1. Introduction to tensorial calculus. 1.1 Definition of a tensor. 1.2 Indicial notation and summation convention. 1.3 Change of base formula. 1.4 Algebraic tensors operations. 1.5 Tensor analysis : differential operators and integral formula. 2. Continuum mechanics. 2.1 Mathematical background. 2.2 Kinematics for finite transformations. 2.3 Stress, Cauchy theorem 2.4 Anisotropic elasticity and constitutive laws.

1 Vibrations. 1.1 Equations and fundamental problems of dynamics. 1.2 Free responses and fundamental parameters. 1.3 Deterministic forced responses and linear filters. 1.4 Time-evolution problem with initial conditions. 1.5 Stationary random vibration. 1.6 Vibration transmissibility and vibration isolation. 1.7 Structural modes of vibration and modal analysis. 2. Waves in elastic bodies. 2.1 Wave propagation in one-dimensional medium. 2.2 Propagation of elastic waves in an infinite homogeneous linear medium. 2.3 Waves in semi-infinite media. 2.4 Wave transmission and reflection with the inclusion of a boundary.

1. Elliptic, parabolic or hyperbolic boundary value problems. 2. Discretization by the finite differences method. 3. Weak formulation and admissible space. 4. Interpolation on a finite element basis; convergence. 5. Numerical integration and reference element. 6. Discretization by the finite elements method. 7. Resolution scheme in time (Euler, Newmark). 8. Nonlinear elasticity (Newton-Raphson, Riks-Crisfield, MAN).

1. Classes of behavior. 2. Mechanics of brittle fracture. 3. Fatigue of materials. 4. Time-dependent behavior : viscoelasticity and viscoplasticity. 5. Elastoplasticity and limit analysis.

1. Classification elastic symmetries. 2. Identification of elastic properties. 3. Formulation of an anisotopic and heterogeneous linear thermoelastic problem. 4. Basic concepts of homogenization theory. 5. Basic homogenization methods for composites. 6. Multilayered composite beams and plates. 7. Spherical and cylindrical multilayered composite shells.

1. Beams and plates 1.1. Kinematic assumptions of beams 1.2. Cases of elementary solicitations 1.3. Internal efforts: calculations and diagrams 1.4. Energy theorems 1.5. Force method and displacement method 1.6. Kinematics of thin and thick plates 1.7. Strain tensor and generalized stress tensor 1.8. Rectangular and circular plates bending 1.9. Approximate resolution method 1.10. Numerical resolution method 2. Instabilities of elastic beams 2.1. Euler method. 2.2. Instability of discrete systems: energy method. 2.3. Numerical method for solving instability problems related to elastic structures.

The internship, lasting at least 2 months, must be done in a private company or in a research laboratory. The objective of the internship is to understand the functioning of business or the research activities and to put in practice the knowledge learned during the courses. Students have to prepare a dissertation and an oral defense.

1. Continuity and Navier-Stokes equations. 2 . Kinetic energy equation and Bernoulli equations. 3 . Isentropic compressible flows of an ideal gas and shock waves. 4. Non Newtonian fluid flows. 5. Laminar external flows and dynamic boundary layers. 6. Introduction to turbulence.

1. Elliptic, parabolic or hyperbolic boundary value problems. 2. Discretization by the finite differences method. 3. Weak formulation and admissible space. 4. Interpolation on a finite element basis; convergence. 5. Numerical integration and reference element. 6. Discretization by the finite elements method. 7. Resolution scheme in time (Euler, Newmark). 8. Nonlinear elasticity (Newton-Raphson, Riks-Crisfield, MAN).

1. Direct static characterization of real samples. 2. Prediction of transport properties from three-dimensional periodic unit-cells. 3. Frequency-dependent visco-inertial and thermal responses. 4. Comparison with standing wave tube measurements. 5. Effective elastic properties of the porous medium.

1. Generality and Principles of reinforced concrete. 2. Properties of the materials. 3. Actions and loadings. 4. Basic hypotheses (ELU et ELS). 5. Design of elements under uniaxial compression. 6. Design of elements under simple bending. 7. Design of elements under shear loading.