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Finite deformation analysis of flexoelectric shells

Farzam Dadgar-Rad, Shahab Sahraee, Mokarram Hossain Orcid Logo, Stefan Hartmann Orcid Logo

Computer Methods in Applied Mechanics and Engineering, Volume: 447, Start page: 118384

Swansea University Author: Mokarram Hossain Orcid Logo

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Abstract

In this work, a nonlinear shell model for the coupled mechanical and electrical analysis of thinflexoelectric polymers is developed. In addition to the classical terms, contributions from thesecond gradient of deformation, electro-mechanical coupling and flexoelectricity are incorporatedinto the fre...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825
Published: Elsevier BV 2025
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URI: https://cronfa.swan.ac.uk/Record/cronfa70379
Abstract: In this work, a nonlinear shell model for the coupled mechanical and electrical analysis of thinflexoelectric polymers is developed. In addition to the classical terms, contributions from thesecond gradient of deformation, electro-mechanical coupling and flexoelectricity are incorporatedinto the free energy density of these materials. Furthermore, starting from a variationalframework, a nonlinear finite element formulation in the material setting is developed toprovide numerical solutions for various problems. By neglecting the electrical and flexoelectriceffects, the present formulation can reflect the deformation of purely mechanical gradient shells.Conversely, by disregarding the gradient and flexoelectric effects, the present formulation isgreatly capable of modeling the deformation of electro-active shells. The midsurface displacementand director difference vectors are interpolated using 1 shape functions, while 0-continuous interpolation functions are used for the thickness stretching and voltage parameters.Several numerical examples are solved to evaluate performance and robustness of the proposedformulation. The results show that the present formulation yields excellent agreement withthose available in the literature. Moreover, the proposed formulation effectively captures theflexoelectric response of both initially flat and initially curved thin structures experiencing finitedeformations.
Keywords: Flexoelectricity; Shell; Soft dielectric; Finite deformation; Finite element method
College: Faculty of Science and Engineering
Start Page: 118384