Study on a straight dislocation in an icosahedral quasicrystal with piezoelectric effects

doi:10.1007/s10483-018-2363-9

Applied Mathematics and Mechanics (English Edition) ›› 2018, Vol. 39 ›› Issue (9): 1259-1266.doi: https://doi.org/10.1007/s10483-018-2363-9

Study on a straight dislocation in an icosahedral quasicrystal with piezoelectric effects

Lianhe LI^1,2, Guanting LIU¹

1. College of Mathematics Science, Inner Mongolia Normal University, Huhhot 010022, China;
2. Inner Mongolia Key Laboratory of Nanoscience and Nanotechnology, Inner Mongolia University, Huhhot 010021, China

收稿日期:2018-01-04 修回日期:2018-03-07 出版日期:2018-09-01 发布日期:2018-09-01
通讯作者: Lianhe LI E-mail:nmglilianhe@163.com
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11462020 and 11502123) and the Natural Science Foundation of Inner Mongolia (Nos. 2017MS0104 and 2017ZRYB003)

Study on a straight dislocation in an icosahedral quasicrystal with piezoelectric effects

Lianhe LI^1,2, Guanting LIU¹

1. College of Mathematics Science, Inner Mongolia Normal University, Huhhot 010022, China;
2. Inner Mongolia Key Laboratory of Nanoscience and Nanotechnology, Inner Mongolia University, Huhhot 010021, China

Received:2018-01-04 Revised:2018-03-07 Online:2018-09-01 Published:2018-09-01
Contact: Lianhe LI E-mail:nmglilianhe@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11462020 and 11502123) and the Natural Science Foundation of Inner Mongolia (Nos. 2017MS0104 and 2017ZRYB003)

摘要/Abstract

摘要： An electro-elastic analysis is performed on an icosahedral quasicrystal with piezoelectric effects containing a straight dislocation. The closed-form expressions for the elastic and electric fields are obtained using the extended Stroh formalism. The effects of piezoelectric constant on the phonon displacement, phason displacement, and electric potential are discussed in detail.

关键词: boundary layer type problem, interpolation, singular perturbation method, dislocation, icosahedral quasicrystal, Stroh formalism, piezoelectric effect

Abstract: An electro-elastic analysis is performed on an icosahedral quasicrystal with piezoelectric effects containing a straight dislocation. The closed-form expressions for the elastic and electric fields are obtained using the extended Stroh formalism. The effects of piezoelectric constant on the phonon displacement, phason displacement, and electric potential are discussed in detail.

Key words: piezoelectric effect, boundary layer type problem, interpolation, singular perturbation method, icosahedral quasicrystal, dislocation, Stroh formalism

中图分类号:

74C20

Lianhe LI, Guanting LIU. Study on a straight dislocation in an icosahedral quasicrystal with piezoelectric effects[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(9): 1259-1266.

参考文献

[1] SUCK, J. B., SCHREIBER, M., and HAUSSLER, P. Quasicrystals:an introduction to structure. Physical Properties and Applications, Springer, Berlin (2002)
[2] FAN, T. Y. Mathematical Theory of Elasticity of Quasicrystals and Its Applications, Springer, Beijing (2011)
[3] ATHANASIOU, N. S., POLITIS, C., SPIRLET, J. C., BASKOUTAS, S., and KAPAKLIS, V. The significance of valence electron concentration on the formation mechanism of some ternary aluminum based quasicrystals. International Journal of Modern Physics B, 16, 4665-4683(2002)
[4] FAN, T. Y. and MAI, Y. W. Elasticity theory, fracture mechanics and some thermal properties of quasicrystalline materials. Applied Mechanics Reviews, 57(5), 325-344(2004)
[5] LI, X. F. and FAN, T. Y. New method for solving elasticity problems of some planar quasicrystals and solutions. Chinese Physics Letter, 15, 278-280(1998)
[6] LI, W. and FAN, T. Y. Exact solutions of the generalized Dugdale model of two-dimensional decagonal quasicrystals. Applied Mathematics and Computation, 218(7), 3068-3071(2011)
[7] LI, Y. S., FENG, W. J., and ZHANG, C. Buckling and vibration of the two-dimensional quasicrystal cylindrical shells under axial compression. Applied Mathematical Modelling, 50, 68-91(2017)
[8] SHI, W. C. Collinear periodic cracks and/or rigid line inclusions of antiplane sliding mode in onedimensional hexagonal quasicrystal. Applied Mathematics and Computation, 215(3), 1062-1067(2009)
[9] AKMAZA, H. K. and AKINCI, Ü. On dynamic plane elasticity problems of 2D quasicrystals. Physics Letters A, 373(22), 1901-1905(2009)
[10] SLADEK, J., SLADEK, V., and PAN, E. Bending analyses of 1D orthorhombic QC plates. International Journal of Solids and Structures, 50, 3975-3983(2013)
[11] TUPHOLME, G. E. An antiplane shear crack moving in one-dimensional hexagonal quasicrystals. International Journal of Solids and Structures, 71, 255-261(2015)
[12] THIEL, P. A. and DUBOIS, J. M. QCs reaching maturity for technological applications. Materials Today, 2, 3-7(1999)
[13] RAMA, K., RAO, M., RAO, P. H., and CHAITANYA, B. S. K. Piezoelectricity in quasicrystals:a group-theoretical study. Pramana, 68, 481-487(2007)
[14] ALTAY, G. and DÖMECI, M. C. On the fundamental equations of piezoelasticity of quasicrystal media. International Journal of Solids and Structures, 49, 3255-3262(2012)
[15] LI, X. Y., LI, P. D., WU, T. H., SHI, M. X., and ZHU, Z. W. Three-dimensional fundamental solutions for one-dimensional hexagonal quasicrystal with piezoelectric effect. Physics Letters A, 378, 826-834(2014)
[16] ZHANG, L. L., ZHANG, Y. M., and GAO, Y. General solutions of plane elasticity of onedimensional orthorhombic quasicrystals with piezoelectric effect. Physics Letters A, 378, 2768-2776(2014)
[17] YU, J., GUO, J. H., PAN, E. N., and XING, Y. M. General solutions of plane problem in one-dimensional quasicrystal piezoelectric materials and its application on fracture mechanics. Applied Mathematics and Mechanics (English Edition), 36(6), 793-814(2015) https://doi.org/10.1007/s10483-015-1947-6
[18] YU, J., GUO, J. H., and XING, Y. M. Complex variable method for an anti-plane elliptical cavity of one-dimensional hexagonal piezoelectric quasicrystals. Chinese Journal of Aeronautics, 53, 1287-1295(2015)
[19] YANG, J. and LI, X. Analytic solutions of problem about a circular hole with a straight crack in one-dimensional hexagonal quasicrystals with piezoelectric effects. Theoretical and Applied Fracture Mechanics, 82, 17-24(2016)
[20] YANG, W. G., FEUERBACHER, M., TAMURA, N., DING, D. H., and WANG, R. H. Atomic model of dislocations in Al-Pd-Mn icosahedral quasicrystals. Philosophical Magazine A, 77, 1481-1497(1998)
[21] LEVINE, D., LUBENSKY, T. C., OSTLUND, S., RAMASWAMY, S., and STEINHARDT, P. J. Elasticity and dislocations in pentagonal and icosahedral quasicrystals. Physical Review Letters, 54, 1520-1523(1985)
[22] SOCOLAR, J. E. S., LUBENSKY, T. C., and STEINHARDT, P. J. Phonons, phasons and dislocations in quasicrystals. Physical Review B, 34, 3345-3360(1986)
[23] EDAGAWA, K. Elasticity, dislocations and their motion in quasicrystals. Dislocation in Solids, 13, 365-417(2007)

Study on a straight dislocation in an icosahedral quasicrystal with piezoelectric effects

Study on a straight dislocation in an icosahedral quasicrystal with piezoelectric effects

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