Exact solution of Eshelby's inhomogeneity problem in strain gradient theory of elasticity and its applications in composite materials

A new micromechanical approach to deal with the problem of Eshelby's inhomogeneity is developed for the prediction of the effective properties of composite materials accord-ing to the strain gradient elasticity theory. The method is based on the Green's function technique leading to an integral equation of the heterogeneous elastic problem. Within the simplified strain gradient elasticity theory, the integral equation for an infinite heteroge-neous medium subjected to non-homogeneous boundary conditions is acquired. Thanks to this integral equation, the exact solution of Eshelby's inhomogeneity problem is detailed for spherical inhomogeneity and isotropic elastic behavior. From the expression of strain localization relations, the effective elastic properties of a two-phase composite material are then predicted through Mori Tanaka's homogenization scheme. To test the relevance of the suggested approach, its predictions are compared with results issued from some reference models and experimental data.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

A new micromechanical approach based on the strain gradient elasticity theory is developed to predict the effective properties of composite materials by dealing with the problem of Eshelby's inhomogeneity. The method uses the Green's function technique to obtain an integral equation for the heterogeneous elastic problem. By utilizing this integral equation, the exact solution for Eshelby's inhomogeneity problem with spherical inhomogeneity and isotropic elastic behavior is determined. The effective elastic properties of a two-phase composite material are then predicted using Mori Tanaka's homogenization scheme through the expression of strain localization relations. The suggested approach is tested against reference models and experimental data to assess its relevance.