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Models of fractional viscous stresses for incompressible materials. (arXiv:2305.01934v1 [cond-mat.soft])

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We present and review several models of fractional viscous stresses from the
literature, which generalise classical viscosity theories to fractional orders
by replacing total strain derivatives in time with fractional time derivatives.
Here we study shearing motions, observing that some models are more convenient
to use than others for the analysis of shear creep and relaxation. Moreover, we
investigate the issues of material frame-indifference and thermodynamic
consistency for these models and find that on these bases, some are physically
unacceptable. Finally, we compute the incremental stresses due to
small-amplitude wave propagation in a deformed material, with a view to
establish acousto-elastic formulas for prospective experimental calibrations.

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