Basic Concepts on Mechanics of Continuous Media (MMC)

Continuous Media Mechanics (CMM), as its title indicates, is based on a main hypothesis of continuity of matter, and is interested in the study of solid or fluid bodies undergoing sudden changes of shape at different scales. In a first part, we will deal with the mathematical reminders of tensor notations, then in the second and third parts, a direct application of the first part is presented, these are the two stress and strain tensors respectively. If the relationship is linear between the stress and strain tensor on a small scale, then we are talking about the elastic behaviour of materials and this is the subject of the fourth chapter (The theory of isotropic and anisotropic linear elasticity). After introducing the elastic law, an overview of the non-linear relationship in large scale deformation (theory of plasticity) is presented, which is the subject of the fifth and last chapter. This course has been written for students and pupils (bachelor, master and engineering cycle of the School), its objective is to present and simplify some of the mathematical and physical concepts observed when using the MMC.