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Numerical study of
the Gurtin–Murdoch model for curved interfaces: benchmark
solutions and analysis of curvature-related effects
Zhilin Han, Sofia G. Mogilevskaya, Yongcheng Liang, Changzheng Cheng and Zhongrong Niu |
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Vol. 16 (2021), No. 1, 23–48
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Abstract |
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This paper presents the boundary element-based study of the two-dimensional plane strain and antiplane problems involving composite systems with the Gurtin–Murdoch interfaces of varying curvatures. Reliable benchmarks are established by comparing the solutions with the corresponding solutions for the problems involving thin interphase layers of membrane type. The comparison with a few available numerical results for the Gurtin–Murdoch interfaces is also performed. The details of the developed boundary element techniques are discussed. They involve treatment of nearly singular integrals that appear in the problems with interphase layers. The developed technique is used to study the combined effects of curvature variation and residual surface tension on the local fields in composite systems. |
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Keywords
Gurtin–Murdoch interface model, membrane-type interphase
layer, residual surface tension, boundary element method,
nearly singular integrals
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Milestones
Received: 23 July 2020
Revised: 26 August 2020
Accepted: 30 August 2020
Published: 15 March 2021
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Authors |
| Zhilin Han | |
| College of Science Donghua University Shanghai China |
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| Sofia G. Mogilevskaya | |
| Department of Civil, Environmental,
and Geo- Engineering University of Minnesota Minneapolis, MN United States |
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| Yongcheng Liang | |
| College of Science Donghua University Shanghai China |
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| Changzheng Cheng | |
| Department of Engineering
Mechanics Hefei University of Technology Hefei China |
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| Zhongrong Niu | |
| Department of Engineering
Mechanics Hefei University of Technology Hefei China |
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