Effective properties of composite materials with periodic microstructure: a computational approach

This study reviews several problems which are specific of composites with p eriodic microstructure composed of linear or nonlinear constituents. The th eoretical background of the method is recalled first. Two different familie s of numerical methods are considered to solve the problem. The first is ba sed on the Finite Element Method. The concept of 'macroscopic degrees of fr eedom' is presented. The implementation of periodicity conditions is discus sed. A general framework permitting either a strain or stress control is pr oposed. The second numerical method is based on Fast Fourier Transforms. It conside rs first the problem of a homogeneous linear reference material undergoing a nonhomogeneous periodic eigenstrain. The solution of this problem is base d on the explicit form of the periodic Green's function of the reference me dium. The relative merits of the two methods are compared and several examp les are discussed. Both methods give very comparable results on test exampl es and their domains of applications appear to be complementary. (C) 1999 E lsevier Science B.V. All rights reserved.