Two kinds of contact problems in three-dimensional icosahedral quasicrystals

doi:10.1007/s10483-015-2006-6

Applied Mathematics and Mechanics (English Edition) ›› 2015, Vol. 36 ›› Issue (12): 1569-1580.doi: https://doi.org/10.1007/s10483-015-2006-6

Two kinds of contact problems in three-dimensional icosahedral quasicrystals

Xuefen ZHAO^1,2, Xing LI¹, Shenghu DING¹

1. School of Mathematics and Computer Science, Ningxia University, Yinchuan 750021, China;
2. Xinhua College, Ningxia University, Yinchuan 750021, China

收稿日期:2015-01-08 修回日期:2015-05-07 出版日期:2015-12-01 发布日期:2015-12-01
通讯作者: Xing LI E-mail:li_x@nxu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China(Nos. 11362018, 11261045, and 11261401) and the Specialized Research Fund for the Doctoral Program of Higher Education of China(No. 20116401110002)

Two kinds of contact problems in three-dimensional icosahedral quasicrystals

Xuefen ZHAO^1,2, Xing LI¹, Shenghu DING¹

1. School of Mathematics and Computer Science, Ningxia University, Yinchuan 750021, China;
2. Xinhua College, Ningxia University, Yinchuan 750021, China

Received:2015-01-08 Revised:2015-05-07 Online:2015-12-01 Published:2015-12-01
Contact: Xing LI E-mail:li_x@nxu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China(Nos. 11362018, 11261045, and 11261401) and the Specialized Research Fund for the Doctoral Program of Higher Education of China(No. 20116401110002)

摘要/Abstract

摘要： Two kinds of contact problems, i.e., the frictional contact problem and the adhesive contact problem, in three-dimensional(3D) icosahedral quasicrystals are discussed by a complex variable function method. For the frictional contact problem, the contact stress exhibits power singularities at the edge of the contact zone. For the adhesive contact problem, the contact stress exhibits oscillatory singularities at the edge of the contact zone. The numerical examples show that for the two kinds of contact problems, the contact stress exhibits singularities, and reaches the maximum value at the edge of the contact zone. The phonon-phason coupling constant has a significant effect on the contact stress intensity, while has little impact on the contact stress distribution regulation. The results are consistent with those of the classical elastic materials when the phonon-phason coupling constant is 0. For the adhesive contact problem, the indentation force has positive correlation with the contact displacement, but the phonon-phason coupling constant impact is barely perceptible. The validity of the conclusions is verified.

关键词: Riemann-Hilbert problem, three-dimensional(3D) icosahedral quasicrystal, complex variable function method, contact problem, singularity

Abstract: Two kinds of contact problems, i.e., the frictional contact problem and the adhesive contact problem, in three-dimensional(3D) icosahedral quasicrystals are discussed by a complex variable function method. For the frictional contact problem, the contact stress exhibits power singularities at the edge of the contact zone. For the adhesive contact problem, the contact stress exhibits oscillatory singularities at the edge of the contact zone. The numerical examples show that for the two kinds of contact problems, the contact stress exhibits singularities, and reaches the maximum value at the edge of the contact zone. The phonon-phason coupling constant has a significant effect on the contact stress intensity, while has little impact on the contact stress distribution regulation. The results are consistent with those of the classical elastic materials when the phonon-phason coupling constant is 0. For the adhesive contact problem, the indentation force has positive correlation with the contact displacement, but the phonon-phason coupling constant impact is barely perceptible. The validity of the conclusions is verified.

Key words: complex variable function method, Riemann-Hilbert problem, contact problem, three-dimensional(3D) icosahedral quasicrystal, singularity

中图分类号:

O346.1

Xuefen ZHAO, Xing LI, Shenghu DING. Two kinds of contact problems in three-dimensional icosahedral quasicrystals[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(12): 1569-1580.

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Two kinds of contact problems in three-dimensional icosahedral quasicrystals

Two kinds of contact problems in three-dimensional icosahedral quasicrystals

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