TY - JOUR

T1 - Differential geometry of viscoelastic models with fractional-order derivatives

AU - Yajima, Takahiro

AU - Nagahama, Hiroyuki

PY - 2010/9/24

Y1 - 2010/9/24

N2 - 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.

AB - 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.

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U2 - 10.1088/1751-8113/43/38/385207

DO - 10.1088/1751-8113/43/38/385207

M3 - Article

AN - SCOPUS:78649530337

VL - 43

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 38

M1 - 385207

ER -