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

Abstract

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.

FEM modeling and experimental validation of quench-induced distortions of large size steel forgings

“…The shape changes during steel hardening are directly linked to the history of generated strains [12]. The volume change could be correlated to the spherical strain tensor, while the distortion could be correlated to the deviatoric part [33]. The total strain induced in the material as a result of quenching could be represented by the sum of five strain components:…”

Modifications of volume, shape and structure during metamorphism: Unearthing some ignored strain paths

“…An attempt -that for the most part could be completed and more clearly exposed -was 257 already made by one of the authors of the present article, to show to a wider audience some 258 consequences of the recognition of two components of the volume change involved by deformation 259 that have different physical meanings (Guzzetta, 2013). This article can be considered also as a 260 necessary prelimimary step for a further exposition that will deal with the relevance of the latter 261 recognition in order to understand the relationship between rock deformation and metamorphism.…”

Thermodynamic Relations among Isotropic Material Properties in Conditions of Plane Shear Stress

“…Since Gibbs’ fundamental contribution in 1876 [ 1 ], the thermodynamic theory of solids under different stress conditions has remained an active field of inquiry, with a recent intensification spurred by interest in amorphous states and glass transition, high pressure physics, and the development of artificial materials [ 2 , 3 , 4 , 5 , 6 , 7 ]. In contrast, continuum mechanics and thermoelasticity have focused more on finite deformations and field theories, traditionally shifting away from homogeneous thermodynamics [ 8 , 9 ] and the related Gibbs equation [ 10 ], in spite of the fact that these concepts are often clearer, at least for infinitesimal transformations and in uniform conditions [ 9 ].…”