Non-Equilibrium Continuum Physics

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

    Amorphous solids

    • Visco-elasticity
    • Plasticity
    • Non-equilibrium internal variables thermodynamics
  7. The emergence of solidity and the glass transition puzzle

     Dissipative Phenomena in Solid Mechanics

  8. Fracture mechanics
  9. Point defects and dislocations


2016 Course Material

The course takes place at Weissman Auditorium.
Lectures are on Tuesdays 11:15-13:00 and TA sessions on Wednesdays 14:15-16:00.

Eran's Lecture notes(PDF) (June 19, 2016)

Yohai's TA Material:

Course Material
TA sessions HW sets
  1. Mathematical preliminaries - index gynmastics
    Last update: May 25, 2016
  2. Kinematics
    Last update: March 23, 2016
  3. The equations of motion in the material coordinates,
    a bit about stress and strain and Onsager relations
    Last update: July 03, 2016
  4. Coarse graining (and some leftovers from last session)
    Last update: April 05, 2016
  5. Linear elasticity I
    Last update: June 27, 2016
  6. Linear elasticity II - waves and a simple composite material
    Last update: May 31, 2016
  7. Linear elasticity III - Conformal mapping, elastic cavitation
    Last update:  May 04, 2016
  8. Finite elasticity
    Last update: May 16, 2016
  9. Visco-elasticity
    Last update:  July 06, 2016

    Watch how cornstarch goo breaks as it smashes on the floor (thanks Yoni)

  10. Dislocations
    Last update:  June 08, 2016
  11. Plasticity
    Last update:  June 08, 2016
  12. Fracture
    Last update:  June 28, 2016
  13. Dynamic fracture
    Last update:  July 06, 2016
  1. Mathematical preliminaries - index gynmastics
    Last update: March 22, 2016


  2. Last update:  April 02, 2016
  3. Thermo-elasticity
    Last update: May 17, 2016
  4. Finite elasticity
    Last update: May 22, 2016
  5. Visco-elasticity
    Last update: June 01, 2016
  6. Plasticity
    Last update: July 06, 2016