Linearization and computation for large-strain visco-elasticity

Patrick Dondl; Martin Jesenko; Martin Kružík; Jan Valdman; Patrick Dondl; Martin Jesenko; Martin Kružík; Jan Valdman

doi:10.3934/mine.2023030

Mathematics in Engineering

2023, Volume 5, Issue 2: 1-15. doi: 10.3934/mine.2023030

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Research article

Linearization and computation for large-strain visco-elasticity

1.
Department for Applied Mathematics, University of Freiburg, Germany
2.
University of Ljubljana, Faculty of Civil and Geodetic Engineering, Ljubljana, Slovenia
3.
Institute of Information Theory and Automation, Czech Academy of Sciences, Praha 8, Czechia
4.
Faculty of Civil Engineering, Czech Technical University, Thákurova 7, CZ-166 29 Praha 6, Czechia
5.
Department of Mathematics, Faculty of Science, University of South Bohemia, České Budějovice, Czechia

Received: 29 October 2021 Revised: 23 March 2022 Accepted: 28 March 2022 Published: 06 May 2022

Time-discrete numerical minimization schemes for simple visco-elastic materials in the Kelvin-Voigt rheology at high strains are not well posed because of the non-quasi-convexity of the dissipation functional. A possible solution is to resort to non-simple material models with higher-order gradients of deformations. However, this makes numerical computations much more involved. Here, we propose another approach that relies on local minimizers of the simple material model. Computational tests are provided that show a very good agreement between our model and the original.
- Kelvin-Voigt rheology,
- visco-elasticity,
- numerical scheme
Citation: Patrick Dondl, Martin Jesenko, Martin Kružík, Jan Valdman. Linearization and computation for large-strain visco-elasticity[J]. Mathematics in Engineering, 2023, 5(2): 1-15. doi: 10.3934/mine.2023030

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Abstract

Time-discrete numerical minimization schemes for simple visco-elastic materials in the Kelvin-Voigt rheology at high strains are not well posed because of the non-quasi-convexity of the dissipation functional. A possible solution is to resort to non-simple material models with higher-order gradients of deformations. However, this makes numerical computations much more involved. Here, we propose another approach that relies on local minimizers of the simple material model. Computational tests are provided that show a very good agreement between our model and the original.

References

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