Free energy and states of fractional-order hereditariness

Luca Deseri, Mario Di Paola, Massimiliano Zingales

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


Complex materials, often encountered in recent engineering and material sciences applications, show no complete separations between solid and fluid phases. This aspect is reflected in the continuous relaxation time spectra recorded in cyclic load tests. As a consequence the material free energy cannot be defined in a unique manner yielding a significative lack of knowledge of the maximum recoverable work that can extracted from the material. The non-uniqueness of the free energy function is removed in the paper for power-laws relaxation/creep function by using a recently proposed mechanical analogue to fractional-order hereditariness.

Original languageEnglish (US)
Pages (from-to)3156-3167
Number of pages12
JournalInternational Journal of Solids and Structures
Issue number18
StatePublished - Sep 2014


  • Dissipation rate
  • Fractional derivatives
  • Free energy
  • Material state
  • Power-law creep/relaxation

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Materials Science(all)
  • Condensed Matter Physics
  • Applied Mathematics
  • Modeling and Simulation


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