A Mixed FE-Meshfree Method for Gradient Plasticity Continuum with Linear Complementary Model

A mixed FE-meshfree method based on gradient plasticity and linear complementary problem (LCP) model is proposed. The plastic multiplier field is assumed and approximately interpolated in terms of its discretized values defined at the integration points with moving least-square (MLS) meshfree method. Whereas the displacement field is discretized in terms of its nodal values with FE interpolation approximations. The weak form of the equilibrium equation along with the non-local constitutive equation and gradient-dependent yield criterion locally enforced at each integration point are combined to educe a normal form of LCP which is solved by means of Lexico-Lemke algorithm. A consistent algorithm based on backward-Euler return mapping integration scheme is devised. There is no need to derive non-local consistent tangent elasto-plastic modulus matrix in the proposed method while the second convergence rate is still retained. Numerical results demonstrate the validity of the method in modeling strain localization problem due to strain softening.