Stochastic Response Analysis of FRP using the Second-Order Perturbation-Based Homogenization Method

Abstract

This paper discusses a stochastic response analysis using the perturbation-based homogenization method for a homogenization problem of a fiber reinforced composite material considering microscopic uncertainty. Since an estimated result of the stochastic characteristics such as the expectation and variance using the first order perturbation-based homogenization method includes a large error in some cases, applicability and effectiveness of the second or higher order perturbation method should be investigated. In this paper, at first, the second order perturbation-based homogenization method is formulated. A second order perturbation-based procedure for estimating the stochastic characteristics of equivalent elastic constants of an orthotropic material is also introduced. Next, the second-order perturbation-based stochastic homogenization method is applied to the stochastic analysis of a homogenized elastic property caused by uncertainty in material property of a microstructure. As a numerical example, the stochastic characteristics of the homogenized elastic properties of a unidirectional fiber reinforced plastic caused by the microscopic material uncertainty are estimated using the Monte-Calro simulation, the first and second order perturbation method. Also, a detailed stochastic analysis for a homogeneous isotropic material is performed. From the numerical results, effectiveness and a problem of the second-order perturbation method are illustrated.