A large deformation isogeometric approach for flexoelectricity and soft materials

Tran Quoc Thai, Timon Rabczuk, Xiaoying Zhuang

Research output: Contribution to journalArticlepeer-review

60 Citations (Scopus)


We propose an isogeometric approach for flexoelectricity in soft dielectric materials at finite deformations accounting for Maxwell stresses on the surface between two different media. In contrast to piezoelectricity where there is a linear dependence between mechanical strain and electric polarization, in flexoelectricity the polarization is related to strain gradients which requires a C1 continuous finite element framework. In electro-mechanical materials, the Maxwell stress emerges as a consequence of the coupling effect between electrostatics and mechanics. If a solid body is embedded in a surrounding medium such as air or vacuum, the Maxwell stress acting on the surfaces governs the interaction between electric fields and deformable media. This is quite difficult to handle due to the surface discontinuity and the traction electrical forces still have to satisfy some certain continuity conditions, hence an appropriate numerical framework is required for the treatment. Here, we employed Non-Uniform Rational B-spline (NURBS) functions with knot insertion technique in order to introduce discontinuities across material interfaces while still maintaining C1 continuity in the domain to evaluate the coupling effect of strain gradient and electric polarization in the regime of finite deformation. The accuracy and robustness of our IGA approach for flexoelectric soft materials are demonstrated in some benchmark numerical examples.

Original languageEnglish
Pages (from-to)718-739
Number of pages22
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusPublished - 2018 Nov 1
Externally publishedYes

Bibliographical note

Funding Information:
The author would like to acknowledge the financial support from the Sofja Kovalevskaja Prize of the Alexander von Humboldt Foundation (Germany) .

Publisher Copyright:
© 2018 Elsevier B.V.


  • Finite deformation
  • Flexoelectricity
  • IGA - C continuity
  • Maxwell stress
  • Soft dielectric

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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