Non-Equilibrium Continuum Physics

This course is intended to introduce graduate students to the essentials of modern continuum physics, with a focus on non-equilibrium phenomena in solids and within a thermodynamic perspective. Special focus is given to emergent phenomena, where collective many-body systems reveal physical principles that cannot be inferred from the microscopic physics of a small number of degrees of freedom. General concepts and principles – such as conservation laws, symmetries, material frame-indifference, dissipation inequalities and non-equilibrium behaviors, spatiotemporal symmetry-breaking instabilities and configurational forces – are emphasized. Examples 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 phenomenon of interest is highlighted. Some basic mathematical tools and techniques are introduced. The course is self-contained and highlights essential ideas and basic physical intuition. Together with courses on fluid mechanics and soft condensed matter, a broad background and understanding of continuum physics will be established.

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

General Principles and Concepts

  1. Introduction: Background and motivation
  2. Mathematical preliminaries: Tensor Analysis
  3. Motion, deformation and stress
    • Strain measures
    • The concept of stress
  4. Equations of motion, the laws of thermodynamics and objectivity
    • Conservation laws
    • The laws of thermodynamics
    • Heat equations
    • Objectivity (frame - indifference)

Reversible processes: non-dissipative constitutive behaviors

  1. The linearized field theory of elasticity
    • General derivation for anisotropic and isotropic materials
    • Two-dimensional Elasticity
      • Scalar elasticity
      • Conformal invariance
      • In-plane elasticity, Airy stress function
    • Elastic waves
  2. The linearized field theory of thermo-elasticity
  3. The non-linear field theory elasticity
    • Entropic elasticity (“Rubber elasticity")
    • Geometric nonlinearities and stress measures
    • Small amplitude waves in nonlinear elastic solids
  4. Spatiotemporal instabilities

Irreversible processes: dissipative constitutive behaviors

  1. Visco-elasticity
    • Viscous deformation
    • Bringing linear viscous and elastic deformation together
    • Oscillatory response
    • Viscoelastic waves
  2. The emergence of solidity: Amorphous solids and the glass transition puzzle
  3. The field theory of plasticity
    • Perfect plasticity
    • The theoretical and practical shear strength (yield stress) -- dislocations needed
    • The field theory of elaso-perfect plasticity: Examples
    • Beyond perfect plasticity
  4. Thermodynamics with internal variables
  5. Material failure
    • Some scaling arguments
    • Rigorous results in the framework of Linear Elastic Fracture Mechanics
    • Configurational forces and the J-integral
    • Fracture toughness and fracture energy
    • Dynamic fracture
    • Limitations of Linear Elastic Fracture Mechanics (LEFM) and beyond it

The first lecture will take place on 06/04/2021 at 11:15 (Perlman 404 + Zoom, a message has been sent to registrants).

Contact us

Lecturer: Prof. Eran Bouchbinder
Perlman Chemical Sciences Building Room 722a

TA: Avraham Moriel & Yuri Lubomirsky
Perlman Chemical Sciences Building Room 720,

Course Email

2021 Course Material

Eran's extended Lecture notes (Last update: June 17, 2021).

TA Material:

TA sessions HW sets
  1. Mathematical preliminaries - Index Gymnastics
    Last update: April 22, 2021
  2. Kinematics - strains and stresses
    Last update: April 22, 2021
  3. Coarse graining (and leftovers)
    Last update: April 28, 2021
  4. Linear Elasticity I
    Last update: May 5, 2021
  5. Linear Elasticity II
    Last update: May 25, 2021
  6. Thermo-elasticity
    Last update: May 25, 2021
  7. Linear Elasticity III
    Last update: May 25, 2021
  8. Finite elasticity
    Last update: May 31, 2021
  9. Visco-elasticity I
    Last update: June 9, 2021
  10. Visco-elasticity II
    Last update: June 9, 2021
  1. Homework set 1: Mathematical Preliminaries
    Last update: April 14, 2021
  2. Homework set 2: Kinematics
    Last update: April 28, 2021
  3. Homework set 3: Thermoelasticity
    Last update: May 13, 2021
  4. Homework set 4: Finite elasticity
    Last update: May 27, 2021
  5. Homework set 5: Viscoelasticity
    Last update: June 17, 2021


Supplemental Materials: