The flexoelectric effect for interface cracks between two dissimilar materials
Tomas Profant, Jan Sladek, Vladimir Sladek
download PDFAbstract. It is developed the procedure of the assessment of the amplitude factors in the asymptotic solution for the interface crack between two flexoelectric materials. The stress exponents with the appropriate eigenvectors of the regular and auxiliary solutions are evaluated from the eigenvalue problem assembled from the boundary conditions prevailing at the tip of the crack. The amplitude factors of the asymptotic solution are computed from the two-state integrals in which the regular, auxiliary, and finite element solution represent the independent equilibrium states. The obtained results show the capability of the two-state integrals to extract the dominant terms of the asymptotic solution from the weak solution of the fracture problem represented by the finite element method. The amplitude factors representing the most singular terms of the asymptotic solution at the crack tip are quantities playing an important role in the problems of crack stability criterions.
Keywords
Dielectric Material, Gradient Theory, Flexoelectricity, Asymptotic Solution, Mixed FEM
Published online 8/10/2023, 10 pages
Copyright © 2023 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA
Citation: Tomas Profant, Jan Sladek, Vladimir Sladek, The flexoelectric effect for interface cracks between two dissimilar materials, Materials Research Proceedings, Vol. 31, pp 99-108, 2023
DOI: https://doi.org/10.21741/9781644902592-11
The article was published as article 11 of the book Advanced Topics in Mechanics of Materials, Structures and Construction
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
References
[1] P. Yudin, A. Tagantsev, Fundamentals of flexoelectricity in solids, Nanotechnology 24 (2013) 432001. https://doi.org/10.1088/0957-4484/24/43/432001
[2] H. Wang, X. Jiang, Y. Wang, R.W. Stark, van Aken, J. Mannhart, Direct observation of huge flexoelectric polarization around crack tips, Nano Letter 20 (2020) 88-94. https://doi.org/10.1021/acs.nanolett.9b03176
[3] X. Tian, M. Xu, H. Zhou, Q. Li, J. Sladek, V. Sladek, Analytical studies on mode III fracture in flexoelectric solids, Journal of Applied Mechanics 89 (2022) 041006. https://doi.org/10.1115/1.4053268
[4] P.A. Gougiotis, H.G. Georgiadis, Plane-strain crack problems in microstructured solids governed by dipolar gradient elasticity, J. Mech. Phys. Solids 57 (2009) 1898-1920. https://doi.org/10.1016/j.jmps.2009.07.005
[5] F. Vasquez-Sancho, A. Abdollahi, D. Damjanovic, G. Catalan, Flexoelectricity in bones, Advanced Materials 30 (2018) 1705316.
[6] X. Tian, J. Sladek, V. Sladek, Q. Deng, Q. Li, A collocation mixed finite element method for the analysis of flexoelectric solids, Int. J. Solids Struct. 217 (2021) 27-39. https://doi.org/10.1016/j.ijsolstr.2021.01.031
[7] J. Sladek, V. Sladek, M. Hrytsyna, T. Profant, Application of the gradient theory to interface crack between two dissimilar dielectric materials, Engineering Fracture Mechanics 276(B) (2022), 108895. https://doi.org/10.1016/j.engfracmech.2022.108895
[8] F. Deng, Q. Deng, W. Yu, S. Shen, Mixed Finite Elements for Flexoelectric Solids, Journal of Applied Mechanics 84(8) (2017) 081004. https://doi.org/10.1115/1.4036939
[9] J. Sladek, V. Sladek, P. Stanak, C. Zhang, C.-L. Tan, Fracture mechanics analysis of size-dependent piezoelectric solids, Int J Solids Struct 113-114 (2017) 1-9. https://doi.org/10.1016/j.ijsolstr.2016.08.011
[10] M.L. Williams, Stress singularities resulting from various boundary conditions in angular corners of plates in extension, Journal of Applied Mechanics 74 (1952) 526–528.
[11] M. Kotoul, T. Profant, Asymptotic solution for interface crack between two materials governed by dipolar gradient elasticity, Engineering Fracture Mechanics 201 (2018) 80-106. https://doi.org/10.1016/j.engfracmech.2018.05.002
[12] T. Profant, J. Sládek, V. Sládek. M. Kotoul, Asymptotic solution for interface crack between two materials governed by dipolar gradient elasticity: Amplitude factor evaluation, Theoretical and Applied Fracture Mechanics 120 (2022) 103378. https://doi.org/10.1016/j.tafmec.2022.103378
[13] S. Mao, P. K. Purohit, Insights Into Flexoelectric Solids From Strain-Gradient Elasticity, Journal of Applied Mechanics 81(8) (2014) 081004(10). https://doi.org/10.1115/1.4027451
