Homogenization with Eshelby: Multiple Inclusions, Effective Moduli

This lecture covers the concept of homogenization with Eshelby, focusing on multiple inclusions and effective moduli. The instructor explains how the field of one inclusion affects the response of all others, leading to a coupled problem. By considering average inclusion and matrix stresses, the lecture delves into the calculation of effective applied fields and strains. The analysis involves inserting infinitesimal 'test' inclusions into the matrix and determining the stress in the inclusions. The lecture concludes with the derivation of the effective stiffness tensor and its significance in composite materials.