Element-Free Galerkin Implementation of Gradient Plasticity - Part II: Applications to 2D Strain Localization and Size Effects

摘要

This is the second part of a two-part article that focuses on strain gradient plasticity implementation within the element-free Galerkin (EFG) framework. In the first part, a generalized flow theory of gradient plasticity has been presented along with its EFG formulation for the solution of incremental boundary value problems. The one-dimensional tensile bar test has also been employed to study the properties of this formulation for an elastic-softening plastic material. In the present part, the aforementioned EFG implementation is employed to solve two-dimensional boundary value problems under plane strain or plane stress conditions. In particular, the following examples are considered: a) Plastic strain localization and size effects in compression of an elastic - gradient plastic material with linear isotropic softening, b) Size effect in uniaxial tension of a perforated strip made of an elastic - gradient plastic material with linear isotropic hardening. As in the one-dimensional problem, the non-pointwise satisfaction of the yield condition, combined with the long-range nodal interaction in the EFG method, induces stress oscillations within the plastic region and non-proper, sub-quadratic convergence. Upon discretization refinement, however, robust applied stress (or normalized load) vs. nominal strain graphs, equivalent plastic strain patterns and traction distributions are obtained.