Spatially fractional-order viscoelasticity, non-locality and a new kind of anisotropy

Details Spatially fractional-order viscoelasticity, non-locality and a new kind of anisotropy Spatially fractional-order viscoelasticity, non-locality and a new kind of anisotropy

2011-11-07

arxiv.org/abs/1111.1680v1

Physics

Mathematical Physics

Scientific paper

Spatial non-locality of space-fractional viscoelastic equations of motion is studied. Relaxation effects are accounted for by replacing second-order time derivatives by lower-order fractional derivatives and their generalizations. It is shown that space-fractional equations of motion of an order strictly less than 2 allow for a new kind anisotropy, associated with angular dependence of non-local interactions between stress and strain at different material points. Constitutive equations of such viscoelastic media are determined. Explicit fundamental solutions of the Cauchy problem are constructed for some cases isotropic and anisotropic non-locality.

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