An investigation on strain and temperature rate-dependent thermoelasticity and its infinite speed behavior

Abstract

The present work is aimed at a mathematical analysis of the newly proposed strain and temperature rate-dependent thermoelasticity theory, also called a modified Green–Lindsay model (MGL) theory, given by Yu et al. (2018). This model is also an attempt to remove the discontinuity in the displacement field observed under temperature rate-dependent thermoelasticity theory proposed by Green and Lindsay. We study thermoelastic interactions in an infinite homogeneous, isotropic elastic medium with a cylindrical cavity based on this model when the surface of the cavity is subjected to thermal shock. The solutions for the distribution of displacement, temperature, and stress components are obtained by using the Laplace transform technique. The inversion of the Laplace transform is carried out by short-time approximation. A detailed comparison of the analytical results predicted by the MGL model with the corresponding predictions by the Lord–Shulman model and the Green–Lindsay model is performed. It is observed that strain rate terms in the constitutive equation avoid the prediction of discontinuity in the displacement field and other significant effects are noted. However, the new theory predicts the infinite speed of disturbance like the classical theory. Variations of field variables at different time are graphically displayed for different models and compared by using a numerical method.