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

Abstract

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.

References in corpus (2)

• The fundamental solution of the space-time fractional diffusion equation
• Analytical properties and applications of the Wright function

Cited by in corpus (5)

• Space-time fractional Zener wave equation
• Dispersion and attenuation for an acoustic wave equation consistent with viscoelasticity
• Spatial dispersion of elastic waves in a bar characterized by tempered nonlocal elasticity
• Attenuation and shock waves in linear hereditary viscoelastic media. Strick-Mainardi, Jeffreys-Lomnitz-Strick and Andrade creep compliances
• On wave propagation in viscoelastic media with concave creep compliance