Analysis of nonlocal smart beams following fractional-order constitutive relations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916376858329088 |
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| author | Desai, Shubham Sidhardh, Sai |
| author_facet | Desai, Shubham Sidhardh, Sai |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00018 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analysis of nonlocal smart beams following fractional-order constitutive relations Desai, Shubham Sidhardh, Sai Computational Engineering, Finance, and Science Numerical Analysis 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. |
| title | Analysis of nonlocal smart beams following fractional-order constitutive relations |
| topic | Computational Engineering, Finance, and Science Numerical Analysis |
| url | https://arxiv.org/abs/2409.00018 |