A thermodynamically consistent formulation of generalized thermoelasticity at finite deformations

A thermodynamically consistent model of non-classical coupled non-linear thermoelasticity capable of accounting for thermal wave propagation is proposed. The heat flux is assumed to consist of both additive energetic and dissipative components. Constitutive relations for the stress, the entropy and the energetic component of the heat flux are derived in a thermodynamically consistent manner. A Lyapunov function for the dynamics is obtained for the case in which the surface of the continuum body is maintained at a reference temperature. It is shown that the system is non-linearly stable. The linearized model is shown to be similar to the type III model of Green and Naghdi, except for some minor differences in the interpretations of some of the parameters

Space–time Galerkin methods for simulation of laser heating using the generalized nonlinear model

The generalized thermal model is a thermodynamically consistent extension of the classical Fourier’s law for describing thermal energy transportation which is very relevant to applications involving very small length, time scales and/or at extremely low temperatures. Under such conditions, thermal propagation has been observed to manifest as waves, a phenomenon widely referred to as second sound effect. However, this is in contrast to the paradoxical prediction of the Fourier’s model that thermal disturbances propagate with infinite speed. In this work, we review the nonlinear model based on the theory of Green and Naghdi for thermal conduction in rigid bodies and present its implementation within a class of space–time methods. The unconditional stability of the time-discontinuous Galerkin method without restriction over the grid structure of the space–time domain is proved. We also perform a number of numerical experiments to study the convergence properties and analyze the thermal response of materials under short-pulsed laser heating in two space dimensions