Polymer indentation: Numerical analysis and comparison with a spherical cavity model

Viggo Tvergaard, A. Needleman

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Three dimensional analyses of indentation of a polymer by a rigid indenter are carried out. The polymer is characterized by a finite strain elastic-viscoplastic constitutive relation and the calculations are carried out with a dynamic finite element program used to simulate quasi-static behavior. Two types of indenter are considered; a conical indenter and a pyramidal indenter. For each indenter type, different values of the sharpness of the indenter are considered and two rates of indentation are analyzed. Significant sink-in is found to occur in all cases considered. The amount of sink-in is found to be smaller for sharper indenters. The calculated values of both the nominal and true hardness do not differ significantly for the two indenter shapes. An expanding spherical cavity model is also considered and the predictions of this model are compared with the finite element results for various indenter shapes and indentation rates. The spherical cavity model is found to give fairly good agreement with the predictions of the finite element analyses for the nominal polymer hardness for both indenter shapes.
Original languageEnglish
JournalJournal of the Mechanics and Physics of Solids
Issue number9
Pages (from-to)1669-1684
Publication statusPublished - 2011


  • Polymer
  • Computer simulation
  • Viscoplasticity
  • Indentation


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