0531495 20240103224314.920200810235959.9 85086593706 000540923400001 10.1007/s00205-020-01547-x 52 s. P cav_un_epca*02561870003-95272381 (2020)489-540Springer von karman viscoelastic plates gradient flow in metric spaces cav_un_auth*0327068 Friedrich M. DE cav_un_auth*0101142 Kružík Martin UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR K Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2020/MTR/kruzik-0531495.pdf https://link.springer.com/article/10.1007/s00205-020-01547-x GA17-04301S GA ČR cav_un_auth*0347023 GF19-29646L GA ČR CZ cav_un_auth*0385134 We apply a quasistatic nonlinear model for nonsimple viscoelastic materials at a finite-strain setting in Kelvin’s-Voigt’s rheology to derive a viscoelastic plate model of von Kármán type. We start from time-discrete solutions to a model of three-dimensional viscoelasticity considered in Friedrich and Kružík (SIAM J Math Anal 50:4426–4456, 2018) where the viscosity stress tensor complies with the principle of time-continuous frame-indifference. Combining the derivation of nonlinear plate theory by Friesecke, James and Müller (Commun Pure Appl Math 55:1461–1506, 2002. Arch Ration Mech Anal 180:183–236, 2006), and the abstract theory of gradient flows in metric spaces by Sandier and Serfaty (Commun Pure Appl Math 57:1627–1672, 2004), we perform a dimension-reduction from three dimensions to two dimensions and identify weak solutions of viscoelastic form of von Kármán plates. WOS BA 10000 10100 10102 2021 2 RVO:67985556 http://hdl.handle.net/11104/0310652 S 3+4 Article Mathematics Applied|Mechanics A MATHEMATICS.APPLIED|MECHANICS 3.236 0.81 20.4 0.01614 2.519 11527 118 2.933 37.61 2.56 1026 Q1 2.558 168 Q1 98.241 73.3 Q1* Q1* 1.18 Q1 87.736 2020 85086593706 SCOPUS PUBMED 000540923400001 WOS cav_un_epca*0256187 Archive for Rational Mechanics and Analysis 0003-9527 1432-0673 Roč. 238 č. 1 2020 489 540 Springer