PSI - Issue 59

M. Levchenko et al. / Procedia Structural Integrity 59 (2024) 724–730 M. Levchenko et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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dimensional case such behavior was also confirmed and was shown that the electric flux in each cross-section demonstrates practically constant values for the main part of the crack region, and only in the immediate vicinity of the crack fronts slight deviations from the constant values are observed. 5. Conclusions Two bonded rectangular piezoelectric parallelepipeds with a limited permeable crack in their interface are considered. The plane strain problem for the middle section of 3-D domain is studied at the beginning, and an analytical solution to this problem is found. The electric flux through the crack region is determined from this solution and used as an initial approximation for the 3-D problem solution. The finite element method was used to analyse the last one. An iterative algorithm for the determination of the electric flux through the crack region was applied, according to which the mentioned flux at each step was determined by the use of FEM and the equation (2). Due to this approach, the values of the electric flux were found with high accuracy, and the conformation concerning its quasi-uniform distribution along the crack faces for any cross-section of the 3-D body was revealed. Acknowledgements A support from the French National Research Agency as part of the “Investissements d’Avenir” through the IMobS3 Laboratory of Excellence (ANR-10-LABX-0016) and the IDEX-ISITE initiative CAP 20-25 (ANR-16 IDEX0001), program WOW and International Research C enter “Innovation Transportation and Production Systems” (CIR ITPS) in the FACTOLAB common laboratory (CNRS, UCA, Michelin), and from the Humboldt Foundation, Germany is gratefully appreciated. References Govorukha, V. B., Loboda, V. V., Kamlah, M., 2006. On the influence of the electric permeability on an interface crack in a piezoelectric bimaterial compound. Int. J. Solids Struct. 43, 1979 – 1990. Hao, T. H., Shen, Z. Y., 1994. A new electric boundary condition of electric fracture mechanics and its applications. Eng. Fract. Mech 47, 793 – 802. Li, Q., Chen Y. H., 2007. Solution for a semi-permeable interface crack between two dissimilar piezoelectric materials. J. Appl. Mech. 74, 833 – 844. Li Q., Chen Y. H., 2008. Solution for a semi-permeable interface crack in elastic dielectric/piezoelectric biomaterials. J. Appl. Mech. 75, 0110101. Lapusta, Y., Komarov A., Labesse-Jied F., Moutou Pitti R., Loboda V., Limited permeable crack moving along the interface of a piezoelectric bi material. European Journal of Mechanics A/Solids 30, 639-649. Loboda, V., Sheveleva, A., Chapelle, F., Lapusta, Y., Multiple electrically limited permeable cracks in the interface of piezoelectric materials. Mechanics of Advanced Materials and Structures, Published online: 22 Feb 2023. https://doi.org/10.1080/15376494.2023.2180695 Muskhelishvili, N.I., 1975. Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff, Groningen. Suo, Z., Kuo, C.M., Barnett, D.M., Willis, J.R., 1992. Fracture mechanics for piezoelectric ceramics. Journal of Mechanics and Physics of Solids 40, 739 - 765.