Thermodynamically Consistent Modified Lord–Shulman Generalized Thermoelasticity With Strain-Rate

Abstract

The analysis of thermoelastic wave propagation in continuum solids at micro/nano-seconds is especially significant for ultra-fast heating technologies, where strain relaxation effects will increase significantly. In most cases, it is commonly accompanied by a relatively small strain-rate; however, this is questionable in the environment of transient thermal wave propagation under the ultra-fast heating case. The present work is dedicated to constitutive modeling of a novel generalized thermoelasticity model by introducing an additional strain-rate term associated with a relaxation time parameter in the Lord–Shulman (LS) thermoelasticity with the aid of an extended thermodynamics framework. As an application, the newly developed model is applied to a one-dimensional half-space problem which is traction free at one end; a time-dependent thermal shock is imposed at the same end to analyze transient responses of thermodynamic field variables (temperature, displacement, strain, and stress). The inclusion of strain-rate in the LS model eliminates the probable propagating jump discontinuities of the strain and stress fields at the wavefront. The current work is expected to be useful in the mathematical modeling and numerical simulation of thermoelastic processes under an ultra-fast heating environment.