Generalized Gradient-Dependent Plasticy Theory

Abstract

Based on the Generalized Plastic Mechanics (GPM) and strain gradient-dependence of yield surfaces, the differential expressions of the volumetric and shear plastic strains are constructed, then the Generalized Gradient-dependent Plastic Mechanics (GGPM) is established to describe the strain localization characteristics and the basic mechanics characteristics of geo-materials. In order to discretize the controlling equations and the boundary conditions of analyses filed, an increment functional in which the displacement and plastic multipliers are independent variables was constructed to build up the variational principle of GGPM. Both the displacement and the plastical factor are discretized in space. A set of non-linear equations taking the displacements and the plastic factors of nodes as the unknown variables are obtained to solve the new proposed mechanic model. The boundary condition and the increment algorithm are also given. The numerical examples indicate that: (1) when strain localization appears,the plastic shear strain and the plastic volumetric strain mainly concentrate in localization band; (2) the mesh- dependency does not appear any more when the size of mesh changes; (3) when the parameters reflecting localization increase,the width of the strain localization band will be wider obviously.