PSI - Issue 52

T. Profant et al. / Procedia Structural Integrity 52 (2024) 455–471 T. Profant et al / Structural Integrity Procedia 00 (2023) 000 – 000

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Majdoub, M.S., Sharma, P., Cagin, T., 2008b. Enhanced size-dependent piezoelectricity and elasticity in nanostructures due to the flexoelectric effect. Phys Rev B , 77(12), p.125424. Mao, S., Purohit, P.K., 2015. Defects in flexoelectric solids. J Mech Phys Solids , 84, p.95 – 115. Mao, S., Purohit, P.K., 2014. Insights into flexoelectric solids from strain-gradient elasticity. Journal of Applied Mechanics, Transactions ASME , 81(8). Mao, S., Purohit, P.K., Aravas, N., 2016. Mixed finite-element formulations in piezoelectricity and flexoelectricity. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences , 472(2190). Maranganti, R., Sharma, N.D., Sharma, P., 2006. Electromechanical coupling in nonpiezoelectric materials due to nanoscale nonlocal size effects: Green’s function solutions and embedded inclusions. Phys Rev B Condens Matter Mater Phys , 74(1), p.014110. Maranganti, R., Sharma, P., 2009. Atomistic determination of flexoelectric properties of crystalline dielectrics. Phys Rev B Condens Matter Mater Phys , 80(5), p.054109. Martin, E., Leguillon, D., Lacroix, C., 2001. A revisited criterion for crack deflection at an interface in a brittle bimaterial. Compos Sci Technol , 61(12), p.1671 – 1679. Martin, R.M., 1972. Piezoelectricity. Phys Rev B , 5(4), p.1607. Mindlin, R.D., 1968. Polarization gradient in elastic dielectrics. Int J Solids Struct , 4(6), p.637 – 642. Newnham, R.E., 2004. Properties of Materials: Anisotropy, Symmetry, Structure. Ponomareva, I., Tagantsev, A.K., Bellaiche, L., 2012. Finite-temperature flexoelectricity in ferroelectric thin films from first principles. Phys Rev B Condens Matter Mater Phys , 85(10), p.104101. Profant, T., Sládek, J., Sládek, V., Kotoul, M., 2023. Assessment of amplitude factors of asymptotic expansion at crack tip in flexoelectric solid under mode I and II loadings. Int J Solids Struct , 269, p.112194. Resta, R., 2010. Towards a bulk theory of flexoelectricity. Phys Rev Lett , 105(12), p.127601. Sharma, N.D., Landis, C.M., Sharma, P., 2010. Piezoelectric thin-film superlattices without using piezoelectric materials. J Appl Phys , 108(2), p.24304. Shu, L., Liang, R., Rao, Z., Fei, L., Ke, S., et al, 2019. Flexoelectric materials and their related applications: A focused review. Journal of Advanced Ceramics , 8(2), p.153 – 173. Sladek, J., Sladek, V., Stanak, P., Zhang, C., Tan, C.L., 2017a. Fracture mechanics analysis of size-dependent piezoelectric solids. Int J Solids Struct , 113 – 114, p.1 – 9. Sladek, J., Sladek, V., Wünsche, M., Tan, C.L., 2017b. Crack analysis of size-dependent piezoelectric solids under a thermal load. Eng Fract Mech , 182, p.187 – 201. Sladek, J., Sladek, V., Wünsche, M., Zhang, C., 2018. Effects of electric field and strain gradients on cracks in piezoelectric solids. European Journal of Mechanics - A/Solids , 71, p.187 – 198. Stengel, M., 2016. Unified ab initio formulation of flexoelectricity and strain-gradient elasticity. Phys Rev B , 93(24), p.245107. Tagantsev, A.K., 1986. Piezoelectricity and flexoelectricity in crystalline dielectrics. Phys Rev B , 34(8), p.5883. Tagantsev, A.K. (Alexander K., Yudin, P. V., Flexoelectricity in solids : from theory to applicat ions. , p.396. Toupin, R.A., 1962. Elastic materials with couple-stresses. Arch Ration Mech Anal , 11(1), p.385 – 414. Vu-Quoc, L., Tran, V.-X., 2006. Singularity analysis and fracture energy-release rate for composites: Piecewise homogeneous-anisotropic materials. John H. Argyris Memorial Issue. Part I , 195(37 – 40), p.5162 – 5197. Wang, B., Gu, Y., Zhang, S., Chen, L.Q., 2019. Flexoelectricity in solids: Progress, challenges, and perspectives. Prog Mater Sci , 106. Yan, Z., Jiang, L., 2013. Size-dependent bending and vibration behaviour of piezoelectric nanobeams due to flexoelectricity. J Phys D Appl Phys , 46(35), p.355502.