Explicit formula for the minimum free energy in linear viscoelasticity

Luca Deseri; Giorgio Gentili; Murrough Golden

doi:10.1023/A:1007646017347

Explicit formula for the minimum free energy in linear viscoelasticity

Luca Deseri, Giorgio Gentili, Murrough Golden

Houston Methodist

Research output: Contribution to journal › Article › peer-review

56 Scopus citations

Abstract

A general explicit formula for the maximum recoverable work from a given state is derived in the frequency domain for full tensorial isothermal linear viscoelastic constitutive equations. A variational approach, developed for the scalar case, is here generalized by virtue of certain factorizability properties of positive-definite matrices. The resultant formula suggests how to characterize the state in the sense of Noll in the frequency domain. The property that the maximum recoverable work represents the minimum free energy according to both Graffi's and Coleman-Owen's definitions is used to obtain an explicit formula for the minimum free energy. Detailed expressions are presented for particular types of relaxation function.

Original language	English (US)
Pages (from-to)	141-185
Number of pages	45
Journal	Journal of Elasticity
Volume	54
Issue number	2
DOIs	https://doi.org/10.1023/A:1007646017347
State	Published - 1999

ASJC Scopus subject areas

Materials Science(all)
Mechanics of Materials
Mechanical Engineering

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title = "Explicit formula for the minimum free energy in linear viscoelasticity",

abstract = "A general explicit formula for the maximum recoverable work from a given state is derived in the frequency domain for full tensorial isothermal linear viscoelastic constitutive equations. A variational approach, developed for the scalar case, is here generalized by virtue of certain factorizability properties of positive-definite matrices. The resultant formula suggests how to characterize the state in the sense of Noll in the frequency domain. The property that the maximum recoverable work represents the minimum free energy according to both Graffi's and Coleman-Owen's definitions is used to obtain an explicit formula for the minimum free energy. Detailed expressions are presented for particular types of relaxation function.",

author = "Luca Deseri and Giorgio Gentili and Murrough Golden",

note = "Funding Information: This work has been supported by the Italian M.U.R.S.T. through the Projects {\textquoteleft}Metodi matematici nella meccanica dei sistemi continui{\textquoteright}, {\textquoteleft}Modelli matematici per la scienza dei materiali{\textquoteright} co.fin. (1998) and by a grant under the Enterprise Ireland International Collaboration Programme (1998). Copyright: Copyright 2004 Elsevier Science B.V., Amsterdam. All rights reserved.",

year = "1999",

doi = "10.1023/A:1007646017347",

language = "English (US)",

volume = "54",

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T1 - Explicit formula for the minimum free energy in linear viscoelasticity

AU - Deseri, Luca

AU - Gentili, Giorgio

AU - Golden, Murrough

N1 - Funding Information: This work has been supported by the Italian M.U.R.S.T. through the Projects ‘Metodi matematici nella meccanica dei sistemi continui’, ‘Modelli matematici per la scienza dei materiali’ co.fin. (1998) and by a grant under the Enterprise Ireland International Collaboration Programme (1998). Copyright: Copyright 2004 Elsevier Science B.V., Amsterdam. All rights reserved.

PY - 1999

Y1 - 1999

N2 - A general explicit formula for the maximum recoverable work from a given state is derived in the frequency domain for full tensorial isothermal linear viscoelastic constitutive equations. A variational approach, developed for the scalar case, is here generalized by virtue of certain factorizability properties of positive-definite matrices. The resultant formula suggests how to characterize the state in the sense of Noll in the frequency domain. The property that the maximum recoverable work represents the minimum free energy according to both Graffi's and Coleman-Owen's definitions is used to obtain an explicit formula for the minimum free energy. Detailed expressions are presented for particular types of relaxation function.

AB - A general explicit formula for the maximum recoverable work from a given state is derived in the frequency domain for full tensorial isothermal linear viscoelastic constitutive equations. A variational approach, developed for the scalar case, is here generalized by virtue of certain factorizability properties of positive-definite matrices. The resultant formula suggests how to characterize the state in the sense of Noll in the frequency domain. The property that the maximum recoverable work represents the minimum free energy according to both Graffi's and Coleman-Owen's definitions is used to obtain an explicit formula for the minimum free energy. Detailed expressions are presented for particular types of relaxation function.

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Explicit formula for the minimum free energy in linear viscoelasticity

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