Differential geometry of viscoelastic models with fractional-order derivatives

Takahiro Yajima, Hiroyuki Nagahama

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)


Viscoelastic materials with memory effect are studied based on the fractional rheonomic geometry. The geometric objects are regarded as basic quantities of fractional viscoelastic models, i.e. the metric tensor and torsion tensor are interpreted as the strain and the fractional strain rate, respectively. The generalized viscoelastic equations are expressed by the geometric objects. Especially, the basic constitutive equations such as Voigt and Maxwell models can be derived geometrically from the generalized equation. This leads to the fact that various viscoelastic models can be unified into one geometric expression.

Original languageEnglish
Article number385207
JournalJournal of Physics A: Mathematical and Theoretical
Issue number38
Publication statusPublished - 2010 Sept 24


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