These notes may serve as a reminder of tensor algebra. The notes supplement the course on advanced elasticity. Several books are listed at the end of the notes.
Update on 17 April. I am now breaking up the notes on tensors, cleaning them up, and posting them as sections on linear algebra.
In the notes on the general theory of finite deformation, we have left the free energy function unspecified. The notes here describe free energy function commonly used to describe the elasticity of rubber-like materials. These notes are part of a course on advanced elasticity
These notes are part of a course on advanced elasticity. The notes recall several phenomena where both elasticity and surface energy are significant, including
The notes also contain a formulation of combined surface energy and elasticity of finite deformation.
These notes are part of a graduate course on advanced elasticity.
In response to a stimulus, a soft material deforms, and the deformation provides a function. We call such a material a soft active material (SAM). This review focuses on one class of soft active materials: dielectric elastomers. Subject to a voltage, a membrane of a dielectric elastomer reduces thickness and expands area, possibly straining over 100%. The phenomenon is being developed as transducers for broad applications, including soft robots, adaptive optics, Braille displays, and electric generators.
The question was raised in class as to what the appropriate equilibrium condition for a column of fluid at rest should be. Specifically, given we expect a hydrostatic gradient in pressure with height, whether the chemical potential must be the same throughout the column was questioned. Here are my first thoughts. In brief, I assert that the chemical potential must be everywhere identical, and that the pv term is balanced, at every height in the column, by the potential energy conferred by position in a gravitational field.
These are slides of poroelasticity and diffusion in elastic solids for final presentation based on ES241 notes.
These slides are based on an on-going paper written by Wei Hong, Xuanhe Zhao and Zhigang Suo and Suo's talk in ucsb.
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.
