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# A course on Advanced Elasticity, with emphasis on thermodynamics and soft active materials

In the field of Solid Mechanics, Harvard has a sequence of 5 graduate courses:

- ES 240 Solid Mechanics
- ES 241 Advanced Elasticity
- ES 242r Solid Mechanics: Advanced Seminar
- ES 246 Plasticity
- ES 247 Fracture Mechanics

The first course goes over linear elasticity, finite element method, vibration, waves, viscoelasticity, as well as some ideas of finite deformation.

I have just finished teaching the second course, and updated most parts of the lecture notes. I start with the fundamental postulate of statistical mechanics, and aim to make entropy an intuitive idea for the students.

I then go over several conservative variables:

- energy
- space
- matter
- charge

Partition of these conservative variables into subsystems introduces the following variables (the thermodynamic forces):

- temperature
- force
- chemical potential
- electric potential

These variables are then used to formulate nonlinear field theories:

- Finite deformation
- Poroelasticity, or diffusion in elastic solids
- Deformation and polarization
- Polyelectrolye gels

In each of the theories, finite deformation is coupled with some other fields. The theories are naturally structured using thermodynamics.

The class ran an 8-hour workshop as a final exam. Each student gave a powerpoint presentation to summarize a part of the course. Perhaps a combination of their powerpoint slides and my lecture notes will give you a better idea of the content of the course.

- Zhigang Suo's blog
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## Comments

## hello

Dear professor Suo,

Thanks for sharing your notes. And I have two questions, First, why did you say that space is also a conservative variable? Second, you said you aim to make entropy an intuitive idea for the students in a course of advanced elasticity. But is the entropy important in elastic deformation

## Space and entropy

The word

spaceis used here in the same sense as when we say "a body occupies some space". For example, a body of gas occupies some space. The amount of space can be measured by volume. The work conjugate of the volume defines the pressure.When the gas is sealed in a cylinder under a piston, the space occupied by the gas can also be represented by the height of the piston. The work conjugate of the height defines the force.

Thus, quantities like volume, area, distance, rotational angle are ways to describe space occupied by a body.

Entropyis a quantity possessed by all bodies. One can teach much of the theory of elasticity without talking about entropy. One does so by restricting to isothermal processes. One also avoids talking about microscopic processes. For example, One avoids talking about how rubber deforms as a network of polymers, or how gels swell by a process of mixing polymers and solvent molecules.These things, however, form the subject of this course, and make entropy central to the theory of elasticity.

These ideas are all classical, and are discussed in my lecture notes.