Perturbation based stochastic finite element method for homogenization of two-phase elastic composites

The main idea of the paper is to apply the second order perturbation and st ochastic second central moment technique to solve the homogenization proble m. In order to determine the effective elasticity tensor, the prevailing co mputational methodology discussed in the literature so far was the Monte-Ca rlo simulation providing appropriate expected values and higher order proba bilistic moments of the effective tensor components. The technique applied in this paper aims at significantly reducing the computational cost of the simulation without sacrificing the solution accuracy. The numerical example substantiates this claim in the case of a periodic fiber-reinforced plane strain composite with random fiber and matrix Young's moduli. (C) 2000 Publ ished by Elsevier Science Ltd. All rights reserved.