Coupled Thermoelasticity of Bars

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Abstract
Several boundary-value problems for semi-infinite bars made of a coupled thermoelastic material are solved by means of new functions. These arise in the solutions as “corrections” to classical tabulated functions such as the error function. However, they are not always small compared to their uncoupled equivalents. It turns out that the numerical differences in the solutions of a specific problem are usually small. But interesting phenomena are still found. The stresses produced in the coupled material are larger than those in the uncoupled one. The temperature generated on the face during impact of identical specimens is less than one might expect on simple intuitive grounds. Its time history is also quite interesting. Stress, strain, and thermal precursors exist but they do not propagate at a unique speed, while discontinuities propagate at the isothermal bar velocity. It is found that there is not much difference between the surface temperatures generated in a constant-velocity problem and one in which a constant acceleration is imposed. The temperature gradients are, however, different in these two problems.

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