Eshelby 3: Modulus Mismatch

This lecture discusses the concept of modulus mismatch in elastic inhomogeneities. It covers the problem of including materials with different elastic moduli, the solution proposed by Eshelby, and the implications of using Green's function. The lecture explains how to fit a homogeneous inclusion to the deformed shape of a real inclusion, ensuring the same stress inside. It also delves into the extra distortion required and the crucial limits that need to be satisfied. The analysis includes the stored elastic energy, the free energy, and the work done by tractions on the outer boundary.