Fractional-order derivative and time-dependent viscoelastic behaviour of rocks and minerals

Yusuke Kawada, Takahiro Yajima, Hiroyuki Nagahama

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


A general constitutive equation for viscoelastic behaviour of rocks and minerals with fractional-order derivative is investigated. This constitutive law is derived based on differential geometry and thermodynamics of rheology, and the fractional order of derivative represents the degree of time delay. Analyzing some laboratory experimental data of high temperature deformation of rocks and minerals such as halite, marble and orthopyroxene, we propose how to determine the orders of fractional derivative for viscoelastic behaviours of rocks and minerals. The order is related to the exponents for the temporal scaling in the relaxation modulus and the stress power-law of strain rate, i.e., the non-Newtonian flow law, and considered as an indicator representing the macroscopic behaviour and microscopic dynamics of rocks.

Original languageEnglish
Pages (from-to)1690-1702
Number of pages13
JournalActa Geophysica
Issue number6
Publication statusPublished - 2013 Dec


  • differential geometry
  • fractional-order derivative
  • memory effect
  • rock rheology
  • viscoelasticity

ASJC Scopus subject areas

  • Geophysics


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