NonEquilibrium Continuum Physics
This course is intended to introduce graduate students to the essentials of modern continuum physics, with a focus on nonequilibrium phenomena in solids and within a thermodynamic perspective. Special focus is given to emergent phenomena, where collective manybody 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 frameindifference, dissipation inequalities and nonequilibrium behaviors, spatiotemporal symmetrybreaking 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 selfcontained 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
 Introduction: Background and motivation
 Mathematical preliminaries: Tensor Analysis

Motion, deformation and stress
 Strain measures
 The concept of stress

Equations of motion, the laws of thermodynamics and objectivity
 Conservation laws
 The laws of thermodynamics
 Heat equations
 Objectivity (frame  indifference)
Reversible processes: nondissipative constitutive behaviors

The linearized field theory of elasticity
 General derivation for anisotropic and isotropic materials

Twodimensional Elasticity
 Scalar elasticity
 Conformal invariance
 Inplane elasticity, Airy stress function
 Elastic waves
 The linearized field theory of thermoelasticity

The nonlinear field theory elasticity
 Entropic elasticity (“Rubber elasticity")
 Geometric nonlinearities and stress measures
 Small amplitude waves in nonlinear elastic solids
 Spatiotemporal instabilities
Irreversible processes: dissipative constitutive behaviors

Viscoelasticity
 Viscous deformation
 Bringing linear viscous and elastic deformation together
 Oscillatory response
 Viscoelastic waves
 The emergence of solidity: Amorphous solids and the glass transition puzzle

The field theory of plasticity
 Perfect plasticity
 The theoretical and practical shear strength (yield stress)  dislocations needed
 The field theory of elasoperfect plasticity: Examples
 Beyond perfect plasticity
 Thermodynamics with internal variables

Material failure
 Some scaling arguments
 Rigorous results in the framework of Linear Elastic Fracture Mechanics
 Configurational forces and the Jintegral
 Fracture toughness and fracture energy
 Dynamic fracture
 Limitations of Linear Elastic Fracture Mechanics (LEFM) and beyond it
The first lecture will take place on 19/04/2023 at 11:15 (Weissman, Seminar Rm A).
Contact us
Lecturer: Prof. Eran Bouchbinder
Perlman Chemical Sciences Building Room 701
eran.bouchbinder@weizmann.ac.il
TA: Avraham Moriel & Roy Wexler
Perlman Chemical Sciences Building Room 704
avraham.moriel@weizmann.ac.il, roy.wexler@weizmann.ac.il
Course Email
groupbouchbinder@gmail.com
2023 Course Material
Eran's extended Lecture notes (Last update: July 10, 2023).
TA Material:
TA sessions  HW sets 



Supplemental Materials:
 Onsager's reciprocal relations
 Lagrangian versus Eulerian frames  youtube
 Discussion on Principle of Objectivity
 Negative Poisson's ratio  youtube
 Rayleigh wave simuation  britannica
 Elastic cavitation  see here, here, and here
 Transition/Reaction rate theory  see here and here
 Surface tension  see this brief summary
 Goldstone’s theorem and Goldstone bosons  see Sect. 4.2.1 here
 A cartoon of the motion of edge disolcation  here
 FrankRead source animation  here
 FrankRead source experimentally observed using TEM  here
 The history behind the discovery of the FrankRead source  here
 A very recent realization of the FrankRead mechanism in nematic liquid crystals  here
 3D Dislocation Dynamics (DD) gallery  here

Here are some necks in bulk metallic glasses (from this paper)