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 ̄ ^p, a variable e ^p 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 ̄ ^p and ∇̄ ^p, here we develop a theory which depends on ̄ ^p, ^ep, and the gradient ∇e ^p, 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.