Elasto-plastic mlpg method for micromechanical modeling of heterogeneous materials

In this study, a truly meshless method based on the meshless local Petrov-Galerkin method is formulated for analysis of the elastic-plastic behavior of heterogeneous solid materials. The incremental theory of plasticity is employed for modeling the nonlinearity of the material behavior due to plastic strains. The well-known Prandtl-Reuss flow rule of plasticity is used as the constitutive equation of the material. In the presented method, the computational cost is reduced due to elimination of the domain integration from the formulation. As a practical example, the presented elastic-plastic meshless formulation is employed for micromechanical analysis of the unidirectional composite material. A quarter of the fiber surrounded in the matrix in a square array is considered as the Representative Volume Element (RVE). The fully bonded fiber-matrix interface condition is assumed and the continuity of displacement and reciprocity of traction are imposed to the interface. A predictor-corrector numerical integration method is used for the solution of the discretized equations of the problem. The numerical results show excellent agreement with the predictions of the finite element analysis. Copyright © 2015 Tech Science Press.