A staggered explicit-implicit isogeometric formulation for large deformation flexoelectricity

authored by: Tran Quoc Thai, Xiaoying Zhuang, Harold S. Park, Timon Rabczuk
Abstract: Flexoelectricity is an electromechanical coupling occurring in dielectric materials that has recently attracted significant attention. The flexoelectric effect is described by a coupled, higher-order electromechanical set of equations that have typically been solved using a computationally expensive monolithic formulation. In the present work, we propose a staggered, explicit-implicit formulation that both significantly reduces the computational expense, while enabling the capturing of electromechanical instabilities through the usage of inertia. The higher order equations are discretized using an isogeometric formulation, and we demonstrate via two numerical examples the combination of increased computational efficiency with comparable accuracy that is gained from the proposed formulation as compared to the standard monolithic approaches.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Boston University (BU)
Ton Duc Thang University
Type: Article
Journal: Engineering Analysis with Boundary Elements
Volume: 122
Pages: 1-12
No. of pages: 12
ISSN: 0955-7997
Publication date: 01.2021
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Analysis, Engineering(all), Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1016/j.enganabound.2020.10.004 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{b5ca665e907f45e3a3eaa203c2ade7c2,
title = "A staggered explicit-implicit isogeometric formulation for large deformation flexoelectricity",
abstract = "Flexoelectricity is an electromechanical coupling occurring in dielectric materials that has recently attracted significant attention. The flexoelectric effect is described by a coupled, higher-order electromechanical set of equations that have typically been solved using a computationally expensive monolithic formulation. In the present work, we propose a staggered, explicit-implicit formulation that both significantly reduces the computational expense, while enabling the capturing of electromechanical instabilities through the usage of inertia. The higher order equations are discretized using an isogeometric formulation, and we demonstrate via two numerical examples the combination of increased computational efficiency with comparable accuracy that is gained from the proposed formulation as compared to the standard monolithic approaches.",
keywords = "Flexoelectricity, Higher-order continuity, Large deformation, Soft dielectric, Staggered scheme",
author = "Thai, {Tran Quoc} and Xiaoying Zhuang and Park, {Harold S.} and Timon Rabczuk",
note = "Funding Information: The authors Tran Quoc Thai and Xiaoying Zhuang would like to acknowledge the ﬁnancial support from NSFC (11772234) and the Sofja Kovalevskaja Prize of the Alexander von Humboldt Foundation (Germany). ",
year = "2021",
month = jan,
doi = "10.1016/j.enganabound.2020.10.004",
language = "English",
volume = "122",
pages = "1--12",
journal = "Engineering Analysis with Boundary Elements",
issn = "0955-7997",
publisher = "Elsevier Ltd.",
}