Homogenization Theory: Effective Material Properties in Composites

This lecture introduces homogenization theory for composites, aiming to replace point-wise Hooke's law with volume-averaged stress and strain. The instructor discusses rigorous bounds development for desired material properties, focusing on total elastic energy in the composite. An emphasis is placed on isotropic and anisotropic phases, with considerations for material orientation and alignment. The lecture concludes with the application of homogenization theory to thermal conductivity, providing rigorous upper and lower bounds for composite properties.