dc.creator | Mao S., Purohit P.K., Aravas N. | en |
dc.date.accessioned | 2023-01-31T08:57:11Z | |
dc.date.available | 2023-01-31T08:57:11Z | |
dc.date.issued | 2016 | |
dc.identifier | 10.1098/rspa.2015.0879 | |
dc.identifier.issn | 13645021 | |
dc.identifier.uri | http://hdl.handle.net/11615/76326 | |
dc.description.abstract | Flexoelectricity, the linear coupling of strain gradient and electric polarization, is inherently a size-dependent phenomenon. The energy storage function for a flexoelectric material depends not only on polarization and strain, but also straingradient. Thus, conventional finite-element methods formulated solely on displacement are inadequate to treat flexoelectric solids since gradients raise the order of the governing differential equations. Here, we introduce a computational framework based on a mixed formulation developed previously by one of the present authors and a colleague. This formulation uses displacement and displacementgradient as separate variables which are constrained in a 'weighted integral sense' to enforce their known relation. We derive a variational formulation for boundary-value problems for piezo- and/or flexoelectric solids. We validate this computational framework against available exact solutions. Our new computational method is applied to more complex problems, including a plate with an elliptical hole, stationary cracks, as well as tension and shear of solids with a repeating unit cell. Our results address several issues of theoretical interest, generate predictions of experimental merit and reveal interesting flexoelectric phenomena with potential for application. © 2016 The Author(s). | en |
dc.language.iso | en | en |
dc.source | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences | en |
dc.source.uri | https://www.scopus.com/inward/record.uri?eid=2-s2.0-84978396759&doi=10.1098%2frspa.2015.0879&partnerID=40&md5=5f918254e6387cd5250f752316d0d916 | |
dc.subject | Boundary value problems | en |
dc.subject | Crystallography | en |
dc.subject | Differential equations | en |
dc.subject | Polarization | en |
dc.subject | Computational framework | en |
dc.subject | Flexoelectricity | en |
dc.subject | Governing differential equations | en |
dc.subject | Gradient elasticity | en |
dc.subject | Mixed finite element formulation | en |
dc.subject | Mixed formulations | en |
dc.subject | Polarization and strains | en |
dc.subject | Variational formulation | en |
dc.subject | Finite element method | en |
dc.subject | Royal Society of London | en |
dc.title | Mixed finite-element formulations in piezoelectricity and flexoelectricity | en |
dc.type | journalArticle | en |