Fractional Calculus for Continuum Mechanics - anisotropic non-locality

TL;DR

This paper extends fractional continuum mechanics to anisotropic non-locality, maintaining a structure similar to classical mechanics, enabling better physical and geometrical understanding of fractional deformation measures.

Contribution

It introduces a novel formulation of fractional continuum mechanics that incorporates anisotropic non-locality while preserving classical structural analogies.

Findings

Framework aligns with classical continuum mechanics

Enables modeling of anisotropic non-local effects

Provides a basis for further physical interpretation

Abstract

In this paper the generalisation of previous author's formulation of fractional continuum mechanics to the case of anisotropic non-locality is presented. The considerations include the review of competitive formulations available in literature. The overall concept bases on the fractional deformation gradient which is non-local, as a consequence of fractional derivative definition. The main advantage of the proposed formulation is its analogical structure to the general framework of classical continuum mechanics. In this sense, it allows, to give similar physical and geometrical meaning of introduced objects.