Document Type

Article

Rights

This item is available under a Creative Commons License for non-commercial use only

Disciplines

1.1 MATHMATICS, Applied mathematics

Publication Details

"Quarterly of applied mathematics", Vol. 74, pp. 137-164. American Mathematical Society. Published electronically: December 4, 2015.

http://dx.doi.org/10.1090/qam/1407

Abstract

Expressions are obtained for free energies of materials with a certain type of non-linear constitutive relation. In particular, the minimum and related free energies are considered in some detail. Minimal states are defined for these materials, and it is shown that any free energy yielding a linear constitutive equation that is a functional of the minimal state has a counterpart in the non-linear case which is also a minimal state functional in this more general context. These results are explored for simple examples, including discrete spectrum materials.

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