Interactions due to body forces in generalized thermo-elasticity III
The generalized thermo-elasticity theory III is employed to study thermo-elastic interactions in a homogeneous isotropic unbounded solid due to distributed continuous and instantaneous body forces. The solutions are derived by using a Laplace transform on time and then a Fourier transform on space. It is found that the interactions consist of a wave part traveling with the speed of the dilatational wave and a diffusive part. For continuous body forces, both temperature and deformation are continuous at the elastic dilatational wave front, while the stress suffers finite discontinuity at this location. For instantaneous body forces, both deformation and temperature suffer finite discontinuities at the elastic wave front, while stress exhibits delta function discontinuity resulting from the Dirac delta function at this location. All the fields suffer exponential attenuation at the elastic wave front and the attenuation is influenced by thermo-elastic coupling and thermal diffusivity of the medium. The results achieved in the present analysis are compared to those obtained by using generalized thermo-elasticity theory II without energy dissipation and other generalized theories. Lastly, numerical results applicable to a copper-like material are presented in order to illustrate the analytical result.
interactions body forces generalized thermo-elasticity iii infinite solid