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, AlanDiethelm, Kai Keywords: Hyper-ElasticityHypo-ElasticityViscoelasticitySoft Biological TissueThree-Dimensional Material ModelCaputo DerivativePolar ConfigurationFractional Polar DerivativeFractional Polar Integral26A3374B2074D1074L15 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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