Caputo Derivatives in Viscoelasticity: A Non-Linear Finite-Deformation Theory for Tissue
Data(s) |
29/08/2010
29/08/2010
2007
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Resumo |
Mathematics Subject Classification: 26A33, 74B20, 74D10, 74L15 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. |
Identificador |
Fractional Calculus and Applied Analysis, Vol. 10, No 3, (2007), 219p-248p 1311-0454 |
Idioma(s) |
en |
Publicador |
Institute of Mathematics and Informatics Bulgarian Academy of Sciences |
Palavras-Chave | #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 |
Tipo |
Article |