Geometry Independent Direct and Converse Flexoelectric Effects in Functionally Graded Dielectrics: An Isogeometric Analysis

Saurav Sharma, Anuruddh Kumar, Rajeev Kumar, Mohammad Talha, Rahul Vaish

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11 Scopus citations


In the present study, a functionally graded material (FGM) based dielectric composite is investigated for direct and converse flexoelectric effects induced due to material inhomogeneity. An Isogeometric analysis based formulation is employed to effectively capture the gradient terms appearing in the electro-elastic coupling constitutive laws of flexoelectricity. Non-uniform stresses and strains generated due to non-uniform elastic properties in the domain induce flexoelectricity inherently without any special geometric and/or boundary conditions. A two-dimensional (2D) FGM structure made by the combination of polyvinylidene fluoride (PVDF) and barium titanate (BaTiO3) is studied under mechanical and thermal loading conditions for its flexoelectric response. The induced polarization and voltage along with its dependence on grading index (n) is analyzed. Further, to extend the study to converse flexoelectricity, the mechanical response of the FG flexoelectric material under an applied electric potential is studied. Finally, the actuation of the structure by an applied electric field is studied. As high as 10% actuation of original displacement is observed for higher values of n. Effectiveness of the grading concept to induce flexoelectric response is established through numerical studies. Longitudinal and transverse modes of flexoelectricity are scrutinized and the concept of grading is proved to inherently induce the flexoelectricity in dielectrics without special geometric modifications.

Original languageEnglish
Article number103456
JournalMechanics of Materials
StatePublished - Sep 2020
Externally publishedYes

Bibliographical note

Funding Information:
The authors gratefully acknowledge the financial support provided by Aeronautics Research and Development Board ( ARDB ), DRDO , Government of India for carrying out this research under project number ARDB/01/1051856/ M /I.

Publisher Copyright:
© 2020 Elsevier Ltd


  • Flexoelectric material
  • Functionally graded material
  • Isogeometric analysis


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