A mesh-free method based on linear complementary model for gradient plasticity continuum

A numerical method attributed to a solution procedure oflinear complementary problem (LCP) for gradient plasticity continuum isproposed. With the mesh-free method based on moving least-squareapproximation (MLS) procedure, the displacements and plastic multipliertaken as primary field variables are interpolated in terms of theirdiscretized counterparts defined at the nodal points and the integrationpoints, respectively. The weak form of the equilibrium equation along withthe non-local constitutive equation and the non-local yield criterionlocally enforced at each integration point are combined to mathematicallyeduce a normal form of LCP solved by means of Lexico-Lemke algorithm. Aniterative procedure based on the Newton-Raphson method is developed with noneed of consistent tangent elasto-plastic modulus matrix to be derived whilestill retaining the second convergence rate for the solution of the boundaryproblem of gradient plasticity continuum. The numerical results for one andtwo dimensional examples demonstrate the validity of the proposed method indealing with the numerical solution of the strain localization problem dueto strain softening.