Elastic Inhomogeneity: Eshelby's Solution

This lecture discusses the concept of elastic inhomogeneity and presents Eshelby's solution to the problem of a homogeneous inclusion in a deformed shape. By choosing the right strain, the homogeneous inclusion can match the real inclusion's shape and stress. The lecture explains how to ensure the same tractions and displacements at the inclusion interface, leading to the same stresses and displacements outside the inclusion. It covers the extra distortion needed and the conditions for stress equivalence. The presentation concludes with the analysis of the free energy and the crucial limits that need to be satisfied in the context of elastic inhomogeneity.