The problem of stress-wave generation in a linear thermoelastic solid by internal heat addition is investigated on the basis of a one-dimensional model of material response. A method of integration of the governing equations is given for the case of power deposition with arbitrary time and space variation. Closed-form results are presented for the half-space and the finite slab for power deposition which is a step function in time and exponential with distance from one surface, assuming negligible heat conduction. The influence of thermal diffusion on the stress field is estimated in terms of a dimensionless parameter representing the ratio of characteristic times of stress-wave propagation and thermal diffusion.

Abstract. A method is developed for the solution of problems of uncoupled dynamic thermoelasticity with arbitrarily prescribed spherically symmetric temperature fields. The technique is based on an integration theorem for hyperbolic initial-value problems, together with the construction of image temperature fields in regions outside the actual body so as to satisfy stress or displacement boundary conditions at surfaces.The image technique is applied to problems of internal thermal shock in spherical shells of arbitrary thickness, both with stress-free and with fixed isothermal external boundaries. The published closed-form solution of the associated simpler problem of thermal shock on a cavity in an infinite solid, which had been obtained by other investigators using transform techniques, is recovered as a special case. The results for the cavity and unrestrained shell problems are compared with those obtained by other techniques. It is shown that the image method resolves accurately the details of the dynamic response at early times in shell problems. The problem of the rigidly embedded shell is of interest in connection with determining the far-field signature of a buried radiation burst.

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