Mathematical vs. Experimental Stress Analysis of Inhomogeneities in Solids

Abstract
The intent of this paper is to apply the discrete Fourier transform to the computation of eigenstress and eigenstrain fields around heterogeneities in composite materials. To this end the discrete Fourier transform is first briefly reviewed and then used to solve the basic equations of linear elasticity as pertinent to eigenstrained bodies under external loads. The results of this procedure are then used to discuss a few typical geometries such as an hexagonal two-dimensional array of thermally as well as elastically mismatched fibers in a composite matrix and a spherical Zirconia inclusion after a phase transformation. The resulting stress-strain fields are finally compared to experimental observations of eigenstress fields. The experimental techniques considered include photoelastic analyses as well as electron diffusion contrast techniques. It will be shown that the discrete Fourier transform as applied to eigenstress problems is capable of simulating the outcome of such experiments.