Command manual

IMPETUS failure criterion is similar to the Cockcroft-Latham failure criterion. However, it has been equipped with one extra parameter $n$ that allows for an anisotropic damage growth. The model is based on the assumption that defects deform with the material. It is further assumed that compressed defects exposed to tensile loading are more harmful than elongated defects. The damage growth is assumed proportional to the maximum eigenvalue $\hat\sigma_1$ of a distorted stress tensor $\hat{\boldsymbol\sigma}$.

$D = \displaystyle{ \frac{1}{W_c} \int_0^{\varepsilon_{eff}^p}} \mathrm{max}(0,\hat\sigma_1) \mathrm{d}\varepsilon_{eff}^p$

The distorted stress tensor $\hat{\boldsymbol\sigma}$ is formed as:

$\hat{\boldsymbol\sigma} = \mathbf{A \boldsymbol{\sigma} A}$

where $\boldsymbol{\sigma}$ is the current stress tensor and $\mathbf{A}$ is a symmetric tensor describing the defect compression. $\mathbf{A}$ is a function of the principal stretches $(\lambda_1, \lambda_2, \lambda_3)$ and of their corresponding eigenvectors $(\mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3)$.

$\mathbf{A} = \displaystyle{\sum_{i=1}^3} \left( \frac{\lambda_1}{\lambda_i} \right)^n \mathbf{v}_i \otimes \mathbf{v}_i$

Note that $\lambda_1$ is the maximum principal stretch. The formulation ensures that the damage growth is equivialent to Cockcroft-Latham in proportional loading where $\lambda_1$ coincides with $\sigma_1$.