Thermodynamics and Wave Propagation in Non-linear Materials with Memory

Résumé du livre

One-dimensional waves in materials which do not conduct heat but have long-range nonlinear viscoelastic memory are discussed. The theory starts with the constitutive assumption that the stress, temperature, and specific internal energy at a material point depend on the temporal histories of the strain and specific entropy at the point. The functionals expressing this dependence are not assumed to have any special properties other than those implied by Coleman and Noll's form of the principle of fading memory and the laws of thermodynamics. Particular emphasis is laid on a theorem in the thermodynamics of materials with memory relating the stress and temperature functionals to the internal-energy functional. Much of the classical theory of Hugoniot curves can be generalized to materials with memory. The conclusion that for weak shocks the jump in the entropy must be of order three or higher in the jump in the strain and the theorems of Bethe and Weyl for shocks of finite strength still hold in the present theory. Duhem's theory of homentropic waves is generalized, explicit and exact expressions for the wave amplitude are calculated. (Author).