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Abstract
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A variational model describing a one-dimensional mechanical system in which heat
conduction phenomena occur is consistently formulated. Lagrangian variational
perspective, too often limited to the study of mechanical phenomena, is extended to
study linear irreversible processes, where dissipation and heat production may occur,
by generalizing the fundamental ideas and results by Biot (“Linear thermodynamics
and the mechanics of solids,” 1958). It is proven here that Cattaneo’s law for heat
conduction can be deduced via a variational argument together with the
Lord–Shulman model.
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Keywords
thermoelasticity, variational formulation, heat conduction,
Cattaneo's law, Lord–Shulman model
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Mathematical Subject Classification
Primary: 74F05
Secondary: 37D35
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Milestones
Received: 26 March 2021
Revised: 4 June 2021
Accepted: 7 July 2021
Published: 14 March 2022
Communicated by Victor A. Eremeyev
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