Standard gradient plasticity: formulation and numerical integration

International audienceThe paper is devoted to the numerical implementation of a strain gradient plasticity model proposed by Q.S Nguyen. The model combining isotropic and kinematic hardening uses gradient of accumulated plastic strain to reproduce micro-mechanical features related to size effect. Its formulation is presented within the general framework of the classical continuum thermodynamics. Its numerical integration meets difficulties by the presence of strain gradients in the local theory formulation, which leads to a Laplacian equation solved at global level and to boundary value problems governed by partial differential equations of higher order with non-standard boundary conditions. A methodology of a diffusion-like problem is used to overcome this difficulty. This work is numerically solved via UMATs constructed in common available FE codes (e.g. Cast3M)