Acta Mechanica

, Volume 230, Issue 6, pp 2233–2247 | Cite as

A numerical elastic–plastic contact model for a half-space with inhomogeneous inclusions and cracks

  • Jing Yang
  • Xu Wang
  • Kun ZhouEmail author
Original Paper


The elastic–plastic contact problem plays an important role in predicting the mechanical properties of materials. In this paper, a semi-analytic solution is developed to investigate the plastic behaviors of a half-space with inhomogeneous inclusions and cracks under contact loading. In this solution, the plastic zones are determined based on the stress field equations and the von Mises yield criterion. The contact area and surface pressure distribution are obtained by solving a set of governing equations via a modified conjugate gradient method. The inhomogeneous inclusions are modeled as homogeneous inclusions with the initial eigenstrains plus unknown equivalent eigenstrains according to the Eshelby’s equivalent inclusion method. The cracks are treated as a collection of distributions of unknown dislocation densities according to the distributed dislocation technique. The case studies of a cylinder loaded against a half-space with inhomogeneous inclusions and vertical or horizontal cracks are conducted to explore the effects of the Young’s moduli and positions of the inhomogeneous inclusions on the plastic behavior of materials.


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The authors acknowledge financial support by SingaporeMaritime 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.School of Mechanical and Aerospace EngineeringNanyang Technological UniversitySingaporeSingapore
  2. 2.College of Mechanical EngineeringZhejiang University of TechnologyHangzhouChina
  3. 3.School of Mechanical and Power EngineeringEast China University of Science and TechnologyShanghaiChina

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