MEC_43031_EP - Mécanique des solides (2024-2025)

This course is an introduction to the mechanics of deformable solids in three space dimensions. The fundamental concepts that will be covered are: (i) kinematics of deforming bodies, (ii) balance laws (which hold for all bodies), and (iii) constitutive relations (which distinguish between different types of materials). We will emphasize elasticity theory because it is at once central to a majority of engineering applications and the cornerstone on which to build more complex theories of material behavior.

Put together, these ingredients (kinematics, balance laws, and elastic constitutive relations) will allow us to formulate and solve initial-boundary value problems, for small deformations (linear elasticity) as for large deformations (finite elasticity).

In linear elasticity, we will also introduce variational principles, which provides the tools for a qualitative analysis of problems in linearized elastostatics and is the basis for numerical techniques such as the finite element method.

In finite elasticity (which is relevant to such materials as elastomers and biological tissues), we will illustrate how nonlinearity leads to unexpected physical phenomena which cannot be captured by the linearized theory.

Finally, we will conclude the course with an opening towards coupled problems, which include thermoelasticity, piezoelectricity, and chemoelasticity), and are encountered in many applications, such as the electrochemistry of batteries and 3D printing. In these problems, the mechanical response of a solid to thermal, electrical, or chemical loadings is governed by the interplay between elasticity and other physical mechanisms (e.g., heat transfer or the diffusion of chemical species). The modeling of these couplings and the study of their effects will be illustrated through selected examples.