in the Y-direction for the quadratic element and in the Z-direction for the cubic element.

The elements are then stretched, first in the X-direction, then in the Y-direction and lastly in the Z-direction. The elements restore the original geometry between the stretches and therefore the loading is uniaxial.

The material used have a stiffness of $10 \ GPa$ in the fiber direction and $5 \ GPa$ perpendicular to the fibers. The maximum stretch in each direction is 5% (nominal).

The maximum stress in the fiber direction should therefore be $10e9 \cdot ln(1+0.05) \approx 487.9 \ MPa$ and $5e9 \cdot ln(1+0.05) \approx 244.0 \ MPa$ perpendicular to the fiber direction. This is checked in the version control.

Figure 1 shows the results from the latest version control together with targets.

Tests

This benchmark is associated with 1 tests.

This model tests the automatic determination of the face normals of a pipe geometry with the command *INITIAL_MATERIAL_DIRECTION_VECTOR.

The direction of the local x-axis is specified to be (1,0,0) which is the central axis of the pipe. The local y-axis is determined from the cross product of the local z- and x-axis.

$$\hat{y} = \hat{z} \ X \ \hat{x}$$

Where the local z-axis is equivalent to the local element face normal $\hat{z} = \hat{n}$ which is automatically determined by the solver.

The test setup is displayed in Figure 1.

An internal pressure is added to the model. The radius of the pipe should expand uniformally. See Figure 2.

Tests

This benchmark is associated with 1 tests.

The command *INITIAL_MATERIAL_DIRECTION_VECTOR is used to define material directions in anisotropic materials. In this command the material direction is defined by user defined vectors.

The test consists of three hexahedron elements, one of each type (linear/quadratic/cubic). Each element is assigned a unique material direction. The fiber direction is defined in the X-direction for the linear element, in the Y-direction for the quadratic element and in the Z-direction for the cubic element.

The elements are then stretched, first in the X-direction, then in the Y-direction and lastly in the Z-direction. The elements restore the original geometry between the stretches and therefore the loading is uniaxial.

The material used have a stiffness of $10 \ GPa$ in the fiber direction and $5 \ GPa$ perpendicular to the fibers. The maximum stretch in each direction is 5% (nominal).

The maximum stress in the fiber direction should therefore be $10e9 \cdot ln(1+0.05) \approx 487.9 \ MPa$ and $5e9 \cdot ln(1+0.05) \approx 244.0 \ MPa$ perpendicular to the fiber direction. This is checked in the version control.

Figure 1 shows the results from the latest version control together with targets.

Tests

This benchmark is associated with 1 tests.

The command *INITIAL_MATERIAL_DIRECTION_WRAP is used to define material directions in anisotropic materials. In this command the material direction is defined by a user defined "ply" in space that is wrapped around the component.

The test consists of three hexahedron elements, one of each type (linear/quadratic/cubic). Each element is assigned a unique material direction. The fiber direction is defined in the X-direction for the linear element, in the Y-direction for the quadratic element and in the Z-direction for the cubic element.

The elements are then stretched, first in the X-direction, then in the Y-direction and lastly in the Z-direction. The elements restore the original geometry between the stretches and therefore the loading is uniaxial.

The material used have a stiffness of $10 \ GPa$ in the fiber direction and $5 \ GPa$ perpendicular to the fibers. The maximum stretch in each direction is 5% (nominal).

The maximum stress in the fiber direction should therefore be $10e9 \cdot ln(1+0.05) \approx 487.9 \ MPa$ and $5e9 \cdot ln(1+0.05) \approx 244.0 \ MPa$ perpendicular to the fiber direction. This is checked in the version control.

Figure 1 shows the results from the latest version control together with targets.

Tests

This benchmark is associated with 1 tests.

Tested parameters: coid, entype, enid, fid, multi.

The model tests the command *INITIAL_PLASTIC_STRAIN_FUNCTION. The command is used to prescribe initial plastic strains. Two options are available when implementing the initial plastic strains:

• Option 1 (multi = 0): plastic strains from previous commands are overwritten
• Option 2 (multi = 1): plastic strains from multiple commands are superimposed

To test both options, two bars with identical dimensions are given an initial plastic strain in two steps:

-First step, the bars are given an initial plastic strain linearly distributed from 0 at one end to 0.05 at the other end.
-Second step, the bars are given an initial plastic strain of 0.10 with option 1 for bar 1 and option 2 for bar 2. This means that the maximum initial plastic strain in aggregate should be 0.1 for bar 1 and 0.15 for bar 2.

See Figure 1.

Output sensors are placed at the middle and at the end of the beams to measure effective plastic strains.

The first values of effective plastic strain is checked for version control.

Tests

This benchmark is associated with 1 tests.

This tests the command *INITIAL_STATE_HAZ. It is used to define mechanical properties in a heat affected zone (HAZ) after a welding operation. Initial yield stress and damage are defined as functions of the distance from the weld. In the test model, two plates have been welded to a beam. The plates are pulled apart. Maximum reaction force is checked for version control.

Tests

This benchmark is associated with 1 tests.

This tests the *INITIAL_STATE_WELDSIM command. It allows the user to import simulation results from WeldSim, in order to define the distribution of material properties in the heat affected zone (HAZ) after a welding operation. In the test model, two plates have been welded to a beam. The plates are pulled apart. Maximum reaction force is checked for version control.

Tests

This benchmark is associated with 1 tests.

An initial stress state can be included by the command *INITIAL_STRESS_FUNCTION. Three different options are available when implementing the initial stress state:

• Option 1 (multi = 0): stresses from previous commands are overwritten
• Option 2 (multi = 1): stresses from multiple commands are superimposed
• Option 3 (multi = 2): stress component with largest absolute value is kept

Three identical plates are used in the verification of this command. Each plate have a sensor in the center to extract the stress state in the plate.

First, a stress state (in MPa) according to $\bar{\sigma}_{state,1}$ is imposed on all three plates with option 1.

$$ \bar{\sigma}_{state,1} = \bar{\sigma}_{plate,1} = \begin{bmatrix} 100 & 10 & 20 \\ 10 & 150 & 15 \\ 20 & 15 & 200 \end{bmatrix} $$

The stresses in sensor.out for the first plate is checked in sensor.out.

Another stress state $\bar{\sigma}_{state,2}$ is then imposed on the second and the third plate, with option 2 in the second plate and option 3 in the third plate.

$$ \bar{\sigma}_{state,2} = \begin{bmatrix} -200 & 20 & 40 \\ 20 & -300 & 30 \\ 40 & 30 & -400 \end{bmatrix} $$

The state of stress in the second and the third plate should be in accordance to $\bar{\sigma}{plate,2}$ and $\bar{\sigma}{plate,3}$.

$$ \bar{\sigma}_{plate,2} = \begin{bmatrix} -100 & 30 & 60 \\ 30 & -150 & 45 \\ 60 & 45 & -200 \end{bmatrix} $$

$$ \bar{\sigma}_{plate,3} = \begin{bmatrix} -200 & 20 & 40 \\ 20 & -300 & 30 \\ 40 & 30 & -400 \end{bmatrix} $$

Tests

This benchmark is associated with 1 tests.

This model tests the command *INITIAL_TEMPERATURE. Three adjacent blocks are given an INITIAL_TEMPERATURE of $-50 \ K$, $50 \ K$ and $150 \ K$. The outer blocks are moving in slightly towards the inner block so that they intersect. No contact is defined. With sensors located at the intersection between the blocks, it is checked that the temperature are still the same.

Tests

This benchmark is associated with 1 tests.

Tested parameters: nid, thickness.

The command *INITIAL_THICKNESS is tested in a simple multi-step forming operation test. The test consists of 2 steps. A single cubic hex element is stretched 2 times in the X-direction reducing its thickness. To keep track of the sheet thickness reduction, the command *OUTPUT_FORMING is used to activate the calculation and output of sheet thickness. This is done through node based initial component thickness (*INITIAL_THICKNESS) which is automatically generated by the Solver Engine when writing a state file. The test setup is seen in Figure 1.

In step 1, the thickness is reduced from $10$ to $9.54 \ mm.$

In step 2, the output from step 1 is included and the element is further streched. The ingoing thickness of $9.54$ is reduced to $9.13 \ mm.$ With an initial thickness of $10 \ mm$ in step 1, the total thickness reduction should be 8.7%.

Final thickness and thickness reduction is checked for version control.

Tests

This benchmark is associated with 2 tests.

This tests the *INITIAL_VELOCITY command. A single cubic element created with *COMPONENT_BOX is given an initial velocity of $5 \ m/s$ in the positive Z-direction. *LOAD_GRAVITY act along the same axis and brings the element to halt before returning to its starting point after $1 \ s$. Initial velocity is checked against "rigid.out" and maximum displacement (target: $1.25 \ m$) is checked against "node.out".

Tests

This benchmark is associated with 1 tests.

Three boxes (*COMPONENT_BOX) and three charges (*LOAD_AIR_BLAST) are positioned as displayed in Figure 1, in which the charges are illustrated with spheres. The charges are of the same size and should only affect the box closest to the charge. Different diffraction levels are used for each box: = 0 for box 1, = 1 for box 2 and = 2 for box 3.

The surface pressure is measured at three different locations on each box: the outer surface (surface closest to the charge), the top surface and the inner surface. This is done by using sensors (*OUTPUT_SENSOR).

The pressure at the outer surface should be equal for all boxes. At the top surface, the pressure should be zero for box 1 and non-zero for box 2 and 3. At the inner surface, the pressure should be zero for box 1 and 2 and non-zero for box 3. The pressure at each surface is plotted vs. time in Figure 2 - 4.

Tests

This benchmark is associated with 1 tests.

The model consists of a spherical explosive charge and a slender structure with a quadratic cross-section (L >> H, W = H). The structure is aligned to the charge in such a way that the blast wave propagates along the length of the structure, parallel to one of the structures faces. The side-on pressure on this face is measured using sensors (*OUTPUT_SENSOR) located at different distances from the charge. An illustration of the test model is presented in Figure 1.

The peak incident pressure at eight different scaled distances in the range of $0.5 - 10$ is compared to emperical data from M. Swisdak, Jr, (1994) [1]. The comparison is displayed in Figure 2 and 3.

Reference
[1] - Swisdak M. (1994), Simplified Kingery Airblast Calculations, Naval Surface Warfare Center.

Tests

This benchmark is associated with 1 tests.

The model consists of four quadratic plates and two explosive charges, positioned as displayed in Figure 1. Two charges are included by using two *LOAD_AIR_BLAST-commands.

Plate 1 and 2 are located on opposite sides of one of the charges. These plates are included in a part set. One of the charges are defined to impinge this part set and reflectivity is assumed. The other charge is defined to affect plate 3 without any reflectivity. Plate 4 is not affected by any of the charges.

For both air blasts, the time offset flag is set to 1, meaning that the time of arrival of the pressure pulse is defined as time = 0.

The max peak pressure for plate 1, 2 and 3 should be equal while the pressure in plate 4 should be zero at all time. For plate 1 and 2, an additional pressure pulse should be seen after the initial pressure pulse due to the reflectivity. The pressure vs. time for the plates are presented in Figure 2.

Tests

This benchmark is associated with 1 tests.

The model consists of a spherical charge and eight quadratic plates. The plates are distributed around the explosive charge with their normal directions coinciding with the direction of propagation of the blast wave. The distance between the plates and the explosive charge differs for each plate. An illustration of the test setup is presented in Figure 1.

The peak reflective pressure at eight different scaled distances in the range of $0.5 - 10$ is compared to emperical data from M. Swisdak, Jr, (1994) [1]. The comparison is displayed in Figure 2 and 3.

Reference
[1] - Swisdak M. (1994), Simplified Kingery Airblast Calculations, Naval Surface Warfare Center.

Tests

This benchmark is associated with 1 tests.

This model tests the *LOAD_AIR_BLAST command. One box (*COMPONENT_BOX) and one charge (*LOAD_AIR_BLAST) is positioned as displayed in Figure 1. Surface pressure is measured with a sensor positioned at the center of the surface that is facing the charge.

The test should result in a rapid increase in pressure followed by an exponential decay to the ambient pressure and a longer phase of negative pressure. See Figure 2.

Target:
-There should be an underpressure phase in the test i.e. p<0

Maximum, minimum and average value of pressure at the sensor is checked for version control.

Tests

This benchmark is associated with 1 tests.

This tests the *LOAD_CENTRIFUGAL command. A centrifugal force is loaded to a rigid sphere with a radius of $r = 0.1 \ m$ and a density of $\rho= 1000 \ kg/m^3$. The force is applied in a local coordinate system.

Rigid body mass:

$$ m = \frac{\rho\cdot 4\pi r^3}{3} = 4.1888 \ kg $$

Vector from COG to spin axis:

$$ \tilde{r} = [0, 0, 2] $$

Spin vector:

$$ \tilde{\omega} = 10 \cdot [0.8, 0.5, 0.33166] $$

Resulting force:

$$ \tilde{F} = -m \times [\tilde{\omega} \times [\tilde{\omega} \times \tilde{r}]] = [-222.3, -138.9, 745.6] \ N $$

The resulting force values found in "rigid.out" and in "prescribed.out" is being checked for version control.

Tests

This benchmark is associated with 1 tests.

This model tests the *LOAD_DAMPING command. Damping is applied to linear, quadratic and cubic hex elements.

The velocity is tested against results in "rigid.out" and in "part.out".

Tests

This benchmark is associated with 1 tests.

Tested parameters: entype, enid, cid, $sf$.

This model tests the mass damping parameters in the command *LOAD_DAMPING. The test consists of an elastic cantilever beam that is exposed to a static pressure load.

Mass damping is used to approach the static equilibrium. The load applied is a distrubuted load of $10 \ kPa$. See Figure 1.

The mass damping force $F_{i}$ acting on node $i$ is:

$$ F_{i} = \Bigg\{ \begin{array}{ll} \ \hspace{10pt} -C \cdot m_{i} \cdot v_{i} \hspace{10pt} : \hspace{10pt} When \ moving \ towards \ equilibrium\\ -sf \cdot C \cdot m_{i} \cdot v_{i} \hspace{10pt} : \hspace{10pt} When \ moving \ away \ from \ equilibrium\\ \end{array} $$

where $C$ is the damping coefficient defined with a CURVE or FUNCTION with ID cid, $m_{i}$ is the node mass, $v_{i}$ is the node velocity and $sf>1$ is a mass damping scale factor which is used for faster dynamic relaxation.

The scale factor is only activated when moving away from equilibrium which is automatically determined from the energy levels.

For comparison, to see the effect of mass damping, three equaivalent beams are tested for with different values for $C$ and $sf$. See Figure 2.

Sensors are placed at the center of the free ends of the beams to measure tip displacements.

The effect of the mass damping can be seen in Figure 3.

First, average, maximum and last values of tip displacements are checked for version control.

Tests

This benchmark is associated with 1 tests.

Tested parameters: entype, enid, $\mu$, $c_{dec}$.

The model tests the viscous damping parameters in the command *LOAD_DAMPING. The test consists of two tip loaded cantilever beams, one with applied viscous damping and one without. See Figure 1.

Two output sensors are placed at the center of the free ends of the beams to measure tip displacement. The effect of damping for the undamped compared to the damped beam can be seen in Figure 2.

First, average and last values of tip displacements are checked for version control.

Tests

This benchmark is associated with 1 tests.

This tests the *LOAD_FORCE command. The subject is a rigid body with a mass of $1 \ kg$.

*GEOMETRY_SEED_COORDINATE is used to specify the loaded nodes. The force is applied in a local coordinate system, with a scale factor ($sf$), and with a birth and death time - both of which are within the time frame of the simulation.

A sine function gives the magnitude of the force:

$$ \lvert F\rvert = sf\cdot sin(\pi \cdot t)\hspace{40pt} t\in [0.1,0.2] $$

Which gives a total impulse of:

$$ \int\limits_{0.1}^{0.2} sf\cdot sin(\pi t) dt = 0.0045213 $$

The final velocity is:

$$ \tilde{v}_{end} = 0.0045213 \cdot [1,1,0]/\sqrt{2} = [0.00319, 0.00319, 0] $$

The velocity found in "rigid.out" and in "part.out" is being checked for version control.

Tests

This benchmark is associated with 1 tests.

Tested parameters: coid, entype${}_1$, enid${}_1$, entype${}_2$, enid${}_2$, fid.

This model tests the command *LOAD_FORCE_INTERACT.

A rectangular bar magnet that consists of a north and south pole is created with the command. It interacts with surrounding pieces of metals through its magnetic field which is constructed by applying a repelling force to the north pole and an attracting force to the south pole. See Figure 1.

The force per unit body volume is defined by a FUNCTION with ID=fid. The relative location of the bodies defines the direction of the force. The magnitude of the force is allowed to depend on their relative distance (intrinsic variable dist).

$$ F = \frac{C}{dist^2} $$

Where the constant C can vary along the length of the magnet. Stronger at the ends and weaker closer to the center of the magnet. The accuracy can thus be increased by dividing the magnet into more elements which will distribute the force intensity further out to the ends.

The magnetic field from the test can be seen in Figure 2, where the path in X & Y-coordinates of the surrounding objects are plotted. The magnet is divided into 4 elements in total.

The result obtained from the simulation can be compared to a physical experiment where the magnetic field is revealed by iron filings on a paper. See Figure 3.

The last X & Y-coordinates of some selected cubes are checked for version control.

Reference
[1] - Newton Henry Black, Harvey N. Davis (1913) Practical Physics, The MacMillan Co., USA, p. 242, fig. 200

Tests

This benchmark is associated with 1 tests.

This tests the *LOAD_GRAVITY command. All element types are tested in three simulations - one simulation for a gravity in each coordinate direction. The gravity constant is set to $10 \ m/s^{2}$, and the velocity at termination ($t=1$) should therefore be $10 \ m/s$.

The velocities are checked based on output in "rigid.out" and in "part.out".

Tests

This benchmark is associated with 3 tests.

This model tests the option of including/excluding added mass due to mass scaling for the command *LOAD_GRAVITY. A cube of $1 \ kg$ is in contact with a rigid plate. Gravity in negative z-direction is acting on the model with a gravitational constant $g=10$. See Figure 1.

Mass scaling is activated with maximum allowed mass scaling factor $ms_{max}=2$ in *TIME.

To control the added mass due to mass scaling from gravity loading, the parameter "addmass" is set to either 0 (include added mass) or to 1 (exclude added mass). The contact force between the cube and the plate should be:

Excluding added mass: $F = m \cdot a = 1 \cdot 10 = 10 \ N$
Including added mass: $F = m \cdot a = (m_{original} + m_{added}) \cdot a = 2 \cdot 10 = 20 \ N$

Contact force is checked for version control.

Tests

This benchmark is associated with 2 tests.

This tests the *LOAD_PRESSURE command. A shell structure modeled by one layer of cubic hexahedral elements is loaded by a triangular pressure time curve. To load only a part of the structure, a patch of shell elements with a defined thickness is created. The patch is positioned so that its thickness covers a part of the structures surface. The command *GEOMETRY_PART is then used to define a geometry equivalent to the patch and this geometry is loaded by *LOAD_PRESSURE. A figure of a simplified case of this test is presented in Figure 1.

The pressure functionality applies to complete element surfaces and surfaces are included in the defined geometry provided that the element surface centroid is within the geometry. This holds regardless of the polynomial order used in the elements. It is therefore important to pay attention to how the geometry covers the mesh-grid. As for the case illustrated in Figure 1, the pressure will operate as illustrated in Figure 2.

The following conditions were used:

The momentum is output to "part.out", which is checked for version control.

Tests

This benchmark is associated with 1 tests.

This tests the *LOAD_PRESSURE command. The pressure is applied to rigid elements of all element types. The command is used with a scale factor and a birth- and death time. For version control, final velocities are checked.

The velocities are checked against output found in "part.out" and in "rigid.out".

Tests

This benchmark is associated with 1 tests.

This model tests the *LOAD_PRESSURE command. A shell is loaded by a triangular pressure time curve. To load the entire shell, the *GEOMETRY_SEED_COORDINATE feature is applied to a coordinate on the shell surface. The total momentum transfer in X- and Y-direction (targets in Equations below) is checked for version control.

$$ A_x \cdot \dfrac{p_{max}\cdot t_{end}}{2}= 3.86 \ Ns $$

$$ A_y \cdot \dfrac{p_{max}\cdot t_{end}}{2}= 5.04 \ Ns $$

The max pressure is checked as well, and should occur half way through the simulation. The set-up parameters used are listed below.

The momentums are output to "part.out" and max pressure to "sensor.out", all of which are checked for version control.

Tests

This benchmark is associated with 1 tests.

This tests the *LOAD_SHEAR command. A shear load is applied to act in positive X-direction on all element types. The load is applied to faces with normals in positive and negative Y-direction.

Solving the differential equation gives the final velocity in X-direction:

$$ v_x = v_0(1 - \exp\dfrac{-2C(t_1-t_0)}{\rho_A}) = {3(1 - \exp(-0.04))} = 0.11763 \ m/s $$

The velocities are checked against data found in "part.out" and in "rigid.out".

Tests

This benchmark is associated with 1 tests.

This tests the *LOAD_THERMAL_BODY command. A thermal load is applied to 9 bodies: all element types are tested.

The final temperature for all elements is checked for version control.

Tests

This benchmark is associated with 1 tests.

Tested parameters: coid, entype, enid, $T_{amb}$.

The thermal radiation properties in *LOAD_THERMAL_RADIATION is verified in this test.

A quadratic plate with side length $200 \ mm$ and thickness $20 \ mm$ is given an initial temperature of $1273.15 \ K$ $(1000°C)$. The ambient temperature surrounding the hot plate is $273.15 \ K$ $(0°C)$. For $100$ seconds the plate is cooling off in the surrounding temperature.

The test setup is displayed in Figure 1.

To simplify the test, the heat conductivity is set to a high value, for a homogeneous temperature response throughout the plate. Thermal emissivity is set to $1$ and the heat capacity $400 \ J/K$. The density of the material is $3000 \ kg/m^3$.

Temperature vs. time and thermal energy vs. time from the simulation is presented in Figure 2 and 3 together with target curves from a verification script.

First, average and last values for temperature and thermal energy is checked for version control.

Tests

This benchmark is associated with 1 tests.

Tested parameters: coid, entype, enid, $T_{amb}$.

This model tests the thermal radiation and interaction between a hot and a cold plate with the command *LOAD_THERMAL_RADIATION.

The test consists of two quadratic plates with side length $200 \ mm$ and thickness $20 \ mm$. The hot plate is given an initial temperature of $1273.15 \ K$ $(1000°C)$ and the cold plate $273.15 \ K$ $(0°C)$. The ambient temperature in the surrounding is $273.15 \ K$ $(0°C)$.

Simulation time is set to $100$ seconds and at the beginning the plates are at a distance of $20 \ mm$, perpendicular from one another. For the duration the plates are moving away from one another at a constant velocity of $2 \ mm/s$. The emissivity of the cold plate is low and a significant amount of energy is reflected back to the hot plate.

The test setup is displayed in Figure 1.

To simplify the test, the heat conductivity is set to a high value, for a homogeneous temperature response throughout the plate.

Thermal emissivity, $\epsilon$, is set to $1$ for the hot plate and $0.1$ for the cold plate.

Heat capacity is set to $400 \ J/K$.

Density of the material is $3000 \ kg/m^3$.

Temperature vs. time and thermal energy vs. time for the hot plate is presented in Figure 2 and 3 together with target curves from a verification script.

First, average and last values for temperature and thermal energy is checked for version control.

Tests

This benchmark is associated with 1 tests.

This test verifies that a temperature dependent specific heat capacity (specified in *PROP_THERMAL) can be used with *LOAD_THERMAL_RADIATION.

A linear element with an initial temperature of $1000 \ K$ and a temperature dependent specific heat capacity is defined. A high thermal conductivity is specified, meaning that the spatial variation in element temperature is negligable. The ambient temperature is set to $293 \ K$. Element temperature vs. time from the simulation is presented in Figure 1 together with target curves from a verification script.

Initial, final and average temperature is checked.

Tests

This benchmark is associated with 1 tests.

This tests the *LOAD_THERMAL_SURFACE command. A thermal load is applied to 9 surfaces: all element types are tested. The thermal surface load is applied to faces with normals in positive Y-direction. Heat conduction will eventually distribute the temperature evenly to all elements.

The final temperature is checked for version control.

Tests

This benchmark is associated with 1 tests.

The command *LOAD_UNDEX is mainly based on equations presented in T. L. Geers & K. S. Hunter (2002) [1].

Underwater explosions are modeled in two phases: a shock-wave phase and an oscillation phase. The shock-wave phase is significantly shorter in time compared to the oscillation phase. Initial conditions for the oscillation phase are set based on the conditions at the end of the shock-wave phase.

An octave script is created to verify the command *LOAD_UNDEX. This script is created based solely on the referenced article and verified by re-creating some relevant figures from the article.

Pressure vs time (non-dimensionalized) from the similitude relation is presented in Figure 1.

Initial conditions for the oscillation phase are to be selected at a time when the pressure is reduced to 5-10% of its peak value, i.e., time between 3 – 7 in Figure 1. Bubble radius vs. time (non-dimensionlized) for this time interval is presented in Figure 2. Bubble radius and its first and second time derivative are used as initial conditions in the oscillation phase.

Bubble radius vs. time from the oscillation phase is presented in Figure 3 Initial conditions were selected at a non-dimensionalized time of 7 for this case.

The script is then used to verify the command *LOAD_UNDEX. The configuration is a $300 \ g$ charge detonated at a depth of $100 \ m$.

Bubble radius vs time is presented in Figure 4. Gas pressure in the bubble vs. time is presented in Figure 5 and Figure 6. Incident pressure $10 \ m$ from the center of the charge vs time is presented in Figure 7 and Figure 8. The Incident pressure is calculated based on the hyperacoustic case (eq. 4 in ref.) during the shock-wave phase, and the acoustic case during the oscillation phase (eq. 3 in ref.).

Reference
[1] T. L. Geers & K. S. Hunter, An integrated wave-effects model for an underwater explosion bubble, Journal of the Acoustical Society of America 111, 2002.

Tests

This benchmark is associated with 1 tests.

This model tests the *MAP command.

A plate with side length $1 \ m$ and thickness $3 \ mm$ is subjected to load pressures of $1 \ MPa$. To apply the load pressure at wanted locations on the plate, the command *MAP is used.

The test is displayed in Figure 1.

Two sensors are created to measure the applied pressure with targets:

• Sensor at $p_{11}$. Applied pressure should be $0 \ MPa$
• Sensor at center of plate. Applied pressure should be $1 \ MPa$

Tests

This benchmark is associated with 1 tests.

Network A in *MAT_BERGSTROM_BOYCE is verified in this test.

Tested parameters: $K$, $\mu$, $\lambda_L$, $a_0$, $a_1$ and $\eta_\mathrm{max}$.

A CHEX element is stretched in the X-direction while fixed in the Y- and Z-direction. Stress in the X-, Y- and Z-direction vs. volumetric strain from the element are presented in Figure 1 together with target curves obtained from a verification script.

Maximum and average volumetric strain and stress in the X-, Y- and Z-direction are checked. The maximum Mullins/network damage is also checked.

Tests

This benchmark is associated with 1 tests.

Network A and Network B (alternative 2) in *MAT_BERGSTROM_BOYCE is verified in this test.

Tested parameters: $K$, $\mu$, $\lambda_L$, $a_0$, $a_1$, $\eta_\mathrm{max}$, $\dot{\gamma}_0$, $\xi$, $b_0$, $b_1$ and $b_2$.

A CHEX element is stretched in the X-direction while fixed in the Y- and Z-direction. Effective stress vs. volumetric strain in the element is presented in Figure 1 together with a target curve from a verification script.

Maximum and average volumetric strain and effective stress are checked.

Tests

This benchmark is associated with 1 tests.

The material model *MAT_CABLE is verified in this test.

Tested parameters: $E$, $\nu$, $E_{t1}$, $E_{t2}$, $E_{tm}$, $\varepsilon_{tf}$, $\sigma_{ty}$.

In this test, two equivalent pipes on either side of the global X-axis are merged at their duplicated nodes creating a "cable". The cable is given a constant prescribed velocity at both ends generating tensile stresses. It is assigned the material model *MAT_CABLE and tensile fiber yield stress is set to $300 \ MPa$. A sensor is created in the middle of the cable.

The test setup is displayed in Figure 1.

Targets:

• Maximum effective stress at sensor should be $300 \ MPa$
• Damage at sensor at $t_{end}$ should be $1$

Tests

This benchmark is associated with 1 tests.

The elastic parameters in *MAT_CABLE are verified in this test.

Tested parameters: $E$, $\nu$ and $E_f$.

Two CHEX elements are used in this test. One of the elements is loaded in tension and the other in compression. The elements are deformed in the X-direction while fixed in the Y- and Z-direction. The element in tension exhibits a higher stiffness due to the additional fiber stiffness term.

Stress in the X-, Y- and Z-direction vs. time from the elements are presented in Figure 1 and Figure 2 together with target curves from a verification script.

Maximum, minimum and average stress in X-, Y- and Z-direction are checked in the elements.

Tests

This benchmark is associated with 1 tests.

Crushing damage in *MAT_CERAMIC is verified in this test.

Tested parameter: $\varepsilon_f$.

A CHEX element is loaded in uniaxial compression. Crushing damage developes gradually based on the plastic strain:

$$ D_c = min\left(1.0, \frac{\varepsilon_{dev}^p}{\varepsilon_f}\right) $$

Crushing damage vs. effective plastic strain from the element is presented in Figure 1 together with a target curve from a verification script.

Maximimum and average damage and effective plastic strain are checked.

Tests

This benchmark is associated with 1 tests.

The direction of plastic flow in *MAT_CERAMIC is verified in this test.

Tested parameter: $\beta$.

Two CHEX elements are compressed in the X-direction while fixed in the Y- and Z-direction. Parameter $\beta$ is set to $0$ in one of the elements and to $1$ in the other. The yield surface and failure surface coincides which means that the shear strength is not reduced with failure. Poisson's ratio is set to $0.0$ and the bulk modulus is defined as linear.

Yield strength, $\sigma_{y0}$:

$$ \sigma_{y0} = A_0 + B_0 \left(\frac{\sigma_{y0}}{3}\right) \implies \sigma_{y0}\left(1-\frac{B_0}{3}\right) = A_0 \implies \sigma_{y0} = \frac{A_0}{1-\frac{B_0}{3}} $$

Pressure at yield, $P_0$:

$$ P_0 = \frac{\sigma_{y0}}{3} $$

Volumetric strain at yield, $\varepsilon_{v0}$:

$$ \varepsilon_{v0} = -\frac{P_0}{K_1} $$

Volumetric strain at termination, $\varepsilon_{v}$:

$$ \varepsilon_{v} = log\left(1 + \frac{L-L_0}{L_0}\right) $$

where $L$ is the length at termination and $L_0$ the initial length.

Pressures at termination:

$$ P^{\beta = 0} = -K \varepsilon_{v} = -\frac{2}{3} G \varepsilon_{v} $$

$$ P^{\beta = 1} = P_0 - G \cdot (\varepsilon_{v} - \varepsilon_{v0}) $$

Effective stresses at termination:

$$ \sigma_{eff}^{\beta = 0} = A_0 + P^{\beta = 0} $$

$$ \sigma_{eff}^{\beta = 1} = A_0 + P^{\beta = 1} $$

Pressure vs. volumetric strain and effective stress vs. volumetric strain from both elements are presented in Figure 1 and 2 together with target curves based on the calculations above.

Last and average values of pressure, effective stress and volumetric strain are checked in the elements.

Tests

This benchmark is associated with 1 tests.

The pressure-volume relationship in *MAT_CERAMIC is verified in this test.

Tested parameters: $G$, $K_1$, $K_2$ and $K_3$.

The model consist of two CHEX elements. One of the elements is stretched and the other is compressed. Pressure vs. volumetric strain from the elements are presented in Figure 1 and 2 together with target curves from a verification script.

Maximum, minimum and average pressure are checked in the elements.

Tests

This benchmark is associated with 1 tests.

Spalling damage in *MAT_CERAMIC is verified in this test.

Tested parameters: $\sigma_s$, $t_s$ and $\alpha_s$.

A CHEX element is loaded in uniaxial tension. The element is stretched to a target stress and then kept at this stress level throughout the simulation. The target stress is greater than the defined spalling stress, meaning that damage starts to develop.

The time, $t$, at which failure should occur is calculated as:

$$ t = \frac{t_s}{\left(\sigma_1/\sigma_s\right)^{\alpha_s}} $$

Time $t$ is used as termination time in the simulation. Damage vs. time from the element is displayed in Figure 1 together with a target curve.

Maximum and average damage are checked.

Tests

This benchmark is associated with 1 tests.

The yield surface and failure surface in *MAT_CERAMIC are verified in this test.

Tested parameters: $A_0$, $B_0$, $\sigma_0^{max}$, $A_f$, $B_f$, $\sigma_f^{max}$ and $\varepsilon_f$.

Four CHEX elements are used in this test, which is divided into two steps.

In step 1, two of the elements are loaded to confinement pressures P3 and P4.

In step 2, one of the elements is stretched while the others are compressed.

The loading continues until failure occurs in all elements. With the selected crushing strain, failure occurs as soon as the effective stress reaches the yield surface. The loading conditions for each of the elements are presented in Table 1.

Effective stress vs. pressure prior to and post failure in the elements are presented in Figure 1 together with the defined yield surface and failure surface.

Note that each loading case is based on a singe element. If several elements were to be used in the specimen loaded in tension, node splitting would occur and the strength post failure would be zero.

Maximum, minimum and average effective stress are checked in the elements.

Tests

This benchmark is associated with 2 tests.

The compaction curve (pressure vs. inelastic volumetric strain) in *MAT_CONCRETE_2018 is verified in this test.

Tested parameters: $K_0$, $K_L$, $P_0$, $P_L$ and $\varepsilon_L$.

A CHEX element is volumetrically compressed. The pressure vs. volumetric strain repsonse is linear up to the crush limit, $P_0$, and defined by the bulk modulus, $K_0$. A quadratic response as a function of the volumetric plastic strain is then assumed until the material is fully compacted, which is defined by $P_L$ and $\varepsilon_L$. With further compaction, the response is linear and defined by the bulk modulus $K_L$.

Pressure vs. volumetric strain from the simulation is displayed in Figure 1 together with a target curve from a verification script.

Maximum and average pressure are checked.

Tests

This benchmark is associated with 1 tests.

Crushing damage in *MAT_CONCRETE_2018 is verified in this test.

Tested parameters: $K_0$, $K_L$, $P_0$, $P_L$, $\varepsilon_L$, $n$ and $\varepsilon_c$.

A CHEX element is loaded in uniaxial compression until failure occurs. Crushing damage vs. effective plastic strain from the element is displayed in Figure 1 together with a target curve from a verification script.

Maximum and average damage and effective plastic strain are checked.

Tests

This benchmark is associated with 1 tests.

This deviatoric yield surface in *MAT_CONCRETE_2018 is verified in this test.

Tested parameters: $f_t$ and $f_c$.

The model consist of two CHEX elements. One of the elements is loaded in uniaxial compression and the other in uniaxial tension. The compressive strength is set to $50 \ MPa$ and the tensile strength to $5 \ MPa$.

Effective stress vs. time from both elements are presented in Figure 1 together with targets of the compressive and tensile strength.

Maximum and average effective stress are checked in the elements.

Tests

This benchmark is associated with 1 tests.

Viscous damping in *MAT_CONCRETE_2018 is verified in this test.

Tested parameters: $c$ and $c_{dec}$.

Two CHEX elements are loaded in uniaxial compression. The compression is done at a prescribed strain rate and damping is used in one of the elements. Effective stress vs. time from the elements are presented in Figure 1 together with target curves from a verification script.

Maximum and average effective stress are checked in the elements.

Tests

This benchmark is associated with 1 tests.

The elasto-plastic response in *MAT_CREEP is verified in this test.

Tested parameters: $E$, $A$, $B$ and $n$.

A CHEX element is stretched in the X-direction while fixed in the Y- and Z-direction. Effective stress vs. volumetric strain from the element is displayed in Figure 1 together with a target curve obtained from a verification script.

Maximum and average effective stress and volumetric strain are checked.

Tests

This benchmark is associated with 1 tests.

The visco-elastic response in *MAT_CREEP is verified in this test.

Tested paramters: $E$, $c_0$, $c_1$, $c_2$ and $c_3$.

A CHEX element is loaded in uniaxial tension. The viscous parameters $c_0$ and $c_1$ are defined as constants while $c_2$ is defined by a function and $c_3$ by a curve. The viscous parameters are selected so that they all have a significant effect on the stress. Temperature is prescribed as a function of time.

Effective stress vs. effective creep strain from the element is presented in Figure 1 together with a target curve obtained from a verification script.

Maximum and average effective stress and effective creep strain are checked.

Tests

This benchmark is associated with 1 tests.

Linear elasticity in *MAT_ELASTIC is verified in this test.

Tested parameters: $E$ and $\nu$.

A CHEX element is stretched in the X-direction while fixed in the Y- and Z-direction. Stress in X-, Y- and Z-direction vs. volumetric strain from the element are presented in Figure 1 together with target curves from a verification script.

Maximum and average volumetric strain and stress in X-, Y- and Z-direction are checked.

Tests

This benchmark is associated with 1 tests.

Non-linear elasticity in *MAT_ELASTIC is verified in this test.

Tested parameters: $E$, $\nu$, $A$ and $B$.

A CHEX element is stretched in the X-direction while fixed in the Y- and Z-direction. Stress in X-, Y- and Z-direction vs. volumetric strain from the element are presented in Figure 1 together with target curves from a verification script.

Maximum and average volumetric strain and stress in X-, Y- and Z-direction are checked.

Tests

This benchmark is associated with 1 tests.

Non-linear elasticity with damping in *MAT_ELASTIC is verified in this test.

Tested parameters: $E$, $\nu$, $a$, $b$, $c$ and $c_{dec}$.

A CHEX element is stretched in the X-direction while fixed in the Y- and Z-direction. Stress in X-, Y- and Z-direction vs. volumetric strain from the element are presented in Figure 1 together with target curves from verification script.

Maximum and average volumetric strain and stress in X-, Y- and Z-direction are checked.

Tests

This benchmark is associated with 1 tests.

The dynamic viscocity in *MAT_FABRIC is verified in this test.

Tested parameter: $\mu$.

Two CHEX elements are loaded in uniaxial compresssion. A dynamic viscosity is defined for one of the elements. Effective stress vs. time from both elements is presented in Figure 1 together with target curves obtained from, a verification script.

Maximum and average effective stress are checked in both elements.

Tests

This benchmark is associated with 1 tests.

The stiffness, locking strain and rate dependent failure strains of the fibers in *MAT_FABRIC are verified in this test.

Tested parameters: $E_f$, $\varepsilon_l$, $\varepsilon_{f0}$, $\varepsilon_{f1}$, $\alpha_1$ - $\alpha_4$, $\eta_1$ - $\eta_4$, $c$ and $\dot{\varepsilon}_0$.

Two CHEX elements with fibers defined in the X-direction are used in this test. One of the elements is loaded in uniaxial tension and the other in uniaxial compression. The loading occurs in the fiber direction. Deformations occur at a constant strain rate and the fiber failure strains are defined to be strain rate dependent.

Stress vs. strain in the fiber direction from both elements are presented in Figure 1 together with target curves obtained from a verification script.

Maximum and average stress in the fiber direction are checked in both elements.

Tests

This benchmark is associated with 1 tests.

The stiffness, yield strength and failure of the matrix in *MAT_FABRIC are verified in this test.

Tested parameters: $E$, $\nu$, $\sigma_y$ and $W_c$.

A CHEX element without fibers is loaded in uniaxial tension until failure occurs. Stress vs. strain from the element is presented in Figure 1 together with a target curve from a verification script.

Maximum and average stress are checked.

Tests

This benchmark is associated with 1 tests.