Mechanics of Deformable Solids II

The aim is to establish the various concepts of the mechanics of deformable solids. This course follows on from the previous semester's course on the mechanics of deformable solids (MS200). Linear behavior laws, elastic or viscoelastic, are established for anisotropic or isotropic materials. Commonly used elastic limit criteria are presented for isotropic, ductile or brittle materials, and for orthotropic materials. The equations used in linear elasticity are established (case of isotropic materials, plane problems, plate equations, etc.).

EM7MS200

[unprocessed].

Chapter 4 Thermodynamics of continuous media

1. Derivative of the volume integral of a scalar function from the point

2. Conservation of mass

3. First principle of thermodynamics

4. Second principle of thermodynamics

Chapter 5 Linear elastic behavior laws

1. General writing
2. Symmetry of the stiffness matrix

3. Material symmetry relationships
4. Orthotropy
5. Thermoelasticity

Chapter 6 Yield strength criteria

1. Tresca criterion

2. Von Mises criterion

3. Mohr's criterion

4. Orthotropic materials

Chapter 7 Equations of linear elasticity

1. Balance sheet
2. Displacement equation
3. [Plane waves in elastic solids].
4. [Beltrami relations (constraints)].
5. [Flat elastostatic].
6. Thin plate equations

[Chapter 8 Simple solicitations]

1. [Traction-compression]
2. [Torsion of a cylindrical shaft ]
3. [Bending a cylindrical beam].

Chapter 9 Notions of linear viscoelasticity

1. Boltzmann's superposition principle
2. Harmonic testing
3. Spectral representation of viscoelastic behavior
4. [Causality principle]
5. Analog models
6. Generalization of the constitutive equation

• Model a structure and its loads in order to predict its mechanical behavior by determining the corresponding system of mathematical equations.
• Identify the laws of behavior of materials as a function of their class and material symmetries
• Predict the areas of validity of linear elastic behavior laws using criteria adapted to the material class
• Apply methods for analytically solving simplified problems in the mechanics of deformable solids
• Develop simplified structural mechanics models using simplifying assumptions