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
- Introduction: background and motivation
- Mathematical preliminaries: tensor analysis
- Motion, deformation and stress
- Conservation laws, the laws of thermodynamics and objectivity
Constitutive laws: the physics that comes after thermodynamics
- Reversible Processes: Non-dissipative Constitutive Behaviors
- Linear elasticity and thermo-elasticity
- Finite (nonlinear) elasticity
- Instabilities
- Irreversible processes: Dissipative constitutive behaviors
- Visco-elasticity
- Plasticity
- Non-equilibrium internal variables thermodynamics
Amorphous solids
- The emergence of solidity and the glass transition puzzle
Dissipative Phenomena in Solid Mechanics
- Fracture mechanics
- Point defects and dislocations