Kinematic yield design computational homogenization of micro-structures using the stabilized iRBF mesh-free method

Abstract

This paper presents a novel numerical formulation based on kinematic theorem and homogenization theory for yield design of periodic heterogeneous materials. Macroscopic strength domains and failure mechanisms of such materials can be directly determined by solving an optimization problem formulated on a representative volume element (RVE). The integrated radial basis function (iRBF) mesh-free method is employed to approximate the fluctuating part of microscopic displacement field. The combination between nodal integration and conic programming leads to the fact that the resulting optimization problem can be solved efficiently, and that accurate solutions can be obtained with minimal computational cost. Various examples are investigated, demonstrating that the proposed method is able to approximate macroscopic limit surfaces of heterogeneous or composite materials, and is capable of capturing failure modes at micro-scale.