The equivalent inclusion method in elasticity and composite materials

The equivalent inclusion method is applied to solve classical elasticity problems and to determine the effective properties of composite materials. The method originally was proposed by Eshelby to obtain the uniform stress field within an ellipsoidal inhomogeneity, which is embedded in an infinite medium. Here the equivalent inclusion method was extended to obtain the exact solution of the stress fields outside the inhomogeneity and the effective mechanical and thermal properties of composite materials.; By applying the equivalent inclusion method and utilizing ellipsoidal harmonic functions, the stress fields of an infinite body which contains an ellipsoidal inhomogeneity were solved and given in closed form. Since ellipsoidal coordinates are used, the stresses along the principal axes and on the surface of the ellipsoid are easily calculated.; Another important feature of this thesis is the application of the Mori-Tanaka method which is essentially developed from the equivalent inclusion method and the concepts of back stress. Here the overall mechanical behavior of elastic-plastic and power-law composites, and the effective thermal expansion coefficients and the specific heats of composites are determined. It is found that using the Mori-Tanaka method, the effective properties of composite materials always give closed form solutions and satisfy the existing bounds for two phase composites. The Mori-Tanaka method was also utilized to obtain the fracture criteria of multiple cracked bodies and to find the linear relation between critical volume fraction of cracks and the applied stress.