Coupled mechanical behaviors I

- Generalized Standard Materials: This course presents a unified framework to describe the thermomechanical behavior of materials. Based on the notions of thermodynamics seen in the preparatory years, it introduces the notion of irreversibility in an extended framework where the nature of the state variables can become tensorial. A link with MMC is essential so that the student understands how a purely mechanical description of continuous media and systems can be completed by a thermodynamic description of the material or the constituents of the medium to be analyzed.

At the end of the course, the student should be able to write the behavioral equations of state and complementary equations associated with a thermomechanical model. He/she should be able to draw up a complete energy balance by calculating in particular the deformation energy, the dissipated energy, the heat sources induced by the thermomechanical couplings

- Heterogeneous Elasticity: In this course, the notion of elasticity is extended to anisotropic media, heterogeneous media (dimensioning of composite materials), and large transformations (entropic elasticity of elastomers).

 - Vibrations and dynamic systems: Basic notions of vibrations for a single degree of freedom modeling, with and without damping. Free vibrations. Forced vibrations. Study of the resonance phenomenon.
Modeling of systems with two degrees of freedom. Resonance and anti-resonance.
Study of systems with a large number of degrees of freedom (e.g. from finite element modeling). Study of eigenmodes.
Dimensioning with respect to dynamic loads.

• write a thermomechanical behavior law
• determine the time-dependent or time-independent character of the behavior of a material.
• Dissipative and coupling effects
• determine the characteristics of an elastic composite
• Static and dynamic behavior of materials and structures
• study the dynamic behavior of an elastic structure

: The concepts of MMC of 3A must be acquired as well as the mathematical and numerical tools related to the solution of differential or partial derivative problems.

This ECUE is evaluated by :

Final score = E