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

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  • College of Mathematics Science, Inner Mongolia Normal University, Huhhot 010022, China

Received date: 2022-12-07

  Revised date: 2023-06-12

  Online published: 2023-08-28

Supported by

Project supported by the National Natural Science Foundation of China (Nos.12162027 and 11962026) and the Natural Science Key Project of Science and Technology Research in Higher Education Institutions of Inner Mongolia Autonomous Region (No.NJZZ22574)

Abstract

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 to 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.

Cite this article

Jing ZHANG, Guanting LIU . A Dugdale-Barenblatt model for elliptical orifice problem with asymmetric cracks in one-dimensional orthorhombic quasicrystals[J]. Applied Mathematics and Mechanics, 2023 , 44(9) : 1533 -1546 . DOI: 10.1007/s10483-023-3027-8

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