Analysis of nonlocal smart beams following fractional-order constitutive relations

TL;DR

This paper introduces a novel fractional-calculus based model for nonlocal smart beams that captures long-range multiphysics interactions, enhancing the understanding and design of advanced metastructures with improved piezoelectric coupling.

Contribution

It develops the first fractional-order constitutive relations for coupled electro-mechanical nonlocal interactions in smart beams, validated through analytical and numerical methods.

Findings

Fractional-order models effectively capture nonlocal interactions.

Numerical framework validated with multiple case studies.

Tuning nonlocal interactions enhances multiphysics coupling.

Abstract

In this study, we develop a fractional-calculus based constitutive model for capturing nonlocal interactions over the multiphysics response in solids. More specifically, we develop constitutive relations for nonlocal piezoelectricity incorporating fractional-order kinematic relations to capture the long-range interactions over electrical and mechanical field variables. This study breaks new ground by developing fractional-order constitutive models for a two-way multiphysics (electro-mechanical) coupling, specifically the direct and converse piezoelectric effect. It is expected that long-range interactions over each field variable (elastic and electrical) can be leveraged to develop metastructures with enhanced multiphysics coupling. To better illustrate this, we choose the example of a smart beam composed of a nonlocal substrate and a piezoelectric layer. We establish the analytical and numerical framework to analyze nonlocal smart beams based on variational principles. The fractional-Finite Element (f-FE) numerical solver, facilitating multiphysics coupling, undergoes comprehensive validation through multiple case studies. Finally, detailed studies point towards tuning the multiphysics coupling possible via nonlocal interactions across the domain.