Modeling elasto-plastic indentation on layered materials using the equivalent inclusion method

W. Wayne Chen, Kun Zhou, Leon M. Keer, Q. Jane Wang

Research output: Contribution to journalArticlepeer-review

66 Scopus citations


This paper develops a fast semi-analytical model for solving the three-dimensional elasto-plastic contact problems involving layered materials using the Equivalent Inclusion Method (EIM). The analytical elastic solutions of a half-space subjected to a unit surface pressure and a unit subsurface eigenstrain are employed in this model; the topmost layer is simulated by an equivalent inclusion with fictitious eigenstrain. Accumulative plastic deformation is determined by a procedure involving an iterative plasticity loop and an incremental loading process. Algorithms of the fast Fourier transform (FFT) and the Conjugate Gradient Method (CGM) are utilized to improve the computation efficiency. An analytical elastic solution of layered body contact (O'Sullivan and King, 1988) and an indentation experiment result involving a layered substrate (Michler et al., 1999) are used to examine the accuracy of this model. Comparisons between numerical results from the present model and a commercial FEM software (Abaqus) are also presented. Case studies of a rigid ball loaded against a layered elasto-plastic half-space are conducted to explore the effects of the modulus, yield strength, and thickness of the coating on the hardness, stiffness, and plastic deformation of the composite body.

Original languageEnglish (US)
Pages (from-to)2841-2854
Number of pages14
JournalInternational Journal of Solids and Structures
Issue number20
StatePublished - Oct 1 2010


  • Contact
  • Elasto-plastic
  • Equivalent inclusion method
  • Layer

ASJC Scopus subject areas

  • Modeling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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