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

Friedrich M, Kruzik M (2020)

Publication Type: Journal article

Publication year: 2020

Journal

Archive for Rational Mechanics and Analysis Springer Verlag (Germany)

Book Volume: 238

Pages Range: 489-540

Journal Issue: 1

DOI: 10.1007/s00205-020-01547-x

Abstract

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.

Authors with CRIS profile

Manuel Friedrich

Involved external institutions

Westfälische Wilhelms-Universität (WWU) Münster DE Germany (DE) Academy of Sciences of the Czech Republic (ASCR) / Akademie věd České republiky (AVČR) CZ Czech Republic (CZ)

How to cite

APA:

Friedrich, M., & Kruzik, M. (2020). Derivation of von Kármán Plate Theory in the Framework of Three-Dimensional Viscoelasticity. Archive for Rational Mechanics and Analysis, 238(1), 489-540. https://doi.org/10.1007/s00205-020-01547-x

MLA:

Friedrich, Manuel, and Martin Kruzik. "Derivation of von Kármán Plate Theory in the Framework of Three-Dimensional Viscoelasticity." Archive for Rational Mechanics and Analysis 238.1 (2020): 489-540.

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