Derivation of a one-dimensional von Kármán theory for viscoelastic ribbons (Q2075809)
From MaRDI portal
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Derivation of a one-dimensional von Kármán theory for viscoelastic ribbons |
scientific article |
Statements
Derivation of a one-dimensional von Kármán theory for viscoelastic ribbons (English)
0 references
16 February 2022
0 references
The one- and two-dimensional models of plates are introduced. The two-dimensional model of viscoelastic von Kármán plates in the Kelvin-Voigt rheology derived from a three-dimensional model is considered. A transition to an one-dimensional model is performed when the width of the plate goes to zero. An effective one-dimensional model for a viscoelastic ribbon is provided using the abstract theory of gradient flows in metric spaces. One of the main goal is to prove the existence of solutions to the one-dimensional model. The existence of solutions to the one-dimensional gradient flow is shown by relying on the theory of generalized minimizing movements. Besides the convergence of the two-dimensional solutions to the one-dimensional solutions, also analogous results for the semi-discretized problems and for vanishing time step and vanishing width of the plate are obtained.
0 references
effective material model
0 references
finite-strain Kelvin-Voigt material
0 references
von Karman plate
0 references
metric gradient flow
0 references
dissipative distance
0 references
maximal slope curve
0 references
gamma-convergence
0 references
0 references
0 references
0 references
0 references
0 references
0 references
