Vol. 16, No. 1, 2021

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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

Vol. 16 (2021), No. 1, 23–48

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.

Gurtin–Murdoch interface model, membrane-type interphase layer, residual surface tension, boundary element method, nearly singular integrals
Received: 23 July 2020
Revised: 26 August 2020
Accepted: 30 August 2020
Published: 15 March 2021
Zhilin Han
College of Science
Donghua University
Sofia G. Mogilevskaya
Department of Civil, Environmental, and Geo- Engineering
University of Minnesota
Minneapolis, MN
United States
Yongcheng Liang
College of Science
Donghua University
Changzheng Cheng
Department of Engineering Mechanics
Hefei University of Technology
Zhongrong Niu
Department of Engineering Mechanics
Hefei University of Technology