Hyperelasticity: Basic Theory and Applications

This lecture introduces the concept of hyperelasticity, focusing on the basic theory and applications. It covers topics such as non-linear but reversible stress-strain response, energy density per unit mass, and the constructive law for stress. The lecture explains the relationship between the internal stored energy and the current state of deformation, emphasizing the use of stretch ratio instead of the Green-Lagrange strain. It also discusses isotropic hyperelastic materials and the importance of principal invariants in determining the energy function. The presentation concludes with a detailed examination of hyperelastic materials in the Principal Axes coordinate system.