Coupled Mechanical Behaviors I

- Generalized Standard Materials: This ECUE presents a unified framework for describing the thermomechanical behavior of materials. Building on the thermodynamic concepts covered in the preparatory years, the goal is to introduce the concept of irreversibility within a broader framework where the nature of the state variables can become tensor-based. A connection to the 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 the constituents of the medium being analyzed.

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

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

 - Vibrations and Dynamic Systems: Basic concepts in vibrations for modeling a single degree of freedom, with and without damping. Free vibrations. Forced vibrations. Study of the phenomenon of resonance.
Modeling of systems with two degrees of freedom. Resonance and antiresonance.
Study of systems with a large number of degrees of freedom (e.g., resulting from finite element modeling). Study of eigenmodes.
Design for dynamic loads.

• formulate a law of thermomechanical behavior
• Determine whether a material's behavior is time-dependent or time-independent.
• Dissipative Effects and Coupling Effects
• determine the properties of an elastic composite
• Static and Dynamic Behavior of Materials and Structures
• to study the dynamic behavior of an elastic structure

: Students must have mastered the concepts covered in the 3A calculus course, as well as the mathematical and numerical tools related to solving differential equations and partial differential equations.

This ECUE is evaluated by:

Final Grade = E