
Accession Number : AD0637609
Title : THERMODYNAMICS AND WAVE PROPAGATION IN NONLINEAR MATERIALS WITH MEMORY.
Descriptive Note : Technical rept.
Corporate Author : BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS
Personal Author(s) : Coleman,Bernard D. ; Gurtin,Morton E.
Report Date : APR 1966
Pagination or Media Count : 49
Abstract : Onedimensional waves in materials which do not conduct heat but have longrange 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 internalenergy 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)
Descriptors : (*MATERIALS, VISCOELASTICITY), THERMODYNAMICS, PROPAGATION, SHOCK WAVES, CONTINUUM MECHANICS, SOLIDS, THEOREMS, FUNCTIONAL ANALYSIS, THEORY, PARTIAL DIFFERENTIAL EQUATIONS
Subject Categories : Mechanics
Thermodynamics
Radiofrequency Wave Propagation
Distribution Statement : APPROVED FOR PUBLIC RELEASE