Multiple ellipsoidal/elliptical inhomogeneities embedded in infinite matrix by equivalent inhomogeneous inclusion method

Abstract

Traditional equivalent inclusion method provides unreliable predictions of the stress concentrations of two spherical inhomogeneities with small separation distance. This paper determines the stress and strain fields of multiple ellipsoidal/elliptical inhomogeneities by equivalent inhomogeneous inclusion method. Equivalent inhomogeneous inclusion method is an inverse of equivalent inclusion method and substitutes the subdomains of matrix with known strains by equivalent inhomogeneous inclusions. The stress and strain fields of multiple inhomogeneities are decomposed into the superposition of matrix under applied load and each solitary inhomogeneous inclusion with polynomial eigenstrains by the iteration of equivalent inhomogeneous inclusion method. Multiple circular and spherical inhomogeneities are respectively used as examples and examined by the finite element method. The stress concentrations of multiple inhomogeneities with small separation distances are well predicted by equivalent inhomogeneous inclusion method and the accuracies improve with the increase of eigenstrain orders. Equivalent inhomogeneous inclusion method gives more accurate stress predictions than equivalent inclusion method in the problem of two spherical inhomogeneities.

Assessment of the equivalent inclusion method for the numerical homogenization of fibrous composites

“…Eq. (38) shows that the singularity cannot be removed in the integral expression of the self-influence coefficients, which makes their analytical evaluation difficult. Rather than attempting a regularized quadrature, and observing that this coefficient can be precomputed off-line prior to the full EIM calculation, we used a numerical approach based on a finite element analysis.…”

“…Several variants of the method have also been considered [38,36]. In particular, Brisard et al [7] introduced a Galerkin-based variational form of the EIM.…”