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

Freed, AlanDiethelm, Kai — 2007

Fractional Calculus and Applied Analysis

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...

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