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.
Highlights
The way in which deformation is considered from a thermodynamic point of view depends largely on the kind of systems and processes in which one is interested
People engaged in applied continuum mechanics, as well as in engineering geology or geotechnical engineering and dealing with short time processes may prefer to consider deformation in the framework of classical thermodynamics considering a non-hydrostatic state of stress as a state quantity
The deformation may result partially from structural modifications, such as those involved in chemical and phase change, that contribute in making a portion of the undergone increment of internal energy unrecoverable as mechanical energy
Summary
The way in which deformation is considered from a thermodynamic point of view depends largely on the kind of systems and processes in which one is interested. A closed thermodynamic system consisting in a volume element of a deformable actual material, whose structure is statistically isotropic in the undeformed state, preserves its original shape together with its original isotropy only if its deformation consists in volume change not involving shape change. The measurable dilatation due to a generic (either irrotational or rotational) strain may be positive, negative or even null It is designated here by dVtotal , since, as it will be shown later, in any deformation involving shape change, the measurable dilatation consists, at any scale, of the algebraic sum of two components to which different thermodynamic meanings must be attributed. The increments, εa , εb and εc , of the unit length appearing in Equations (6) and (7) can be considered as the principal components of the Cauchy strain tensor, so that the measurable dilatation may be expressed as follows: dVtotal /V0 = I1 + I2 + I3. It must be pointed out that, the extended tensor here defined may be considered both as an infinitesimal and a finite strain tensor
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
