一维正交准晶中不对称裂纹椭圆孔问题的Dugdale-Barenblatt模型

IF 4.5 2区工程技术 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Mechanics-English Edition Pub Date : 2023-08-08 DOI:10.1007/s10483-023-3027-8

Jing Zhang, Guanting Liu

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引用次数: 0

摘要

利用Muskhelishvili方法和广义保角映射技术，将准晶体中的物理平面问题转化为正则数学问题。得到了一维正交qc中具有不对称裂纹的椭圆孔问题的解析解。采用Dugdale-Barenblatt模型，对一维正交型塑性混凝土中具有非对称裂纹的椭圆孔口裂纹尖端进行了塑性模拟。最后，精确地确定了原子内聚力区大小，得到了单裂纹和双对称裂纹椭圆孔裂纹尖端周围原子内聚力区的大小。

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A Dugdale-Barenblatt model for elliptical orifice problem with asymmetric cracks in one-dimensional orthorhombic quasicrystals

By means of Muskhelishvili’s method and the technique of generalized conformal mapping, the physical plane problems are transformed into regular mathematical problems in quasicrystals (QCs). The analytical solution of an elliptical orifice problem with asymmetric cracks in one-dimensional (1D) orthorhombic QCs is obtained. By using the Dugdale-Barenblatt model, the plastic simulation at the crack tip of the elliptical orifice with asymmetric cracks in 1D orthorhombic QCs is performed. Finally, the size of the atomic cohesive force zone is determined precisely, and the size of the atomic cohesive force zone around the crack tip of an elliptical orifice with a single crack or two symmetric cracks is obtained.

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来源期刊

Applied Mathematics and Mechanics-English Edition 数学-力学

CiteScore

6.70

自引率

9.10%

发文量

106

审稿时长

2.0 months

期刊介绍： Applied Mathematics and Mechanics is the English version of a journal on applied mathematics and mechanics published in the People''s Republic of China. Our Editorial Committee, headed by Professor Chien Weizang, Ph.D., President of Shanghai University, consists of scientists in the fields of applied mathematics and mechanics from all over China. Founded by Professor Chien Weizang in 1980, Applied Mathematics and Mechanics became a bimonthly in 1981 and then a monthly in 1985. It is a comprehensive journal presenting original research papers on mechanics, mathematical methods and modeling in mechanics as well as applied mathematics relevant to neoteric mechanics.