A generalized fractional-order elastodynamic theory for non-local attenuating media

Area of Science:

• Continuum Mechanics
• Wave Propagation
• Fractional Calculus

Background:

• Classical elastodynamics fails to model hybrid transport processes involving simultaneous propagation and diffusion.
• Non-local solids and interfaces exhibit complex behaviors not captured by traditional theories.

Purpose of the Study:

• To develop a generalized elastodynamic theory using fractional-order operators for non-local attenuating solids and interfaces.
• To investigate the impact of space-fractional terms on elastodynamics and wave phenomena.
• To generalize Snell's Law and Fresnel's coefficients for fractional-order elastodynamics.

Main Methods:

• Formulation of a continuum mechanics model incorporating fractional operators in both time and space.
• Derivation of fractional-order versions of Snell's Law and Fresnel's coefficients.
• Validation of theoretical results through direct numerical simulations.

Main Results:

• The proposed theory accurately models diverse combinations of multiscale, non-local, dissipative, and attenuating elastic energy transport.
• The space-fractional term significantly influences the elastodynamics of solids.
• A generalized fractional-order Snell's Law and Fresnel's coefficients are derived, enabling prediction of coupled elastic wave interactions with non-local interfaces.

Conclusions:

• The generalized fractional-order elastodynamic theory provides a powerful framework for modeling complex wave phenomena in non-local media.
• This approach overcomes limitations of classical elastodynamics in capturing hybrid transport processes.
• The validated theory offers new possibilities for analyzing wave interactions at complex interfaces.