Since both of my major projects as well as my coursework are hitting on the subject this week, I though I'd talk about elastic moduli. However, before I can talk about that, we need to talk a bit about stress, strain and the concept of anisotropy.
Stress is fundamentally defined as force per unit area. Strain is the change in length per unit length. In a Cartesian coordinate system (which we use unless we're doing pipes or spheres), this means that to fully describe the stress and strain in three dimension, we end up with matrices.
Stress is typically written as