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Effective two dimensional theories for multi-layered plates

This work introduces a family of effective plate theories for multilayered materials with internal misfit. This is done for scaling laws ranging from Kirchhoff's theory to the linearised von Kármán one. An intermediate von Kármán-like theory is introduced to play a central interpolating role wi...

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Bibliographic Details
Main Author: de Benito Delgado, Miguel
Format: eBook
Language:English
Published: Berlin/Germany Logos Verlag Berlin 2019
Series:Augsburger Schriften zur Mathematik, Physik und Informatik
Subjects:
Gamma Convergence
Integral Calculus And Equations / Bicssc
Kirchhoff
Non-conforming Penalty Method
Elastic Plates
Effective Model Hierarchy
Online Access:
Collection: Directory of Open Access Books - Collection details see MPG.ReNa
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520 |a This work introduces a family of effective plate theories for multilayered materials with internal misfit. This is done for scaling laws ranging from Kirchhoff's theory to the linearised von Kármán one. An intermediate von Kármán-like theory is introduced to play a central interpolating role with a new parameter which switches between the adjacent regimes. After proving the necessary Gamma-convergence and compactness results, minimising configurations are characterised. Finally, the interpolating theory is numerically approximated using a discrete gradient flow and the relevant Gamma-convergence and compactness results for the discretisation are proved. This provides empirical evidence for the existence of a critical region of the parameter around which minimisers experience a stark qualitative change. 

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