, Volume 7, Issue 6, pp 587–602 | Cite as

Three-dimensional finite element analysis of shallow indentation of rough strain-hardening surface

  • Chenghui Gao
  • Henry ProudhonEmail author
  • Ming LiuEmail author
Open Access
Research Article


Three-dimensional finite element modeling of the contact between a rigid spherical indenter and a rough surface is presented when considering both the loading and unloading phases. The relationships among the indentation load, displacement, contact area, and mean contact pressure for both loading and unloading are established through a curve fitting using sigmoid logistic and power law functions. The contact load is proportional to the contact area, and the mean contact pressure is related to the characteristic stress, which is dependent on the material properties. The residual displacement is proportional to the maximum indentation displacement. A proportional relationship also exists for plastically dissipated energy and work conducted during loading. The surface roughness results in an effective elastic modulus calculated from an initial unloading stiffness several times larger than the true value of elastic modulus. Nonetheless, the calculated modulus under a shallow spherical indentation can still be applied for a relative comparison.


finite element modeling surface analysis contact mechanics indentation spherical indenter 



This project is supported by National Natural Science Foundation of China (Grant Nos. 51705082, 51875016), Fujian Provincial Minjiang Scholar (No. 0020-510486), and Fujian Provincial Collaborative Innovation Center for High-end Equipment Manufacturing (No. 0020-50006103).


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Authors and Affiliations

  1. 1.School of Mechanical Engineering and AutomationFuzhou UniversityFuzhouChina
  2. 2.Centre des MatériauxMINES Paris TechEvry CedexFrance

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