Adiabatic Processes and Constraints in Thermoelasticity

Abstract

The aim of this paper is to briefly outline an approach to the thermomechanics of thermoelastic solids based on the notion of multiple natural states and the use of adiabatic processes. We use a statement of the second law attributed to Kelvin for certain special cycles and show that the work done in adiabatic cycles of deformation is non-positive. With these and other assumptions on the nature of thermoelastic solids, we demonstrate the existence of an entropy function and the absolute temperature scale. In this, we closely follow the arguments of Caratheodory (1976). Finally, we briefly address the issues of a class of thermomechanical constraints and show that they naturally lead to considering constraints on adiabatic processes. The principal results are the following: 1. Demonstration of the existence of the absolute temperature and entropy functions based on the consideration of adiabatic processes 2. A one-to-one correspondence between the stress-free states and the entropy, leading to a “decomposition” of the deformation gradient as Fκr = FκnG(η). 3. Physical interpretation of the constraints of the form f(Eκr,η) = 0.