Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Maximum recoverable work, minimum free energy and state space in linear viscoelasticity


Author: Giorgio Gentili
Journal: Quart. Appl. Math. 60 (2002), 153-182
MSC: Primary 74D05; Secondary 45E10, 74A15
DOI: https://doi.org/10.1090/qam/1878264
MathSciNet review: MR1878264
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Abstract: The various formulations of the maximum recoverable work used in the literature are proved to be equivalent. Then an explicit formula of the minimum free energy is derived, starting from the formulation of the maximum recoverable work given by Day. The resulting expression is equivalent to that found by Golden and other authors. However, the particular formulation allows us to prove that the domain of definition of minimum free energy is the whole state space. Finally, the maximum recoverable work is shown to be put as the basis of the thermodynamics of viscoelastic materials under isothermal conditions. In this context the usual relation between the Clausius-Duhem inequality and the dissipation of the material is restored.


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DOI: https://doi.org/10.1090/qam/1878264
Article copyright: © Copyright 2002 American Mathematical Society


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