Principle of Local State and Thermodynamic Potentials

The theory in this chapter is based on the Principle of Local State given in chapter 4. Kestin has noted that this principle implies that “the local and instantaneous gradients of the thermodynamic properties as well as their local and instantaneous rates of change do not enter into the description of the state and do not modify the equations of state.” It follows that the thermodynamic potentials are assumed to be of the same form as for an equilibrium state.

The important potentials in finite deformation thermoelasticity are the Helmholtz free energy and the internal energy, since, as for linear thermoelasticity, the Helmholtz free energy at constant temperature is the isothermal strain energy and the internal energy at constant entropy is the isentropic strain energy. This indicates the relation between hyperelasticity and thermoelasticity.

Application of thermoelasticity to finite deformation of idealized rubber-like materials involves the concept of entropic response and energetic response and this is discussed in this chapter.

Basic Relations for Finite Deformation Thermoelasticity

The theory in this section is presented in terms of the absolute temperature Θ, the specific entropy s, and the referential variables, S, the second Piola-Kirchhoff stress, and C, the right Green tensor, or E, Green's strain tensor.

There are four thermodynamic potentials that are fundamental equations of state, that is, all the thermodynamic properties can be obtained from a potential by differentiation if the potential is expressed as a function of the appropriate thermodynamic properties.