Linearization and computation for large-strain visco-elasticity

0558930 - ÚTIA 2024 RIV US eng J - Journal Article
Dondl, P. - Jesenko, M. - Kružík, Martin - Valdman, Jan
Linearization and computation for large-strain visco-elasticity.
Mathematics in Engineering. Roč. 5, č. 2 (2023), s. 1-15. E-ISSN 2640-3501
R&D Projects: GA MŠMT 8J21AT001; GA ČR GF21-06569K
Institutional support: RVO:67985556
Keywords : Kelvin-Voigt rheology * visco-elasticity * numerical scheme
OECD category: Applied mathematics
Impact factor: 1, year: 2022
Method of publishing: Open access
http://library.utia.cas.cz/separaty/2022/MTR/kruzik-0558930.pdf https://www.aimspress.com/article/doi/10.3934/mine.2023030

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 higherorder 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.
Permanent Link: https://hdl.handle.net/11104/0333415