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Gradient piezoelectricity for cracks under an impact load

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Abstract

The flexoelectric effect on elastic waves is investigated in nano-sized cracked structures. The strain gradients are considered in the constitutive equations of a piezoelectric solid for electric displacements and the higher-order stress tensor. The governing equations with the corresponding boundary conditions are derived from the variational principle. The finite element method (FEM) is developed from the principle of virtual work. It is equivalent to the weak-form of derived governing equations in gradient elasticity. The computational method can be applied to analyze general 2D boundary value problems in size-dependent piezoelectric elastic solids with cracks under a dynamic load. The FEM formulation is implemented for strain-gradient piezoelectricity under a dynamic load.

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Acknowledgements

The authors acknowledge the support by the Slovak Science and Technology Assistance Agency registered under number APVV-14-0216, VEGA 1/0145/17 and the Slovak Academy of Sciences Project (SASPRO) 0106/01/01.

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Authors and Affiliations

  1. Institute of Construction and Architecture, Slovak Academy of Sciences, 84503, Bratislava, Slovakia

    Jan Sladek, Vladimir Sladek & Michael Wünsche

  2. Faculty of Special Technology, University of Trencin, 91150, Trencin, Slovakia

    Jozef Kasala

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  1. Jan Sladek
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  2. Vladimir Sladek
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  3. Michael Wünsche
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  4. Jozef Kasala
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Correspondence to Jan Sladek.

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Sladek, J., Sladek, V., Wünsche, M. et al. Gradient piezoelectricity for cracks under an impact load. Int J Fract 210, 95–111 (2018). https://doi.org/10.1007/s10704-018-0264-0

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  • DOI: https://doi.org/10.1007/s10704-018-0264-0

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