Potentials and Equations of State for Two Special Reference Configurations

On the basis of the mathematical formulation of the principle of reference invariance of the functions of state of deformed bodies, we consider two special representations of the potential of state in which the reference configuration is variable and related to the current state of the body. The first of these representations (natural) follows from the general representation of the potential of state if a current state of the basis is regarded as the reference state and the corresponding stress-free configuration is taken as the reference configuration. The second (strain-free) representation is obtained if the role of the reference configuration is played by the current configuration. For both representations, we deduce the equations of state in the form of expressions for stresses and the parameters of state connected with the basis parameters. As a constructive proof of the unconditional existence of the elastic potential, we deduce the expression for the elastic potential via the potential of state by using the natural potential of state. It is proved that the general system of equations of state consists of four independent systems of equations, namely, of the equations of elasticity, piezoeffects, stress-free distortion, and stress-free state.