0493138 20240103220442.420180910235959.9 85055251741 000443341200029 10.1137/17M1131428 31 s. P cav_un_epca*02575970036-1410504 (2018)4426-4456SIAM Society for Industrial and Applied Mathematics viscoelasticity metric gradient flows curves of maximal slope minimizing movements cav_un_auth*0327068 Friedrich M. DE cav_un_auth*0101142 Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory 50 Kružík Martin UTIA-B Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2018/MTR/kruzik-0493138.pdf cav_un_auth*0342514 7AMB16AT015 GA MŠk GF16-34894L GA ČR CZ cav_un_auth*0331681 We formulate a quasistatic nonlinear model for nonsimple viscoelastic materials at a finite-strain setting in the Kelvin-Voigt rheology where the viscosity stress tensor complies with the principle of time-continuous frame indifference. We identify weak solutions in the nonlinear framework as limits of time-incremental problems for vanishing time increment. Moreover, we show that linearization around the identity leads to the standard system for linearized viscoelasticity and that solutions of the nonlinear system converge in a suitable sense to solutions of the linear one. The same property holds for time-discrete approximations, and we provide a corresponding commutativity result. Our main tools are the theory of gradient flows in metric spaces and Γ-convergence. WOS BA 10000 10100 10101 2019 2 4 A hod 4ah 20231122143400.7 RVO:67985556 http://hdl.handle.net/11104/0287001 1 1 Department of Decision Making Theory UTIA-B 10102 MATHEMATICS, APPLIED S 1 Article Mathematics Applied MATHEMATICS.APPLIED 1.845 0.28 13.2 0.0151 1.525 6078 2.396 1.235 200 Q2 91.304 63.6 Q1* Q1* 1.07 Q2 63.583 2018 Soubory v repozitáři: kruzik-0493138.pdf 85055251741 SCOPUS PUBMED 000443341200029 WOS cav_un_epca*0257597 SIAM Journal on Mathematical Analysis 0036-1410 1095-7154 Roč. 50 č. 4 2018 4426 4456 SIAM Society for Industrial and Applied Mathematics