Meshless Local Petrov-Galerkin Formulation for Problems in Composite Micromechanics

In this paper we present the meshless local Petrov-Galerkin formulation for the generalized plane strain problem with specific emphasis on micromechanics of composite materials containing material discontinuities. The problem requires the introduction of an extra discrete degree of freedom, the out-of-plane uniform normal strain. The treatment of material discontinuity at the interface between the two phases of the composite is presented by means of direct imposition of interface boundary conditions. The meshless local Petrov-Galerkin method is used in the micromechanical model for predicting the elastic constants of the composite. To our knowledge, this is the first study in which the meshless local Petrov-Galerkin method is formulated for the so-called meshless local Petrov-Galerkin method based micromechanical analysis. Examples are presented to illustrate the effectiveness of the current method, and it is validated by comparing the results with available analytical and numerical solutions. The current method has the potential for use in micromechanics, especially for textile composites, where the meshing of the unit cell has been quite difficult. [PUBLICATION ABSTRACT]