A strain-gradient isotropic elastoplastic damage model with J₃ dependence

A "plastic strain gradient" version of an isotropic elastoplastic damage model that depends on the third invariant J(3) of the stress deviator is developed. The model is based on the "non-local" equivalent plastic strain e(p) defined by Peerlings et al. (2001) and Engelen et al. (2003) and introduces a "material length" l to the constitutive equations. It is shown that the non-local equivalent plastic strain e(p) at a material point P can be identified with the average value of the local von Mises equivalent plastic strain (epsilon) over bar (p) over a sphere centered at P and of radius approximately equal to 3 l. A methodology for the numerical integration of the constitutive equations is presented. The algorithm is appropriate for rate-independent as well as rate-dependent (viscoplastic) models. The model is implemented in the ABAQUS general-purpose finite element program and both quasi-static and dynamic problems are solved. Two possible ABAQUS implementations are discussed. First,"user elements" are developed, which can be used for the solution of both quasi-static and dynamic problems. Reduced 1-point Gauss integration is discussed in 8-node hexahedral elements and the "physical stabilization" method of Puso (2000) is used to remove the resulting numerical singularities (hourglass control). Second, the implementation of the model via "user material" subroutines is discussed. Quasi-static problems can be solved with ABAQUS/Standard using a *COUPLED TEMPERATURE-DISPLACEMENT, STEADY STATE analysis together with user subroutine UMAT, in which temperature is identified with the non-local equivalent plastic strain e(p); the solution of dynamic problems requires use of ABAQUS/Explicit together with a *DYNAMIC TEMPERATURE-DISPLACEMENT analysis option and user subroutines VUMAT and DFLUX. Several example problems are solved. (C) 2019 Elsevier Ltd. All rights reserved.