A thermodynamically consistent formulation of generalized thermoelasticity at finite deformations

Wakeni, Mebratu F.; Reddy, B. D.; McBride, Andrew

doi:10.1016/j.ijengsci.2016.08.008

Cited by 2 publications

(4 citation statements)

References 38 publications

(50 reference statements)

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“…In this section, we summarize the generalized model of thermal conduction which was derived based on the theory of Green and Naghdi in [34]. The nonlinear stability of the initial-boundary value problem is analyzed using the energy method.…”

Section: The Generalized Thermal Conductivity Problemmentioning

confidence: 99%

“…This has led to considerable attention towards a unified formulation of a widely valid thermal conduction theory with a broader validity than the classical Fourier's law, and consistent with the statistical physics as well as the laws of thermodynamics [3,[32][33][34] . In the 1990s Green and Naghdi [35][36][37][38][39] proposed a unified thermoelastic framework capable of reproducing the second sound phenomenon.…”

Section: Introductionmentioning

confidence: 99%

“…In this article, we present two methods that belong to the family of space-time Galerkin finite element method for the numerical solution of the nonlinear generalized thermal model due to the formulation in [34]. The first is an extension of the time-discontinuous Galerkin method proposed in [51] to the nonlinear generalized thermal model.…”

Section: Introductionmentioning

confidence: 99%

“…These equations are obtained when the hyperthermoelastic constitutive equations of neo-Hookean-type are extended to the generalized theory (see the article[34]) in the framework of the theory ofGreen and Naghdi[35][36][37][38][39], and specialized to the purely thermal case.…”

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confidence: 99%

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

Wakeni

Reddy

2019

Computer Methods in Applied Mechanics and Engineering

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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 phenomena 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.

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Section: The Generalized Thermal Conductivity Problemmentioning

confidence: 99%