Lattice with Long-Range Interaction of Power-Law Type for Fractional Non-Local Elasticity

TL;DR

This paper introduces a lattice model with power-law long-range interactions as a microscopic basis for fractional non-local elasticity, deriving continuum equations with Riesz derivatives that generalize classical elasticity models.

Contribution

It proposes a novel lattice model with power-law interactions and derives corresponding fractional continuum equations, connecting microscopic interactions to non-local elasticity.

Findings

Derived continuum equations with Riesz derivatives from lattice models.

Provided particular solutions and asymptotics for static displacement fields.

Established a link between microscopic lattice interactions and fractional elasticity.

Abstract

Lattice models with long-range interactions of power-law type are suggested as a new type of microscopic model for fractional non-local elasticity. Using the transform operation, we map the lattice equations into continuum equation with Riesz derivatives of non-integer orders. The continuum equations that are obtained from the lattice model describe fractional generalization of non-local elasticity models. Particular solutions and correspondent asymptotic of the fractional differential equations for displacement fields are suggested for the static case.