Computation of Stresses and Strains in Heterogeneous Bodies by Use of the Discrete Fourier Transform

Abstract

AbstractDiscrete Fourier transforms are used to derive a numerical solution for the stresses and strains in a Representative Volume Element (RVE) which is filled with heterogeneities. The so‐called “equivalent inclusion method” (Mura 1987) is applied to reduce the original problem by determination of an auxiliary strain field. This field is related to the stresses by virtue of a spatially constant auxiliary stiffness tensor. By means of discrete Fourier transforms the resulting Partial Differential Equations (PDE) are mapped onto a linear system of equations which can be solved explicitly. A functional relation for the auxiliary strain field results. It can be solved approximately by means of a Neumann iteration procedure. Two heterogeneity problems of the Kirsch type are considered for which an analytical solution exists against which the accuracy of the numerical method can be checked.