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
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Fractional Calculus and Applied Analysis, Vol. 10, No 3, (2007), 219p-248p
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.