Disturbance due to Thermal and Mass Loads in Generalized Elasto-thermodiffusive Solids

Abstract

The one-dimensional problem of a generalized elasto-thermodiffusive solid half-space, whose surface is maintained traction free but subjected to the action of thermal or mass concentration loads, has been investigated. The model, composed of basic governing equations and boundary conditions, has been solved by using the Laplace transform technique. As we know that the ‘second sound’ effects are short lived, thus, short-time approximations of solutions for dilatation, chemical potential, and stress functions have been obtained. The short-time solutions for each considered function consist of three waves, namely, elasto-diffusive, mass-diffusive, and thermo-diffusive waves traveling with distinct speeds. The discontinuities at the wave fronts of various considered physical quantities have also been discussed. To obtain the dilatation, chemical potential, and stress in the physical domain due to instantaneous, continuous, and periodic loads, the transformed solutions of these functions have been inverted by employing a numerical technique. Finally, the dilatation, chemical potential, and stress functions have been computed numerically for copper and brass materials. The computer-simulated results so obtained have been presented graphically to illustrate the analytical developments.