Introduction to the Thermodynamics of Solids

Arguing that there is a gap between what is covered in most elementary thermodynamics courses and what is used in current research on nonlinear phenomena encountered in solids, 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 thermo-elastic 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, braking bars, buckling of beams and instabilities produced by electromagnetic fields in liquid crystals.
Non-equilibrium theory is illustrated by heat 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 shockwaves and slower-moving phase boundaries. Drawing on all these experience, the final chapter treats general ideas in a more abstract way. Included here are discussions of some of the real difficulties encountered in trying to apply thermodynamics to some phenomena, for example plasticity and visco-elasticity, and of differences of opinions of experts, as to what should be considered to be the basic laws.