Hyper-Elasticity Hypo-Elasticity Viscoelasticity Soft Biological Tissue Three-Dimensional Material Model Caputo Derivative Polar Configuration Fractional Polar Derivative Fractional Polar Integral 26A33 74B20 74D10 74L15
Issue Date:
2007
Publisher:
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Fractional Calculus and Applied Analysis, Vol. 10, No 3, (2007), 219p-248p
Abstract:
The popular elastic law of Fung that describes the non-linear stress-
strain behavior of soft biological tissues is extended into a viscoelastic material
model that incorporates fractional derivatives in the sense of Caputo. This one-dimensional material model is then transformed into a
three-dimensional constitutive model that is suitable for general analysis.
The model is derived in a configuration that differs from the current, or
spatial, configuration by a rigid-body rotation; it being the polar configuration. Mappings for the fractional-order operators of integration and differentiation between the polar and spatial configurations are presented as a theorem. These mappings are used in the construction of the proposed viscoelastic model.
