A linear complementarity formulation of meshfree method for elastoplastic analysis of gradient-dependent plasticity

This work presents a linear complementarity formulation for elastoplastic analysis of the gradient-dependent plasticity including large deformation problems. The formulation is based on the meshfree smoothed radial point interpolation method, where the parametric variational principle (PVP) is used in the form of linear complementarity and the gradient-dependent plasticity is represented by the linearization of yield criterion. The yield stress is linearly evolved through equivalent plastic strain as well as its Laplacian (namely second gradient). The global discretized system equations are transformed into a standard linear complementarity problem (LCP), which can be solved readily using the Lemke method. The proposed approach is capable of simulating material hardening/softening and strain localization. An extensive numerical study is performed to validate the proposed method and to investigate the effects of various parameters. The numerical results demonstrate that the proposed approach is accurate and stable for the elastoplastic analysis of 2D solids with gradient-dependent plasticity on strain localization.