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Caputo Derivatives in Viscoelasticity: A Non-Linear Finite-Deformation Theory for Tissue

By Alan Freed and Kai Diethelm


Mathematics Subject Classification: 26A33, 74B20, 74D10, 74L15The 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

Topics: 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
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Year: 2007
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