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Fundamental elastic field in an infinite plane of two-dimensional piezoelectric quasicrystal subjected to multi-physics loads. (English) Zbl 1480.74073

Summary: By utilizing the extended Stroh formalism, the Green’s function of infinite plane is obtained for the problem of two-dimensional decagonal quasicrystals with the piezoelectric effect subjected to multi-physics loads. By numerical computations, the piezoelectric effect of the two-dimensional decagonal quasicrystals is revealed; the changes of the stress and displacement fields with multi-physics loads are discussed. The variation laws of material constants in stress and displacement fields are investigated. The results show that the effect of the phason field on the generalized displacement is larger than that on the generalized stress; and the effects of material parameters are different in diverse field.

MSC:

74F15 Electromagnetic effects in solid mechanics
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[1] Shechtman, D.; Blech, I.; Gratias, D.; Cahn, J. W., Metallic phase with long-range orientational order and no translational symmetry, Phys. Rev. Lett., 53, 20, 1951-1953 (1984)
[2] Stadnik, Z. M., Physical Properties of Quasicrystals (1999), Springer Science & Business Media: Springer Science & Business Media New York
[3] Socolar, J. E.S.; Lubensky, T. C.; Steinhardt, P. J., Phonons, phasons, and dislocations in quasicrystals, Phys. Rev. B, 34, 5, 3345 (1986)
[4] Ding, D. H.; Yang, W. G.; Hu, C. Z.; Wang, R. H., Generalized elasticity theory of quasicrystals, Phys. Rev. B, 48, 10, 7003 (1993)
[5] Fan, T. Y., Mathematical Theory of Elasticity of Quasicrystals and Its Applications (2011), Springer: Springer Berlin
[6] K. Kelton, P. Gibbons: Hydrogen storage in quasicrystals, MRS bulletin. 22 (1997) 69-72.; K. Kelton, P. Gibbons: Hydrogen storage in quasicrystals, MRS bulletin. 22 (1997) 69-72.
[7] Rüdiger, A.; U., Köster, Corrosion behavior of Al-Cu-Fe quasicrystals, Mater. Sci. Eng.: A, 294-296, 890-893 (2000)
[8] Kang, S.; Dubois, J.-M.; J., VonStebut, Tribological properties of quasicrystalline coatings, J. Mater. Res., 8, 2471-2481 (1993)
[9] Li, X. F.; Duan, X. Y.; Fan, T. Y.; Sun, Y. F., Elastic field for a straight dislocation in a decagonal quasicrystal, J. Phys. Condens. Matter, 11, 3, 703 (1999)
[10] Ding, D. H.; Wang, R. H.; Yang, W. G.; Hu, C. Z., General expressions for the elastic displacement fields induced by dislocations in quasicrystals, J. Phys. Condens. Matter, 7, 28, 5423 (1995)
[11] Barnett, D. M., The precise evaluation of derivatives of the anisotropic elastic Green’s functions, Phys. Status Solidi B, 49, 2, 741-748 (1972)
[12] Qin, Q. H., 2D Green’s functions of defective magnetoelectroelastic solids under thermal loading, Eng. Anal. Boundary Elem., 29, 6, 577-585 (2005) · Zbl 1182.74052
[13] Sevostianov, I.; Da Silva, U. P.; Aguiar, A. R., Green’s function for piezoelectric 622 hexagonal crystals, Int. J. Eng. Sci., 84, 18-28 (2014) · Zbl 1423.74321
[14] Ding, H. J.; Jiang, A. M.; Hou, P. F.; Chen, W. Q., Green’s functions for two-phase transversely isotropic magneto-electro-elastic media, Eng. Anal. Boundary Elem., 29, 6, 551-561 (2005) · Zbl 1182.74050
[15] Gao, Y.; Ricoeur, A., Green’s functions for infinite bi-material planes of cubic quasicrystals with imperfect interface, Phys. Lett. A, 374, 42, 4354-4358 (2010) · Zbl 1248.74003
[16] Gao, Y.; Ricoeur, A., Three-dimensional Green’s functions for two-dimensional quasi-crystal bimaterials, Proc. R. Soc. A., 467, 2133, 2622-2642 (2011) · Zbl 1227.82078
[17] Li, P. D.; Li, X. Y.; Zheng, R. F., Thermo-elastic Green’s functions for an infinite bi-material of one-dimensional hexagonal quasi-crystals, Phys. Lett. A, 377, 8, 637-642 (2013) · Zbl 1428.74177
[18] Zhang, L. L.; Wu, D.; Xu, W. S.; Yang, L. Z.; Ricoeur, A.; Wang, Z. B.; Gao, Y., Green’s functions of one-dimensional quasicrystal bi-material with piezoelectric effect, Phys. Lett. A, 380, 39, 3222-3228 (2016)
[19] Rao, K. R.M.; Rao, P. H.; Chaitanya, B. S.K., Piezoelectricity in quasicrystals: a group-theoretical study, Pramana J. Phys., 68, 3, 481-487 (2007)
[20] Rapp, Ö., Electronic Transport Properties of Quasicrystals—Experimental Results (1999), Springer: Springer Berlin
[21] Hu, C. Z.; Wang, R. H.; Ding, D. H.; Yang, W. G., Piezoelectric effects in quasicrystals, Phys. Rev. B, 56, 5, 2463-2469 (1997)
[22] Altay, G.; Dökmeci, M. C., On the fundamental equations of piezoelasticity of quasicrystal media, Int. J. Solids Struct., 49, 23, 3255-3262 (2012)
[23] Grimmer, H., The piezoelectric effect of second order in stress or strain: its form for crystals and quasicrystals of any symmetry, ActaCrystallogr. Sect. A: Found.Crystallogr., 63, 6, 441-446 (2007)
[24] Yu, J.; Guo, J.; Pan, E.; Xing, Y., General solutions of plane problem in one-dimensional quasicrystal piezoelectric materials and its application on fracture mechanics, Appl. Math. Mech., 36, 6, 793-814 (2015) · Zbl 1322.74006
[25] Li, X. Y.; Li, P. D.; Wu, T. H.; Shi, M. X.; Zhu, Z. W., Three-dimensional fundamental solutions for one-dimensional hexagonal quasicrystal with piezoelectric effect, Phys. Lett. A, 378, 10, 826-834 (2014) · Zbl 1323.82048
[26] Wang, R. H.; Hu, C. Z., Symmetry groups, physical property tensors, elasticity and dislocation in quasicrystals, Rep. Prog. Phys, 63, 1-39 (2000)
[27] Fan, T. Y., Mathematical theory and methods of mechanics of quasicrystalline materials, Engineering, 5, 407-448 (2013)
[28] Hwu, C., Anisotropic Elastic Plates (2010), Springer: Springer New York · Zbl 1196.74001
[29] Qin, Q. H., Green’s Function and Boundary Elements of Multifield Materials (2010), Elsevier
[30] Ting, T. C., Anisotropic Elasticity: Theory and Applications, 235 (1996), Oxford University Press on Demand · Zbl 0883.73001
[31] Lee, J. S.; Jiang, L. Z., Exact electroelastic analysis of piezoelectric laminae via state space approach, Int. J. Solids Struct., 33, 7, 977-990 (1996) · Zbl 0919.73291
[32] Chernikov, M. A.; Ott, H. R.; Bianchi, A.; Miglion, A.; Darling, T. W., Elastic moduli of a single quasicrystal of decagonal Al-Ni-Co: evidence for transverse elastic isotropy, Phys. Rev. Lett., 80, 2, 321-324 (1998)
[33] Jeong, H. C.; Steinhardt, P. J., Finite-temperature elasticity phase transition in decagonal quasicrystals, Phys. Rev. B., 48, 13, 9394-9403 (1993)
[34] Yang, L. Z.; Y., Gao; Pan, E.; Waksmanski, N., An exact solution for a multilayered two-dimensional decagonal quasicrystal plate, Int. J. Solids Struct., 51, 9, 1737-1749 (2014)
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