A long polymer consists of many monomers. The monomers are covalently bonded, and two bonded monomers may rotate relative to each other. Consequently, the polymer may be modeled as a chain of many links, each link representing a monomer. At a finite temperature, the polymer rapidly changes from one configuration to another.

A large number of long, flexible polymers can be crosslinked by covalent bonds to form a three-dimensional network. Subject to forces, the network undergoes large elastic deformation. The network is commonly called an elastomer.

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.

Attached is my final presentation.

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.

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.

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.

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

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

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

The notes on finite deformation have been divided into two parts: special cases and general theory (http://imechanica.org/node/538). In class I start with special cases, and then sketch the general theory. But the two parts can be read in any order.

So far we have used the fundamental postulate to study experimental phenomena by following an algorithm. For a given phenomenon, we construct an isolated system with an internal variable. The isolated system has a whole set of quantum states. Associated with each value of the internal variable, the isolated system flips among a subset of the quantum states. The fundamental postulate implies that the internal variable evolves in time, from one value corresponding to a subset of the quantum states to another value corresponding to a subset of a larger number of quantum states. After a long time, the internal variable attains an equilibrium value, corresponding to a subset of the largest number of quantum states.

For a system in thermal contact with the rest of the world, we have described three quantities: entropy, energy, and temperature. We have also described the idea of a constraint internal to the system, and associated this constraint to an internal variable.

The system can be isolated at a particular value of energy. For such an isolated system, of all values of the internal variable, the most probable value maximizes entropy. We will paraphrase this statement under two different conditions, either when the entropy is fixed, or when the temperature is fixed. Under these conditions, the system is no longer isolated. Consequently, we need to maximize or minimize quantities other than entropy.

Hi,

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.

The linked two of my studies can be used as references for Zhigang’s lecture on Instabilities.

(1) Catastrophic fracture

• 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

This blog focuses on the micromechanics modeling of composite materials.

This blog focuses on viscoelasticity (http://en.wikipedia.org/wiki/Viscoelasticity)

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.

How to measure the temperature of a nanotube?

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.