Analytical solutions are obtained for stress, velocity, and strain at the wave front in a suddenly loaded semi-infinite rod of a material with a linear instantaneous response and nonlinear inelastic response. The material properties are assumed to depend on position directly or through a dependence on a prescribed nonuniform temperature field. Detailed solutions are obtained for two examples—a nonlinear viscoelastic material with temperature dependent parameters and a rate-sensitive plastic material which may have temperature dependent parameters and yield point.
Wave-Front Stress Relaxation in a One-Dimensional Nonlinear Inelastic Material With Temperature and Position Dependent Properties
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Shaw, R. P., and Cozzarelli, F. A. (March 1, 1971). "Wave-Front Stress Relaxation in a One-Dimensional Nonlinear Inelastic Material With Temperature and Position Dependent Properties." ASME. J. Appl. Mech. March 1971; 38(1): 47–50. https://doi.org/10.1115/1.3408765
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