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arXiv · 2409.00018

Analysis of nonlocal smart beams following fractional-order constitutive relations

Shubham Desai·Sai Sidhardh
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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.

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Shubham Desai, Sai Sidhardh. 2024-08-16. Analysis of nonlocal smart beams following fractional-order constitutive relations. https://arxiv.org/abs/2409.00018

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