Generalized Helmholtz Energy
In the more general case, the mechanical term must be replaced by the product of the volume times the stress times an infinitesimal strain:
where is the stress tensor, and is the strain tensor. In the case of linear elastic materials that obey Hooke's Law, the stress is related to the strain by:
where we are now using Einstein notation for the tensors, in which repeated indices in a product are summed. We may integrate the expression for to obtain the Helmholtz energy:
Read more about this topic: Helmholtz Free Energy
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