THE DECAY OF PLANE WAVES IN THE LINEAR THEORY OF VISCOELASTICITY

This paper is the sequel to AD-604 661 in which we have derived a necessary propagation condition governing the wavespeeds with which shocks and all higher order singular surfaces must propagate in a material subject to linear viscoelastic behavior. Of obvious interest is the manner in which the wave front varies with time. This subject, in the case of nonlinear, one-dimensional acceleration waves, has been treated by Coleman and Gurtin. Their work on general materials with memory includes onedimensional linear viscoelastic wave propagation as a special case. They show that when the stressstrain law is non-linear, the strength of an acceleration wave may either grow or decay; but it always decays in the linear theory providing the initial slope of the relaxation function is negative. These same results were established simultaneously by Varley for a slightly less general constitutive assumption (a constitutive equation of integral type), but for more general motions (plane, cylindrical, and spherical waves). Chen has also treated this problem. (Author)