CAPUTO DERIVATIVES IN VISCOELASTICITY: A NON-LINEAR FINITE-DEFORMATION THEORY FOR TISSUE

The popular elastic law of Fung that describes the non-linear stressstrain 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. Mathematics Subject Classification: 26A33, 74B20, 74D10, 74L15

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