On the fundamental solutions for the strain and temperature rate-dependent generalized thermoelasticity theory

Abstract

The present paper concerns with the fundamental solutions for strain and temperature rate-dependent thermoelasticity theory recently developed by Yu et al. (2018). This recently developed model is theoretically established with the aid of principles of thermodynamics and by adding the strain-rate term in temperature rate-dependent thermoelasticity theory, which was proposed by Green and Lindsay (GL)(1972). This model has attempted to remove the drawback of discontinuity in the displacement field under Green-Lindsay (GL) model. We consider this modified Green-Lindsay (MGL) model for the case of homogeneous and isotropic bodies. Two cases, namely, concentrated body force and concentrated heat source have been taken for deriving the fundamental solutions for thermoelasticity in the context of MGL model. The fundamental solutions for the distributions of displacement components and temperature are obtained by the Laplace transform method. Fundamental solutions in the physical domain are obtained by Laplace inversion and the solution of displacement and temperature is obtained for short-time approximation. Lastly, we get the fundamental solution of the system of equations in the case of steady oscillations.