Mathematical and computational modeling of flexoelectricity
We first revisit the mathematical modeling of the flexoelectric effect in the context of continuum mechanics at infinitesimal deformations. We establish and clarify the relation between the different formulations, point out theoretical and numerical issues related to the resulting boundary value pro...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/366124 |
| Acceso en línea: | https://hdl.handle.net/2117/366124 https://dx.doi.org/10.1063/5.0067852 |
| Access Level: | acceso abierto |
| Palabra clave: | Numerical analysis Strength of materials Anàlisi numèrica Resistència de materials Classificació AMS::65 Numerical analysis::65K Mathematical programming, optimization and variational techniques Classificació AMS::74 Mechanics of deformable solids::74S Numerical methods Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics |
| Sumario: | We first revisit the mathematical modeling of the flexoelectric effect in the context of continuum mechanics at infinitesimal deformations. We establish and clarify the relation between the different formulations, point out theoretical and numerical issues related to the resulting boundary value problems, and present the natural extension to finite deformations. We then present a simple B-spline based computational technique to numerically solve the associated boundary value problems, which can be extended to handle unfitted meshes, hence allowing for arbitrarily-shaped geometries. Several numerical examples illustrate the flexoelectric effect in simple benchmark setups, as well as in new flexoelectric devices and metamaterials engineered for sensing or actuation. |
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