Coupled mechanical behavior I

- Generalized Standard Materials: This ECUE presents a unified framework for describing the thermomechanical behavior of materials. Building on the notions of thermodynamics introduced in the preparatory years, it introduces the notion of irreversibility in a broader framework where the nature of 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 complemented by a thermodynamic description of the material or constituents of the medium to be analyzed.

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

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

 - Vibration and dynamic systems: Vibration basics for 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. resulting from finite element modeling). Study of eigenmodes.
Sizing for dynamic loads.

• write a thermomechanical behavior law
• determine whether a material's behavior is time-dependent or time-independent.
• 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

3A MMC concepts must be acquired, as well as the mathematical and numerical tools needed to solve differential and partial derivative problems.

This ECUE is evaluated by :

Final score = E