Permanent set

Abaqus uses isotropic hardening Mises plasticity with an associated flow rule to capture permanent set. Since the underlying material is hyperelastic in nature, plasticity calculations are based on a multiplicative split of the deformation gradient into elastic and plastic components:

where ${\mathbf{F}}^e$ is the elastic part of the deformation gradient, representing the hyperelastic behavior, and ${\mathbf{F}}^p$ is the plastic part of the deformation gradient, representing the stress-free intermediate configuration.

The plastic part of the deformation rate tensor based on the associated flow rule of the Mises yield condition is given by

In the above equation $\overline{\tau }$ is the deviatoric part of the Kirchoff stress tensor $\tau$, $q$ is the effective Kirchoff stress, and ${\overline{\epsilon }}^p$ is the equivalent plastic strain. The resulting system of equations is solved using standard techniques outlined in Weber and Anand (1990) and Simo (1992).

An application that uses the above mentioned approach can be found in Govindarajan et al. (2007).