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Quasistatic Viscoelasticity with Self-Contact at Large Strains

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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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Authors and Affiliations

  1. Institute of Information Theory and Automation, Czech Acad. Sci., Pod vodárenskou věží 4, 182 08, Praha 8, Czech Republic

    Stefan Krömer

  2. Mathematical Institute, Charles University, Sokolovská 83, 186 75, Praha 8, Czech Republic

    Tomáš Roubíček

  3. Institute of Thermomechanics, Czech Acad. Sci., Dolejškova 5, 182 08, Praha 8, Czech Republic

    Tomáš Roubíček

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  1. Stefan Krömer
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  2. Tomáš Roubíček
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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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  • DOI: https://doi.org/10.1007/s10659-020-09801-9

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