A numerical study on the visco-plastic regularization of a rate-independent strain gradient crystal plasticity formulation

A common practice in computational investigations of rate-independent plasticity is to approximate the rate-independent behavior by a visco-plastic regularization. As the fidelity of the approximation increases, the numerical solution of the non-linear problem becomes challenging and it can eventually lead to divergence; thus, there is a numerical limit to the regularization parameter. This limit may be exacerbated by complex material models and critical values of material parameters. Due to these constraints, the regularization may be rendered insufficient and the artificially introduced rate-dependency may lead to a behavior that can be mistakenly attributed to the material model and that we thus identify as spurious in a rate-independent context. To study these spurious effects and their onset, here the problem of an infinite strip under shear loading is numerically solved using a visco-plastic regularized gradient crystal plasticity formulation. The required accuracy of the rate-dependent approximation is found to vary with respect to the type of loading. Furthermore, a set of sigmoid functions used for the regularization is investigated and a subset is shown to deliver improved approximation of the rate-independent case.

Automated summary

It is common practice to use visco-plastic regularization to approximate rate-independent behavior in computational investigations of plasticity. However, there is a numerical limit to the regularization parameter, which may be exacerbated by complex material models and critical values of material parameters. Insufficient regularization can introduce artificial rate-dependency and lead to behavior that is mistakenly attributed to the material model. In this study, the problem of an infinite strip under shear loading is numerically solved using a visco-plastic regularized gradient crystal plasticity formulation. The required accuracy of the rate-dependent approximation is found to vary with the type of loading.