Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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The minimum and other free energies for non-linear materials with memory


Author: J. M. Golden
Journal: Quart. Appl. Math. 74 (2016), 137-164
MSC (2010): Primary 80A17, 74D10
DOI: https://doi.org/10.1090/qam/1407
Published electronically: December 4, 2015
MathSciNet review: 3472523
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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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Additional Information

J. M. Golden
Affiliation: School of Mathematical Sciences, Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland
Email: murrough.golden@dit.ie

DOI: https://doi.org/10.1090/qam/1407
Keywords: Thermodynamics, memory effects, free energy functional, non-linear constitutive equation, rate of dissipation
Received by editor(s): June 16, 2014
Published electronically: December 4, 2015
Article copyright: © Copyright 2015 Brown University


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