Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Unique characterization of materials with memory


Author: J. M. Golden
Journal: Quart. Appl. Math. 74 (2016), 361-374
MSC (2010): Primary 80A17, 74A15
DOI: https://doi.org/10.1090/qam/1428
Published electronically: March 16, 2016
MathSciNet review: 3505608
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Abstract: In general, materials with linear memory constitutive relations are characterized by a relaxation function. This leads to a situation where the free energy for most materials with memory is not unique. There is a convex set of free energy functionals with a minimum and a maximum element. An alternative procedure is proposed which characterizes a material by the kernel of the rate of dissipation functional. Using some recent results, we find that a unique free energy and relaxation function may then be deduced.

An example is given for discrete spectrum materials. Also, the new results are used to show that a previously derived general representation of rate of dissipation and free energy functionals is not complete, in the sense that there are valid functionals which cannot be described by this general formula.


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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/1428
Keywords: Thermodynamics, memory effects, rate of dissipation kernel, unique free energy functional
Received by editor(s): January 15, 2015
Published electronically: March 16, 2016
Article copyright: © Copyright 2016 Brown University

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