Explicit formula for the minimum free energy in linear viscoelasticity

Luca Deseri, Giorgio Gentili, Murrough Golden

Research output: Contribution to journalArticlepeer-review

56 Scopus citations


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 languageEnglish (US)
Pages (from-to)141-185
Number of pages45
JournalJournal of Elasticity
Issue number2
StatePublished - 1999

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering


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