Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Variational-Lagrangian irreversible thermodynamics of nonlinear thermorheology


Author: M. A. Biot
Journal: Quart. Appl. Math. 34 (1976), 213-248
MSC: Primary 80.49
DOI: https://doi.org/10.1090/qam/462245
MathSciNet review: 462245
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Abstract: A principle of virtual dissipation generalizing d'Alembert's principle to nonlinear irreversible thermodynamics provides a unifying foundation which leads to an extremely general variational-Lagrangian analysis of dissipative phenomena. Thus a synthesis is achieved between thermodynamics and classical mechanics. The present paper applies this principle to the nonlinear thermomechanics of continua with dissipation and heat conduction. Field equations, constitutive equations and Lagrangian equations with generalized coordinates are derived for nonlinear thermoviscoelastcity, nonlinear thermoelasticity and heat conduction, plasticity, and compressible heat conducting fluids with Newtonian and non-Newtonian viscosity. The thermodynamics of instability is also analyzed from the same fundamental viewpoint.


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DOI: https://doi.org/10.1090/qam/462245
Article copyright: © Copyright 1976 American Mathematical Society


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