Internal Energy in An Elastic Medium
For an elastic medium the mechanical energy term of the internal energy must be replaced by the more general expression involving the stress and strain . The infinitesimal statement is:
where Einstein notation has been used for the tensors, in which there is a summation over all repeated indices in the product term. The Euler theorem yields for the internal energy:
For a linearly elastic material, the stress can be related to the strain by:
Where Cijkl is an element of the 4th-rank elastic constant tensor of the medium.
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