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, Zhongrong Niu

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)22-47
Number of pages26
JournalJournal of Mechanics of Materials and Structures
Volume16
Issue number1
DOIs
StatePublished - 2021

Bibliographical note

Funding Information:
Zhilin Han gratefully acknowledges the support from the Fundamental Research Funds for the Central Universities (20D110913) and National Natural Science Foundation of China (NSFC number 12002084). Sofia G. Mogilevskaya gratefully acknowledges the support provided by the Theodore W. Bennett Chair, University of Minnesota. Yongcheng Liang gratefully acknowledges the support by NSFC number 51671126. Changzheng Cheng gratefully acknowledges the support by the Fundamental Research Funds, the Central Universities (PA2019GDQT0016), and NSFC number 11772114.

Publisher Copyright:
© 2021. All Rights Reserved.

Keywords

  • Gurtin–Murdoch interface model
  • boundary element method
  • membrane-type interphase layer
  • nearly singular integrals
  • residual surface tension

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