Introduction to the Thermodynamics of Solids (Applied Mathematical Sciences)

Jerald L. Ericksen

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There is a large and growing gap between what is covered in most elementary thermodynamics courses and what is used in current research on nonlinear phenomena encountered in solids. In an attempt to fill that gap, Professor Ericksen has drawn on his experience in research on solids, to devise a series of lectures for graduate students from various departments at the University of Minnesota. The aim is to introduce and illustrate uses of various important ideas with analysis which can be done, using elementary mathematics. Often, important applications involve using the thermodynamic theory of equilibrium. In part, this involves a strategy for designing experiments to determine equations of state. Simple strategies are discussed for thermoelastic bars and an ideal gas-solid mixture. A simple strategy can fail when instabilities are encountered. Illustrative examples of thermodynamic stability theory include rudimentary analysis of cold-drawing in polymers, martensitic transformations in plates, instabilities in rubber balloons and sheets, peeling tapes, breaking bars, buckling of beams and instabilities produced by electromagnetic fields in liquid crystals. Non-equilibrium theory is illustrated by head conduction in rigid and deformable bars, including a fairly common way of using the Clausius- Duhem inequality to get thermodynamic restrictions on constitutive equations. Also covered is some elementary one-dimensional theory of shock waves and slower-moving phase boundaries. Drawing on all these experiences, the final chapter treats general ideas in a more abstract way. Included here are discussions of some of the real difficulties.
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