Indentation of pressurized viscoplastic polymer spherical shells

Viggo Tvergaard, A. Needleman

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The indentation response of polymer spherical shells is investigated. Finite deformation analyses are carried out with the polymer characterized as a viscoelastic/viscoplastic solid. Both pressurized and unpressurized shells are considered. Attention is restricted to axisymmetric deformations with a conical indenter. The response is analyzed for various values of the shell thickness to radius ratio and various values of the internal pressure. Two sets of material parameters are considered: one set having network stiffening at a moderate strain and the other having no network stiffening until very large strains are attained. The transition from an indentation type mode of deformation to a structural mode of deformation involving bending that occurs as the indentation depth increases is studied. The results show the effects of shell thickness, internal pressure and polymer constitutive characterization on this transition and on the deformation modes in each of these regimes.
Original languageEnglish
JournalJournal of the Mechanics and Physics of Solids
Pages (from-to)16–33
Publication statusPublished - 2016


  • Indentation
  • Polymer
  • Pressurized shell
  • Viscoplasticity


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