journal article·2026-01

Green’s Function for Two-Dimensional Piezoelectric Quasicrystals Containing Elliptical Defects

Tangrui Lai, Xiaoyu Fu, Xiang Mu, Liangliang Zhang, Yang Gao

Acta Mechanica Solida Sinica· Volume 39· Issue 1
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OpenAlex topics: Quasicrystal Structures and Properties · Liquid Crystal Research Advancements

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References (42)

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1. Pasternak V, Sulym H, Pasternak IM, et al. Extended Stroh formalism for plane problems of thermoelasticity of quasicrystals with applications to Green’s functions and fracture mechanics. Int J Eng Sci. 2024;203: 104124.
2. Shechtman D, Blech I, Gratias D, et al. Metallic phase with long-range orientational order and no translational symmetry. Phys Rev Lett. 1984;53(20):1951.10.1103/PhysRevLett.53.1951 ↗
3. Dubois JM. Properties-and applications of quasicrystals and complex metallic alloys. Chem Soc Rev. 2012;41(20):6760–77.10.1039/c2cs35110b ↗
4. Hu CZ, Wang RH, Ding DH, et al. Piezoelectric effects in quasicrystals. Phys Rev B. 1997;56(5):2463.10.1103/PhysRevB.56.2463 ↗
5. Li LH, Liu GT. The interaction between the dislocation and elliptic notch in one-dimensional hexagonal quasi-crystals. Mod Phys Lett B. 2009;23(28):3397–407.10.1142/S0217984909021430 ↗
6. Mu X, Zhu ZW, Zhang LL, et al. Coupled Solutions for Two-Dimensional Decagonal Piezoelectric Quasicrystals with Cracks. Acta Mech Solida Sin. 2024;38:115–24.10.1007/s10338-024-00517-0 ↗
7. Wang X, Schiavone P. Unconventional cracks with dislocation-free zones. Int J Solids Struct. 2022;243: 111566.10.1016/j.ijsolstr.2022.111566 ↗
8. Wang X, Schiavone P. An unstressed screw dislocation pileup against two circular elastic inhomogeneities. Int J Solids Struct. 2022;259: 112011.10.1016/j.ijsolstr.2022.112011 ↗
9. Wang X, Pan E, Chung P. On a semi-infinite crack penetrating a piezoelectric circular inhomogeneity with a viscous interface. Int J Solids Struct. 2009;46(1):203–16.10.1016/j.ijsolstr.2008.08.022 ↗
10. Wang X, Pan E, Chung P. Misfit dislocation dipoles in wire composite solids. Int J Plast. 2010;26(9):1415–20.10.1016/j.ijplas.2010.03.004 ↗
11. Li LH, Liu GT. Stroh formalism for icosahedral quasicrystal and its application. Phys Lett A. 2012;376(8–9):987–90.10.1016/j.physleta.2012.01.027 ↗
12. Zhang ZG, Ding SH, Li X. A spheroidal inclusion within a 1D hexagonal piezoelectric quasicrystal. Arch Appl Mech. 2020;90:1039–58.10.1007/s00419-020-01657-8 ↗
13. Zhang ZG, Li X, Ding SH. Analytical solution of the interference between elliptical inclusion and screw dislocation in one-dimensional hexagonal piezoelectric quasicrystal. Crystals. 2023;13(10):1419.10.3390/cryst13101419 ↗
14. Gao Y, Ricoeur A, Zhang LL. Plane problems of cubic quasicrystal media with an elliptic hole or a crack. Phys Lett A. 2011;375(28–29):2775–81.10.1016/j.physleta.2011.06.003 ↗
15. Zhao MH, Li Y, Fan CY, et al. Analysis of arbitrarily shaped planar cracks in two-dimensional hexagonal quasicrystals with thermal effects. Part I: theoretical solutions. Appl Math Modell. 2018;57:583–602.10.1016/j.apm.2017.07.023 ↗
16. Li XY, Wang T, Zheng RF, et al. Fundamental thermo-electro-elastic solutions for 1D hexagonal QC. ZAMM-J Appl Math Mech/Zeitschrift für Angewandte Mathematik und Mechanik. 2015;95(5):457–68.
17. Guo JH, Liu GT. Analytic solutions to problem of elliptic hole with two straight cracks in one-dimensional hexagonal quasicrystals. Appl Math Mech. 2008;29(4):485–93.10.1007/s10483-008-0406-x ↗
18. Loboda V, Sheveleva A, Komarov O, et al. Arbitrary number of electrically permeable cracks on the interface between two one-dimensional piezoelectric quasicrystals with piezoelectric effect. Eng Fract Mech. 2022;276: 108878.10.1016/j.engfracmech.2022.108878 ↗
19. Li LH, Cui XW, Guo JH. Interaction between a screw dislocation and an elliptical hole with two asymmetrical cracks in a one-dimensional hexagonal quasicrystal with piezoelectric effect. Appl Math Mech. 2020;41(6):899–908.10.1007/s10483-020-2615-6 ↗
20. Zhou YB, Li XF. A Yoffe-type moving crack in one-dimensional hexagonal piezoelectric quasicrystals. Appl Math Model. 2019;65:148–63.10.1016/j.apm.2018.08.005 ↗
21. Mu X, Xu W, Zhu Z, et al. Image force in cubic piezoelectric quasicrystal half-space and bi-material composite space. Acta Mech. 2023;234(11):5331–47.10.1007/s00707-023-03651-x ↗
22. Mu X, Hu ZM, Zhu ZW, et al. Analytical solutions for two-dimensional piezoelectric quasicrystal composite wedges and spaces. Mech Adv Mater Struct. 2023;30(21):4303–16.10.1080/15376494.2022.2092796 ↗
23. Jiang YJ, Liao LJ, Chen G, et al. The electric susceptibility, piezoelectric, elastic, photoelastic, Brillouin and Raman tensors for point groups with twelvefold rotation axes. Acta Crystallogr A. 1992;48(3):350–2.10.1107/S0108767391013892 ↗
24. Hu K, Gao C, Fu J, et al. Interference of two cylindrical inclusions in an infinite piezoelectric quasicrystal medium. J Inner Mong Univ Technol. 2023;3:230–6.
25. Yu J, Guo JH, Pan E, et al. General solutions of plane problem in one-dimensional quasicrystal piezoelectric materials and its application on fracture mechanics. Appl Math Mech. 2015;36(6):793–814.10.1007/s10483-015-1949-6 ↗
26. Guo JH, Lu ZX. Exact solution of four cracks originating from an elliptical hole in one-dimensional hexagonal quasicrystals. Appl Math Comput. 2011;217(22):9397–403.
27. Li Y, Li X, Su G, et al. Influence of deformation process on mechanical, electrical and friction and wear properties of MnS/Cu composite materials. J Inner Mong Univ Technol (Nat Sci Ed). 2024;43(05):394–401.
28. Hwu C. Anisotropic elastic plates. Boston: Springer Science & Business Media; 2010.10.1007/978-1-4419-5915-7 ↗
29. Stroh AN. Steady state problems in anisotropic elasticity. J Math Phys. 1962;41(1–4):77–103.10.1002/sapm196241177 ↗
30. Pan E. Green’s functions for geophysics: a review. Rep Prog Phys. 2019;82(10): 106801.10.1088/1361-6633/ab1877 ↗
31. Fu XY, Mu X, Zhang JM, et al. Green’s functions of two-dimensional piezoelectric quasicrystal in half-space and bimaterials. Appl Math Mech. 2023;44(2):237–54.10.1007/s10483-023-2955-9 ↗
32. Wu D, Zhang LL, Xu WS, et al. Electroelastic Green’s function of one-dimensional piezoelectric quasicrystals subjected to multi-physics loads. J Intell Mater Syst Struct. 2017;28(12):1651–61.10.1177/1045389X16679290 ↗
33. Xu WS, Wu D, Gao Y. Fundamental elastic field in an infinite plane of two-dimensional piezoelectric quasicrystal subjected to multi-physics loads. Appl Math Model. 2017;52:186–96.10.1016/j.apm.2017.07.014 ↗
34. Zhang LL, Wu D, Xu WS, et al. Green’s functions of one-dimensional quasicrystal bi-material with piezoelectric effect. Phys Lett A. 2016;380(39):3222–8.10.1016/j.physleta.2016.07.043 ↗
35. Dunn ML, Wienecke HA. Green’s functions for transversely isotropic piezoelectric solids. Int J Solids Struct. 1996;33(30):4571–81.10.1016/0020-7683(95)00282-0 ↗
36. Liu JX, Liu XL, Zhao YB. Green’s functions for anisotropic magnetoelectroelastic solids with an elliptical cavity or a crack. Int J Eng Sci. 2001;39(12):1405–18.
37. Fan TY. Mathematical theory and methods of mechanics of quasicrystalline materials. Engineering. 2013;5:407–48.10.4236/eng.2013.54053 ↗
38. Gao Y, Zhao BS. General solutions of three-dimensional problems for two-dimensional quasicrystals. Appl Math Model. 2009;33(8):3382–91.10.1016/j.apm.2008.11.001 ↗
39. Li Y, Yang LZ, Gao Y, et al. Cylindrical bending analysis of a layered two-dimensional piezoelectric quasicrystal nanoplate. J Intell Mater Syst Struct. 2018;29(12):2660–76.10.1177/1045389X18770920 ↗
40. Yang LZ, Li Y, Gao Y, et al. Three-dimensional exact electric-elastic analysis of a multilayered two-dimensional decagonal quasicrystal plate subjected to patch loading. Compos Struct. 2017;171:198–216.10.1016/j.compstruct.2017.02.036 ↗
41. Pan E. Three-dimensional Green’s functions in anisotropic magneto-electro-elastic bimaterials. Zeitschrift für angewandte Mathematik und Physik ZAMP. 2002;53(5):815–38.10.1007/s00033-002-8184-1 ↗
42. Ting TCT, Horgan CO. Anisotropic elasticity: theory and applications. J Appl Mech. 1996;63(4):1056–1056. https://doi.org/10.1115/1.2787237.10.1115/1.2787237 ↗