Quasistatic Viscoelasticity with Self-Contact at Large Strains

Abstract

The frame-indifferent viscoelasticity in Kelvin-Voigt rheology at large strains is formulated in the reference configuration (i.e., using the Lagrangian approach) considering also the possible self-contact in the actual deformed configuration. Using the concept of 2nd-grade nonsimple materials, existence of certain weak solutions which are a.e. injective is shown by converging an approximate solution obtained by the implicit time discretisation.

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Acknowledgements

This research has been supported by the Czech Science Foundation through the grants 17-04301S (in particular concerning dissipative evolutionary systems), 19-29646L (especially pertaining large strains in materials science) and 19-04956S (in particular concerning nonlinear behavior of structures). Also the institutional support RVO:61388998 is acknowledged.

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Correspondence to Stefan Krömer.

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Krömer, S., Roubíček, T. Quasistatic Viscoelasticity with Self-Contact at Large Strains. J Elast 142, 433–445 (2020). https://doi.org/10.1007/s10659-020-09801-9

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Keywords

  • Kelvin-Voigt material
  • Frame indifference
  • Non-selfinterpenetration
  • Implicit time discretisation
  • Lagrangian description
  • Pullback

Mathematics Subject Classification

  • 35K86
  • 35Q74
  • 74A30
  • 74B20
  • 74M15