Limit analysis of microstructures based on homogenization theory and the element-free Galerkin method

Abstract

This paper presents a novel numerical formulation of computational homogenization analysis of materials at limit state. The fluctuating displacement field are approximated using the Element-Free Galerkin (EFG) meshless method. The estimated yield surface of materials can be determined by handling the multiscale (macro-micro) transition. Taking advantage of high-order EFG shape function and the second-order cone programming, the resulting optimization problem can be solved rapidly with the great accuracy. Several benchmark examples will be investigated to demonstrate the computational efficiency of proposed method.