Advanced Elasticity

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.

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.