A large-deformation gradient theory for elastic–plastic materials: Strain softening and regularization of shear bands

We present a large deformation gradient theory for rate-independent, isotropic elastic–plastic materials in which in addition to the standard equivalent tensile plastic strain image, a variable ep is introduced for the purpose of regularization of numerical simulations of shear band formation under strain softening conditions. Specifically, in contrast to traditional gradient theories which are based on image and image, here we develop a theory which depends on image, and the gradient ∇ep, with the latter chosen to represent a measure of the inhomogeneity of the microscale plasticity. We have numerically implemented a two-dimensional plane strain version of our theory in a commercial finite element program by writing a user-element subroutine. Representative examples which demonstrate the ability of the theory and its numerical implementation to satisfactorily model large-deformation strain-softening response accompanied by intense localized shear bands — with no pathological mesh-dependence — are provided.