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An Explicit Formula for the Minimum Free Energy in Linear Viscoelasticity

Journal of Elasticity volume 54, pages 141–185 (1999)Cite this article

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.

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Authors and Affiliations

  1. Dipartimento di Ingegneria, Università degli Studi di Ferrara, 44100, Ferrara, Italy; e-mail

    Luca Deseri & Giorgio Gentili

  2. School of Mathematics, Statistics and Computer Science, Dublin Institute of Technology, Dublin, Ireland; e-mail: jmgolden@maths1.kst.dit.ie

    Murrough Golden

Authors
  1. Luca Deseri
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  2. Giorgio Gentili
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  3. Murrough Golden
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Deseri, L., Gentili, G. & Golden, M. An Explicit Formula for the Minimum Free Energy in Linear Viscoelasticity. Journal of Elasticity 54, 141–185 (1999). https://doi.org/10.1023/A:1007646017347

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  • DOI: https://doi.org/10.1023/A:1007646017347

  • linear viscoelasticity
  • recoverable work
  • minimum free energy.