Document Type
Article
Rights
Available under a Creative Commons Attribution Non-Commercial Share Alike 4.0 International Licence
Disciplines
1.1 MATHEMATICS, Applied mathematics
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.
DOI
https://doi.org/10.1090/qam/1407
Recommended Citation
Golden, M. (2015) The Minimum and Other Free Energies for Non-Linear Materials With Memory. "Quarterly of applied mathematics" Vol. 74, pg. 137-164. American Mathematical Society. Published electronically: December 4, 2015. doi:10.1090/qam/1407 http://dx.doi.org/10.1090/qam/1407
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