Update on 23 May 2009:  I'm adding links to the slides as they are uploaded.

The final exam will take the form of a pedagogical workshop. We have 8 students taking the class for credit. I have divided the lecture notes into 8 parts as follows.

• Free energy and generalized coordinate. Equilibrium and stability
• Control parameter
• Configurational transitions of two types
• Critical point of configurational transition of the second type. Bifurcation analysis
  
  

• What types of PDEs can be solved using complex variable methods
• Anti-plane shear
• Elements of a function of a complex variable (contour integral, analytic continuation, conformal mapping)
• Line force
• Screw dislocation
• Crack
• Circular hole
• Elliptic hole
• Plemelj formulas
• Riemann-Hilbert problem
• Crack interacting with a point singularity
• In-plane deformation
• Dundurs parameters
• Interfacial cracks
• Anisotropic materials. Stroh formalism

Return to the outline of ES 421 Advanced Elasticity

To the students of ES 241:

Although finite deformation was introduced in ES 240 (Solid Mechanics), finite deformation is a building block of ES 241. To review the subject, please go over a set of problems compiled by Jim Rice. If you need a reference, see my outline of finite deformation, where you can also find a short list of textbooks.

A sponge is an elastic solid with connected pores. When immersed in water, the sponge absorbs water. When a saturated sponge is squeezed, water will come out. More generally, the subject is known as diffusion in elastic solids, or elasticity of fluid-infiltrated porous solids, or poroelasticity. The theory has been applied to diverse phenomena. Here are a few examples.

• A homogeneous field in a parallel-plate capacitor
• Particles and places
• A field of stress
• A field of electric displacement
• Helmholtz function
• Invariance under rigid-body rotation
• Materials laws expressed in true fields
• Nonpolar material
• Isotropic material
• Electrical Gibbs function
• Fluid dielectrics
• Solid dielectrics
• Coulomb attraction between the two electrodes in a parallel-plate capacitor.
• A lateral force in a parallel-plate capacitor
• Rupture of a charged sphere
• Piezoelectric actuators and sensors

• Electric charge
• Movements of charged particles
• Elastic dielectric
• Work done by a battery and by a weight
• Electromechanical coupling
• Conservative system
• Experimental determination of electric potential
• Lagendre transformation
• parallel-plate capacitor

Return to the outline of Statistical Mechanics

• A system that can exchange particles with the rest of the world
• Chemical potential
• Ideal gas
• Experimental determination of chemical potential
• Lagendre transformation
• Ideal gas once more
• Experimental determination of chemical potential
• A system in contact with a reservoir of energy, volume and particles
• A kinetic model

Return to the outline of Statistical Mechanics

So far we have been mainly concerned with systems of a single independent variable: energy (http://imechanica.org/node/4878). We now consider a system of two independent variables: energy and volume. A thermodynamic model of the system is prescribed by entropy as a function of energy and volume.

The partial derivatives of the function give the temperature and the pressure. This fact leads to an experimental procedure to determine the function for a given system.

The laws of ideal gases and osmosis are derived. The two phenomena illustrate entropic elasticity.

Spring 2011, Tuesday and Thursday 10:00 am - 11:30 am, Cruft Lab 309. First meeting of the class:  25 January 2011

• Instructor: Zhigang Suo, 617-495-3789, suo@seas.harvard.edu, Pierce Hall 309.
• Office hour: Tuesday 2:00 pm - 3:00 pm.
• No textbook is required.

This is a second graduate course in solid mechanics.  The course builds on elements of thermodynamics, and explores coupled mechanical, thermal, electrical and chemical actions.  The course draws heavily upon phenomena in soft active materials.

This page is updated for ES 241 taught in Spring 2011. See also

• A small system in thermal contact with a large system
• The Boltzmann factor
• Partition function
• The probability for a system in thermal equilibrium with a reservoir to be in a specific state
• The probability for a system in thermal equilibrium with a reservoir to be in a configuration
• Thermal fluctuation of an RNA molecule
• A matter of words
  

Return to the outline of Statistical Mechanics.

We have described two great principles of our world: the fundamental postulate and the conservation of energy. The former is the foundation of thermodynamics, as we have learned in a previous lecture. The latter is not specific to thermodynamics: we borrow the concept of energy—along with the principle of the conservation of energy—from other branches of science, such as mechanics and electrodynamics. Both principles are abstracted from many empirical observations.

Of our world the following facts are known:

• An isolated system has a set of quantum states.
• The isolated system ceaselessly flips from one quantum state to another.
• A system isolated for a long time is equally probable to be in any one of its quantum states.

Thus, an isolated system behaves like a fair die. The following notes remind you what an isolated system is, and translate the theory of probability of rolling a fair die to the thermodynamics of an isolated system.