Acta Mechanica

, Volume 230, Issue 12, pp 4463–4479 | Cite as

Plastic deformation of a film-substrate with inhomogeneous inclusions under contact loading

  • Jing Yang
  • Qihong Fang
  • Guozheng Kang
  • Kun ZhouEmail author
Original Paper


In this paper, a semi-analytic solution is developed to investigate the plastic deformation of a film-substrate with inhomogeneous inclusions subjected to contact loading. In this solution, the surface pressure distribution and contact area can be determined by solving a set of governing equations via a modified conjugate gradient method. The inhomogeneous inclusions and the coating material are modeled as homogeneous inclusions with known initial eigenstrains plus unknown equivalent eigenstrains, according to the Eshelby’s equivalent inclusion method. A plasticity loop and an incremental loading process are used to obtain the accumulative plastic strain iteratively. This model considers not only the interactions among the contact loading body, embedded inhomogeneous inclusions and film materials, but also the plastic deformation of the film-substrate system. This solution is of great significance to understand the plastic deformation mechanism of a film-substrate with inhomogeneous inclusions under contact loading.



The authors acknowledge financial support by Singapore Maritime Institute (Grant No: SMI-2014-MA11) and the National Natural Science Foundation of China (Grant No: 11472200).


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Mechanical EngineeringZhejiang University of TechnologyHangzhouPeople’s Republic of China
  2. 2.School of Mechanical and Aerospace EngineeringNanyang Technological UniversitySingaporeSingapore
  3. 3.State Key Laboratory of Advanced Design and Manufacturing for Vehicle BodyHunan UniversityChangshaPeople’s Republic of China
  4. 4.Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and EngineeringSouthwest Jiaotong UniversityChengduPeople’s Republic of China

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