A strong discontinuity wave in thermoelasticity with relaxation times

TLDR: In this article, it was shown that in linear homogeneous isotropic thermoelasticity with two relaxation times the disturbances produced by an instantaneous concentrated source of heat in an infinite region represent a wave of order n = −1 with respect to the displacement u and temperature θ, i.e., 1 * u and 1 * ǫ, where * denotes convolution with regard to time, suffer jump discontinuities across a propagating spherical surface.

Abstract: It is shown that in linear homogeneous isotropic thermoelasticity with two relaxation times the disturbances produced by an instantaneous concentrated source of heat in an infinite region represent a wave of order n = −1 with respect to the displacement u and temperature θ, i.e., 1 * u and 1 * θ, where * denotes convolution with respect to time, suffer jump discontinuities across a propagating spherical surface. Proof of the assertion is based on analysis of an exact series solution to a central initial boundary value problem of the theory. Also, closed forms of the decaying with lime displacement and temperature “amplitudes” of order 1.0 and +1 and hence closed forms of the radial and hoop-stress jumps are obtained. A way to weaken the strong discontinuity thermoelastic wave by improving the smoothness in time of the concentrated source of heat is discussed.