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Journal Article

Derivation of von Kármán Plate Theory in the Framework of Three-Dimensional Viscoelasticity

Friedrich M., Kružík Martin

: Archive for Rational Mechanics and Analysis vol.238, 1 (2020), p. 489-540

: GA17-04301S, GA ČR, GF19-29646L, GA ČR

: von karman viscoelastic plates, gradient flow in metric spaces

: 10.1007/s00205-020-01547-x

: http://library.utia.cas.cz/separaty/2020/MTR/kruzik-0531495.pdf

: https://link.springer.com/article/10.1007/s00205-020-01547-x

(eng): 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.

: BA

: 10102

2019-01-07 08:39