Internal Energy of Elastic Dielectrics

When in a dielectric body the material is polarized by the application of an electric field work is done by electric forces. As in the analogous case of a deformed elastic body where the work per unit volume may be interpreted as an elastic energy density called deformation energy, the work of the electric forces may be understood as increasing the electrostatic field energy density. For an infinitesimal increment this takes the form 

Extending Eq. (3.84) by this electrostatic energy the infinitesirrral change in internal energy density becomes 

This relation is the basis of the thermodynamics of an elastic dielectric. Components Z), and Ei are rrrriquely defined for a certain thermodynamic eqiri-librium state and, therefore, take the place of additional variables of state in the thermo namic sense. In what follows we will use the simple term variable to designate a thermodynamic state variable unless the distinction becomes necessary. 

In addition to the short range strrface forces acting on contact it is necessary also to consider electrostatic long range forces in dielectrics. This is to say that in order 

Finally, there are certain implications imposed by crystal symmetry. According to Neumaim s principle the number of independent tensor coordinates characterizing a certain physical property of a crystal is limited by the symmetry of the crystal in its reference state. However, subjected to an external action the crystal, in general, has lower symmetry. In this case the set of symmetry elements is the intersection of the symmetry elements of the reference state crystal and those of the external action before being applied to the crystal. 

---