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Caputo derivatives in viscoelasticity: a non-linear finite-deformation theory for tissue. (English) Zbl 1152.26303
Summary: The popular elastic law of Fung that describes the non-linear stress-strain behavior of soft biological tissues is extencied 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.

26A33 Fractional derivatives and integrals
74B20 Nonlinear elasticity
74D10 Nonlinear constitutive equations for materials with memory
74L15 Biomechanical solid mechanics
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