Vol. 9, No. 4, 2021

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A variational formulation for one-dimensional linear thermoviscoelasticity

Ivan Giorgio

Vol. 9 (2021), No. 4, 397–412
DOI: 10.2140/memocs.2021.9.397
Abstract

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.

Keywords
thermoelasticity, variational formulation, heat conduction, Cattaneo's law, Lord–Shulman model
Mathematical Subject Classification
Primary: 74F05
Secondary: 37D35
Milestones
Received: 26 March 2021
Revised: 4 June 2021
Accepted: 7 July 2021
Published: 14 March 2022

Communicated by Victor A. Eremeyev
Authors
Ivan Giorgio
Department of Civil, Construction-Architectural and Environmental Engineering (DICEAA)
International Research Center on Mathematics and Mechanics of Complex Systems (M&MoCS)
Università degli Studi dell’Aquila
L’Aquila
Italy