A fractional-order model for aging materials: An application to concrete

Angela Beltempo, Massimiliano Zingales, Oreste S. Bursi, Luca Deseri

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


In this paper, the hereditariness of aging materials is modeled within the framework of fractional calculus of variable order. A relevant application is made for the long-term behavior of concrete, for which the creep function is evaluated with the aid of Model B3. The corresponding relaxation function is derived through the Volterra iterated kernels and a comparison with the numerically-obtained relaxation function of Model B3 is also reported. The proposed fractional hereditary aging model (FHAM) for concretes leads to a relaxation function that fully agrees with the well-established Model B3. Furthermore, the FHAM takes full advantage of the formalism of fractional-order calculus to yield semi-analytic expressions in terms of material parameters.

Original languageEnglish (US)
Pages (from-to)13-23
Number of pages11
JournalInternational Journal of Solids and Structures
StatePublished - May 1 2018


  • Concrete creep
  • Concrete relaxation
  • Fractional aging concrete
  • Fractional hereditary aging materials
  • RILEM database
  • Variable-order fractional calculus

ASJC Scopus subject areas

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


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