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Spring 2011

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Elastomer in equilibrium with forces and solvent

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.

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Theory of dielectric elastomers

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.

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Finite Deformation: Special Cases

The notes on finite deformation have been divided into two parts: special cases and general theory (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.

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Free Energy

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.

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Poroelasticity, or migration of matter in elastic solids

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.

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Pressure

So far we have been mainly concerned with systems of a single independent variable: energy (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.

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Engineering Sciences 241: Advanced Elasticity

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

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