Effective two dimensional theories for multi-layered plates / / Miguel de Benito Delgado.

• VerfasserIn: de Benito Delgado, Miguel,
• Place / Publishing House: Berlin, Germany : : Logos Verlag Berlin GmbH,, [2019]; ©2019
• Year of Publication: 2019
• Language: English
• Series: Augsburger Shriften zur Mathematik, Physik und Informatik
• Physical Description: 1 online resource (147 pages) :; illustrations, charts; digital file(s).
• Notes: Author's doctoral thesis, Universität Augsburg -- page [1].

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.