Mechanics of Deformable Solids I

The aim is to establish the various concepts of the mechanics of deformable solids. The various tensors of deformation and stress are defined in the case of finite transformations. The classical case of infinitesimal transformations is treated as a special case. Linear behavior laws, elastic or viscoelastic, are established for anisotropic or isotropic materials. Elastic limit criteria are presented for isotropic, ductile and brittle materials, and for orthotropic materials. The equations used in linear elasticity are established (case of isotropic materials, plane problems, plate equations, etc.). The more general energetic approach is also covered.

Chapter 1 Introduction

1. The objectives of solid mechanics
   2. Dimensioning
   3. Course content


Chapter 2 Kinematics of deformable solids

1. Definitions
2. Finite transformation deformation tensors
3. Interpretation of Green-Lagrange tensor terms
4. Main directions for the gradient tensor

5. Invariants

6. Infinitesimal transformations
7. Mohr representation
8. Compatibility equations

Chapter 3 Constraints

1. Notions of external and internal forces
2. Cut-off principle and stress vector
3. Stress tensors
4. Properties of the Cauchy tensor


• Model a structure and its loads in order to predict its mechanical behavior by determining the corresponding system of mathematical equations.
• Use the concepts of stress and strain, choosing quantities appropriate to the situation under consideration (finite or infinitesimal transformations) and to the simplifying hypotheses formulated.
• Apply methods for analytically solving simplified problems in the mechanics of deformable solids
• Develop simplified structural mechanics models using simplifying assumptions