Flexoelectric Effect for Cracks in Piezoelectric Solids


Article Preview

The finite element method (FEM) is developed to analyse 2-D crack problems where the electric field and displacement gradients exhibit a size effect penomenon. This phenomenon in micro/nanoelectronic structures is described by the strain-and electric field-gradients in constitutive equations. The governing equations are derived using variational principles with the corresponding boundary conditions. The FEM formulation with C1-continuous elements is subsequently developed and implemented. An example is presented and discussed to demonstrate the effects of the strain-and electric intensity-gradients on the electro-mechanical behavior of cracked solids.



Edited by:

Luis Rodríguez-Tembleque, Jaime Domínguez and Ferri M.H. Aliabadi




J. Sladek et al., "Flexoelectric Effect for Cracks in Piezoelectric Solids", Key Engineering Materials, Vol. 774, pp. 90-95, 2018

Online since:

August 2018




* - Corresponding Author

[1] S. Buhlmann, B. Dwir, J. Boborowski, P. Muralt: Appl. Phys. Lett. Vol. 80 (2002), p.3195.

[2] L.E. Cross: J. Mater. Sci. Vol. 41 (2006), p.53.

[3] A.C. Eringen, C.G. Speziale, B.S. Kim: J. Mech. Phys. Sol. 25 (1977), p.339.

[4] R.D. Mindlin: Int. J. Sol. Struct. 1 (1965), p.417.

[5] E. Aifantis: ASME J. Engn. Mater. Technol. 106 (1984), p.326.

[6] Y. Huang, L. Zhang, T.F. Guo, K.C. Hwang: J. Mech. Phys. Sol. 45 (1997), p.439.

[7] J. Sladek, V. Sladek, P. Stanak, Ch. Zhang, C.L. Tan: Int. J. Sol. Struct. 113 (2017), p.1.

[8] P. Sharma, R. Maranganti, N.D. Sharma: Phys. Rev. B 74 (2006), p.014110.

[9] J. Yang: Int. J. Fracture 127 (2004), p. L111.

[10] A. Beheshti: Acta Mechanica 228 (2017), p.3543.

[11] S.L. Hu, S.P. Shen: CMC-Computers, Materials & Continua 13 (2009), p.63.

[12] S.T. Yaghoubi, S.M. Mousavi, J. Paavola: Int. J. Sol. Struct. 109 (2017), p.84.

[13] J. Sladek, V. Sladek, M. Wunsche, Ch. Zhang: Eur. J. Mech./Solids 71 (2018) 187-198.