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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.

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