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Relating Deformation and Thermodynamics: An Opportunity for Rethinking Basic Concepts of Continuum Mechanics

Via Calamandrei 12, Nizza Monferrato 14049, Italy
Retired from the Department of Earth Sciences, Universit´a di Napoli Federico II, Naples, Italy. 
Entropy 2013, 15(7), 2548-2569; https://doi.org/10.3390/e15072548
Received: 29 March 2013 / Revised: 4 June 2013 / Accepted: 21 June 2013 / Published: 26 June 2013
In order to treat deformation as one of the processes taking place in an irreversible thermodynamic transformation, two main conditions must be satisfied: (1) strain and stress should be defined in such a way that the modification of the symmetry of these tensorial quantities reflects that of the structure of the actual material of which the deforming ideal continuum is the counterpart; and (2) the unique decomposition of the above tensors into the algebraic sum of an isotropic and an anisotropic part with different physical meanings should be recognized. The first condition allows the distinction of the energy balance in irrotational and rotational deformations; the second allows the description of a thermodynamic transformation involving deformation as a function of both process quantities, whose values depend on the specific transition, or path, between two equilibrium states, and of state quantities, which describe equilibrium states of a system quantitatively. One of the main conclusions that can be drawn is that, dealing with deformable materials, the quantities that must appear in thermodynamic equations cannot be tensorial quantities, such as the stress tensor and the infinitesimal or finite strain tensor usually considered in continuum mechanics (or, even worse, their components). The appropriate quantities should be invariants involved by the strain and stress tensors here defined. Another important conclusion is that, from a thermodynamic point of view, the consideration of the measurable volume change occurring in an isothermal deformation does not itself give any meaningful information. View Full-Text
Keywords: deformation; deviator; internal rotation; non-hydrostatic thermodynamics; non-equilibrium thermodynamics; entropy production; negentropy production; chemical potential; chemical and phase changes; process quantities deformation; deviator; internal rotation; non-hydrostatic thermodynamics; non-equilibrium thermodynamics; entropy production; negentropy production; chemical potential; chemical and phase changes; process quantities
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Guzzetta, G. Relating Deformation and Thermodynamics: An Opportunity for Rethinking Basic Concepts of Continuum Mechanics. Entropy 2013, 15, 2548-2569.

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