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 ultrafast 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 ultrafast heating case. The present work is dedicated to constitutive modelling 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 half-space one-dimensional 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 possible propagating jump discontinuities of the strain and stress fields at the wavefront. The current work is expected to be useful in the mathematical modelling and numerical simulation of thermoelastic processes under an ultrafast heating environment.

Study of Thermoelectric Responses of a Conductive Semi-Solid Surface to Variable Thermal Shock in the Context of the Moore–Gibson–Thompson Thermoelasticity

“…To remedy the shortcomings found in the Biot theory [18], Lord and Shulman [19] and Green and Lindsay [20] improved it by including the idea of the relaxation time coefficient in the heat transfer vector based on the idea of Cattaneo-Vernotte [21][22][23]. Using an expanded thermodynamics system, Sarkar and Singh [24] provided the constitutive modeling of a new generalized thermoelasticity framework by incorporating a strain-rate term coupled with a relaxation time coefficient into the Lord-Shulman (LS) thermoelasticity theory. Sherief et al [25] considered a two-dimensional axisymmetric problem involving an infinite body.…”