Coupled mechanical behaviors I

- Generalized Standard Materials: This ECUE presents a unified framework for describing the thermomechanical behavior of materials. Building on the concepts of thermodynamics covered in preparatory years, it introduces the concept of irreversibility in a broader framework where the nature of state variables can become tensorial. A link with MMC is essential so that students understand how a purely mechanical description of continuous media and systems can be supplemented 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 in particular the deformation energy, the dissipated energy, and the heat sources induced by thermomechanical couplings.

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

 - Vibrations and dynamic systems: Basic concepts of vibrations for single-degree-of-freedom modeling, with and without damping. Free vibrations. Forced vibrations. Study of the phenomenon of resonance.
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 natural modes.
Dimensioning with respect to dynamic stresses.

• write a thermomechanical behavior law
• determine whether the behavior of a material 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

: Students must have acquired the concepts of 3A MMC as well as the mathematical and numerical tools related to solving differential problems or partial derivatives.

This ECUE is evaluated by:

Final grade = E