Effective elastic properties of one-dimensional hexagonal quasicrystal composites

doi:10.1007/s10483-021-2778-8

Applied Mathematics and Mechanics (English Edition) ›› 2021, Vol. 42 ›› Issue (10): 1439-1448.doi: https://doi.org/10.1007/s10483-021-2778-8

Effective elastic properties of one-dimensional hexagonal quasicrystal composites

Shuang LI, Lianhe LI

College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, China

收稿日期:2021-04-21 修回日期:2021-06-30 发布日期:2021-09-23
通讯作者: Lianhe LI, E-mail:nmglilianhe@163.com
基金资助:
the National Natural Science Foundation of China (Nos. 11962026, 12002175, 12162027, and 62161045) and the Inner Mongolia Natural Science Foundation of China (No. 2020MS01018)

Effective elastic properties of one-dimensional hexagonal quasicrystal composites

Shuang LI, Lianhe LI

College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, China

Received:2021-04-21 Revised:2021-06-30 Published:2021-09-23
Contact: Lianhe LI, E-mail:nmglilianhe@163.com
Supported by:
the National Natural Science Foundation of China (Nos. 11962026, 12002175, 12162027, and 62161045) and the Inner Mongolia Natural Science Foundation of China (No. 2020MS01018)

摘要/Abstract

摘要： The explicit expression of Eshelby tensors for one-dimensional (1D) hexagonal quasicrystal composites is presented by using Green's function method. The closed forms of Eshelby tensors in the special cases of spheroid, elliptic cylinder, ribbon-like, penny-shaped, and rod-shaped inclusions embedded in 1D hexagonal quasicrystal matrices are given. As an application of Eshelby tensors, the analytical expressions for the effective properties of the 1D hexagonal quasicrystal composites are derived based on the Mori-Tanaka method. The effects of the volume fraction of the inclusion on the elastic properties of the composite materials are discussed.

关键词: one-dimensional (1D) hexagonal quasicrystal, Eshelby tensor, Mori-Tanaka method

Abstract: The explicit expression of Eshelby tensors for one-dimensional (1D) hexagonal quasicrystal composites is presented by using Green's function method. The closed forms of Eshelby tensors in the special cases of spheroid, elliptic cylinder, ribbon-like, penny-shaped, and rod-shaped inclusions embedded in 1D hexagonal quasicrystal matrices are given. As an application of Eshelby tensors, the analytical expressions for the effective properties of the 1D hexagonal quasicrystal composites are derived based on the Mori-Tanaka method. The effects of the volume fraction of the inclusion on the elastic properties of the composite materials are discussed.

Key words: one-dimensional (1D) hexagonal quasicrystal, Eshelby tensor, Mori-Tanaka method

中图分类号:

52C23
74A40

Shuang LI, Lianhe LI. Effective elastic properties of one-dimensional hexagonal quasicrystal composites[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(10): 1439-1448.

参考文献

[1] SHECHTMAN, D., BLECH, I., GRATIAS, D., and CAHN, J. W. Metallic phase with long-range orientational order and no translational symmetry. Physical Review Letters, 53(20), 1951-1953(1984)
[2] DUBOIS, J. M., KANG, S. S., and STEBUT, J. V. Quasicrystalline low-friction coatings. Journal of Materials Science Letters, 10(9), 537-541(1991)
[3] DUBOIS, J. M., BRUNET, P., COSTIN, W., and MERSTALLINGER, A. Friction and fretting on quasicrystals under vacuum. Journal of Non-Crystalline Solids, 334, 475-480(2004)
[4] DING, D. H., YANG, W. G., HU, C. Z., and WANG, R. H. Generalized elasticity theory of quasicrystals. Physical Review B, 48(10), 7003-7009(1993)
[5] YANG, W. G., WANG, R. H., DING, D. H., and HU, C. Z. Linear elasticity theory of cubic quasicrystals. Physical Review B, 48(10), 6999-7002(1993)
[6] HU, C. Z., WANG, R. H., YANG, W. G., and DING, D. H. Point groups and elastic properties of two-dimensional quasicrystals. Acta Crystallographica, A52, 251-256(1996)
[7] HU, C. Z., WANG, R. H., and DING, D. H. Symmetry groups, physical property tensors, elasticity and dislocations in quasicrystals. Reports on Progress in Physics, 63, 1-39(2000)
[8] FAN, T. Y. Mathematical Theory of Elasticity of Quasicrystals and Its Applications, Science Press, Beijing (2011)
[9] LI, X. F. and FAN, T. Y. A straight dislocation in one-dimensional hexagonal quasicrystals. Physica Status Solidi, 212(1), 19-26(1999)
[10] FAN, T. Y., LI, X. F., and SUN, Y. F. A moving screw dislocation in a one-dimensional hexagonal quasicrystal. Acta Physica Sinica (Overseas Edition), 8(4), 288-295(1999)
[11] LI, X. Y. Elastic field in an infinite medium of one-dimensional hexagonal quasicrystal with a planar crack. International Journal of Solids and Structures, 51(6), 1442-1455(2014)
[12] YANG, J., LI, X., and DING, S. H. Anti-plane analysis of a circular hole with three unequal cracks in one-dimensional hexagonal piezoelectric quasicrystals Chinese Journal of Engineering Mathematics, 33(2), 185-198(2016)
[13] SHI, W. C. Collinear periodic cracks and/or rigid line inclusions of antiplane sliding mode in one-dimensional hexagonal quasicrystal. Applied Mathematics and Computation, 215, 1062-1067(2009)
[14] GAO, Y. and RICOEUR, A. Three-dimensional analysis of a spheroidal inclusion in a twodimensional quasicrystal body. Philosophical Magazine, 92(34), 4334-4353(2012)
[15] WANG, X. and SCHIAVONE, P. Decagonal quasicrystalline elliptical inclusions under thermomechanical loadings. Acta Mechanica Solida Sinica, 27(5), 518-530(2014)
[16] GUO, J. H., ZHANG, Z. Y., and XING, Y. M. Antiplane analysis for an elliptical inclusion in 1D hexagonal piezoelectric quasicrystal composites. Philosophical Magazine, 96(4), 349-369(2016)
[17] GUO, J. H. and PAN, E. Three-phase cylinder model of one-dimensional hexagonal piezoelectric quasi-crystal composites. Journal of Applied Mechanics, 83(8), 081007(2016)
[18] WANG, Y. B. and GUO, J. H. Effective electroelastic constants for three-phase confocal elliptical cylinder model in piezoelectric quasicrystal composites. Applied Mathematics and Mechanics (English Edition), 39(6), 797-812(2018) https://doi.org/10.1007/s10483-018-2336-9
[19] ESHELBY, J. D. The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proceedings of the Royal Society of London, 241(1226), 376-396(1957)
[20] MORI, T. and TANAKA, K. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurgica, 21(5), 571-574(1973)
[21] BENVENISTE, Y. A new approach to the application of Mori-Tanaka's theory in composite materials. Mechanics of Materials, 6(2), 147-157(1987)
[22] FAN, T. Y. Mathematical theory and methods of mechanics of quasicrystalline materials. Engineering, 5(4), 407-448(2013)
[23] SLADEK, J., SLADEK, V., and PAN, E. Bending analysis of 1D orthorhombic quasicrystal plates. International Journal of Solids and Structures, 50(24), 3975-3983(2013)
[24] LOTHE, J. and BARNETT, D. M. Integral formalism for surface waves in piezoelectric crystals:existence considerations. The Journal of Applied Physics, 47, 1799-1807(1976)
[25] DEEG, W. F. The Analysis of Dislocation, Crack, and Inclusion Problems in Piezoelectric Solids, Ph. D. dissertation, Stanford University, Stanford (1980)
[26] MURA, T. Micromechanics of Defects in Solids, 2nd ed., Martinus Nijhoff Publishers, Amsterdam (1987)
[27] DUNN, M. L. and TAYA, M. Micromechanics predictions of the effective electroelastic moduli of piezoelectric composites. International Journal of Solids and Structures, 30(2), 161-175(1993)
[28] DUNN, M. L. and TAYA, M. Electromechanical properties of porous piezoelectric ceramics. Journal of the American Ceramic Society, 76(7), 1697-1706(1993)
[29] AGUIAR, A. R., BRAVO-CASTILLERO, J., and SILVA, U. P. D. Application of Mori-Tanaka method in 3-1 porous piezoelectric medium of crystal class 6. International Journal of Engineering Science, 123, 36-50(2018)

Effective elastic properties of one-dimensional hexagonal quasicrystal composites

Effective elastic properties of one-dimensional hexagonal quasicrystal composites

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