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Time-reversal and symmetry in the thermodynamics of materials with memory
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Gurtin et al. as discussed by the authors studied the notion of invariance under time-reversal and established conditions that are both necessary and sufficient for the infinitesmal entropy production to display such invariance.Abstract:
TIME-REVERSAL AND SYMMETRY IN THE THERMODYNAMICS OF MATERIALS WITH MEMORY by Morton E. Gurtin We here study, within the framework of the thermodynamics of materials with memory, the notion of invariance under timereversal. In particular, we establish conditions that are both necessary and sufficient for the infinitesmal entropy production to display such invariance.read more
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The foundations of thermodynamics, its basic postulates and implications. A review of modern thermodynamics
TL;DR: In this article, the authors present a review of modern theories of irreversible thermodynamics, motivated from the balance law of entropy, showing how the Clausius-Duhem theory, the entropy free thermodynamics of Meixner and the theory of Muller naturally follow from such a balance law.
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Exponential decay in one-dimensional type III thermoelasticity with voids
TL;DR: It is proved that generically the authors have exponential stability of the solutions of the thermoelastic theory with voids and that the decay is generically slower than the classical Fourier law.
Journal ArticleDOI
On a theory of interacting continua with memory
Dorin Ieşan,Ramón Quintanilla +1 more
TL;DR: In this paper, a linear theory for thermoviscoelastic composites modeled as interpenetrating solid continua with memory is developed, and the response functionals are considered to depend on the past history of displacement fields, displacement gradients, temperature field, and temperature gradient.
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Exponential stability in type III thermoelasticity with microtemperatures
Antonio Magaña,Ramón Quintanilla +1 more
TL;DR: In this paper, the authors consider the type III thermoelastic theory with microtemperatures and study the time decay of the solutions and prove that under suitable conditions for the constitutive tensors, the solutions decay exponentially.
References
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The non-linear field theories of mechanics
TL;DR: A theory aiming to describe their mechanical behavior must take heed of their deformability and represent the definite principles it obeys as mentioned in this paper, which is not the case in modern physics, since it concerns solely the small particles of matter.
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A general theory of heat conduction with finite wave speeds
TL;DR: In this article, the authors developed a general theory of heat conduction for nonlinear materials with memory, a theory which has associated with it finite propagation speeds, i.e., a thermal disturbance at any point in the body is felt instantly at every other point; or in terms more suggestive than precise, the speed of propagation of disturbances is infinite.
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An Approximation Theorem for Functionals, with Applications in Continuum Mechanics
Bernard D. Coleman,Walter Noll +1 more
TL;DR: In this paper, a brief discussion of the physical motivation behind the mathematical considerations to be presented in Part I of this paper is presented. But this discussion is limited to the case where the authors are concerned with a single point of view.