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Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/1317

Title: Caputo Derivatives in Viscoelasticity: A Non-Linear Finite-Deformation Theory for Tissue
Authors: Freed, Alan
Diethelm, Kai
Keywords: 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.
Description: Mathematics Subject Classification: 26A33, 74B20, 74D10, 74L15
URI: http://hdl.handle.net/10525/1317
ISSN: 1311-0454
Appears in Collections:2007

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