# ES 241

## Poroelasticity and diffusion in elastic solids

These are slides of poroelasticity and diffusion in elastic solids for final presentation based on ES241 notes.

## advanced elasticity 2009 slides (polyelectrolyte gels)

These slides are based on an on-going paper written by Wei Hong, Xuanhe Zhao and Zhigang Suo and Suo's talk in ucsb.

## Final presentation

Attached is my final presentation.

## Final presentation slides

Here are the slides for my final presentation for ES 241.  During the presentation, a few suggestions were made, which I plan to follow up on.  Please check back here or subscribe for updates.

## Slides on Pressure and Chemical Potential

Here are some slides I made on the subject of "Pressure and Chemical Potential" for the final meeting of Prof. Zhigang Suo's ES 241 class in the Spring of 2009.

## ES 241 Presentation: Electric Potential / Deformation and Polarization

Please see the attached slides on electric potential, deformation and polarization.

## ES 241 Presentation: Heat Conduction and the Boltzmann Distribution

Please see attachment for ES 241 final presentation on heat conduction and the Boltzmann distribution.

## ES241Presentation: General theory of finite deformation

Please see attachment for ES241 final presentation--general theory of finite deformation

## ES 241 Advanced Elasticity Final Examination

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.

## Complex variable methods

• 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

## Homework on finite deformation

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.

## Deformation and polarization

• 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

## Electric potential

• 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