Hyperbolic Thermoelasticity: A Review of Recent Literature

Abstract

This review article is a continuation of a previous article by the author, Thermoelasticity with second sound: A review, which appeared in this journal in March, 1986 (Appl Mech Rev39(3) 355-376). Here, attention is focused on papers published during the past 10-12 years. Contributions to the theory of thermoelasticity with thermal relaxation and the temperature-rate dependent thermoelasticity theory are reviewed. The recently developed theory of thermoelasticity without energy dissipation is described, and its characteristic features highlighted. A glance is made at the new thermoelasticity theory which includes the so-called dual-phase-lag effects. There are 338 references.

Strain gradient theory of chiral Cosserat thermoelasticity without energy dissipation

“…Moreover, the heat flux vector is determined by the same potential function that determines the stress. The Green-Naghdi theory has been studied in various papers (see, e.g., Chandrasekharaiah 1998;Hetnarski and Ignazack 1999;Quintanilla andStraughan 2000, 2004;Quintanilla 2003;Puri and Jordan 2004;Ieşan and Quintanilla 2009;Bargmann 2012 and references therein). The gradient theories of thermomechanics have been studied in various papers (see, e.g., Ahmadi and Firoozbakhsh, 1975;Ieşan, 1983Ieşan, , 2004Ieşan and Quintanilla, 1992;Ciarletta and Ieşan, 1993;Martinez and Quintanilla, 1998;Forest et al, 2000Forest et al, , 2002Forest and Amestoy, 2008;Forest and Aifantis, 2010).…”

Phase-lag heat conduction: decay rates for limit problems and well-posedness

“…From a physical point of view this is a drawback of the model because it predicts that heat waves propagate with infinite speed. To save the principle of causality, several heat conduction theories were suggested in the second part of the last century (see [2,6,7]). In the books [10,20,22], several studies concerning the applicability of nonclassical thermoelastic theories are considered.…”

Numerical modelling of thermoelastic processes using nonlinear theories with thermal relaxation time

“…Such an assumption is physically unrealistic and, in a number of practically important situations, is inadequate as a description of heat conduction [2,3,16]. A finite speed of thermal disturbances can be taken into account by using models with thermal relaxation time, which are based on hyperbolic-type equations for temperature.…”

“…The literature dedicated to the hyperbolic thermoelastic models is quite large and its detailed review can be found in [2,3]. However, the majority of the works in this field has been devoted to various aspects of linear models with some noticeable exceptions such as [10,8], where simplified (elastically linear) nonlinear models have been considered, and [18,19,12], where wellposedness issues have been studied.…”