On the form of the elastic potential relative to different reference states (Q1112648)

The present paper considers the change in the form of the free energy function and mechanical characteristics connected with it when the state to which these quantities are referred undergoes a change. The results are based on the relationship between strain tensors relative to two different reference states. An explicit form of the free energy function in terms of the measures of the changed reference state is obtained when a wide class of materials is considered. The relationships between the components of the Kirchhoff stress tensor in the changed reference state are found in the case of elastic material when these components are related to the measures of this state and to the measures of the primary reference state of the body. Analogous relationships are obtained for the components of the tensor of elastic moduli.