Courses

Non-Equilibrium Solid Mechanics

Solids make a large part of the material world around us, both natural and man-made. The physical processes of deformation, flow and failure of solids pose intriguing fundamental questions. This course is intended to introduce graduate students to the essentials of modern continuum physics, with a focus on solid mechanics and within a thermodynamic perspective. Emphasis will be given to general concepts and principles, and examples will cover a wide range of physical phenomena and applications in diverse disciplines. The power of field theory as a mathematical structure that does not make direct reference to microscopic length scales well below those of the phenomena of interest will be highlighted.

No prior acquaintance with the subject is assumed. Basic knowledge of statistical thermodynamics, vector calculus, differential equations and complex analysis is required.

    General Principles and Concepts

  1. Introduction: background and motivation
  2. Mathematical preliminaries: tensor analysis
  3. Motion, deformation and stress
  4. Conservation laws, the laws of thermodynamics and objectivity

    Constitutive laws: the physics that comes after thermodynamics

  5. Reversible Processes: Non-dissipative Constitutive Behaviors
    • Linear elasticity and thermo-elasticity
    • Finite (nonlinear) elasticity
    • Instabilities
  6. Irreversible processes: Dissipative constitutive behaviors
    • Visco-elasticity
    • Plasticity
    • Non-equilibrium internal variables thermodynamics

    Amorphous solids

  7. The emergence of solidity and the glass transition puzzle

    Dissipative Phenomena in Solid Mechanics

  8. Fracture mechanics
  9. Point defects and dislocations

Lecture notes

TA Material

A list of useful formulae

# TA Problem Sets Notes
1 Mathematical preliminaries Problem set Tutorial notes
2 Kinematics, symmetries, rotational invariance Problem set Tutorial notes
3 Stress, strain, Hooke's law and a (not so) simple problem - Tutorial notes
4 Conformal mapping and elastic waves Problem set Tutorial notes
5 Finite (non linear) elasticity Problem set Tutorial notes
6 Rayleigh waves & Euler-Bernoulli beam theory - Tutorial notes
7 Visco-elasticity, Kramers-Kronig Problem set Tutorial notes
8 Onsager Relations & ATG instability - Tutorial notes
9 Plasticity Problem set Tutorial notes
10 Plasticity II - Dislocations - Tutorial notes
11 Dynamic Fracture Problem set Tutorial notes