The mathematics of thin structures

Author:

Babadjian Jean-François,Di Fratta Giovanni,Fonseca Irene,Francfort Gilles,Lewicka Marta,Muratov Cyrill

Abstract

This article offers various mathematical contributions to the behavior of thin films. The common thread is to view thin film behavior as the variational limit of a three-dimensional domain with a related behavior when the thickness of that domain vanishes. After a short review in Section 1 of the various regimes that can arise when such an asymptotic process is performed in the classical elastic case, giving rise to various well-known models in plate theory (membrane, bending, Von Karmann, etc…), the other sections address various extensions of those initial results. Section 2 adds brittleness and delamination and investigates the brittle membrane regime. Sections 4 and 5 focus on micromagnetics, rather than elasticity, this once again in the membrane regime and discuss magnetic skyrmions and domain walls, respectively. Finally, Section 3 revisits the classical setting in a non-Euclidean setting induced by the presence of a pre-strain in the model.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics

Reference218 articles.

1. Existence and regularity for mixtures of micromagnetic materials;Acerbi, Emilio;Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.,2006

2. A. Aharoni, Introduction to the Theory of Ferromagnetism, volume 109 of International Series of Monographs on Physics, Oxford University Press, New York, 2nd ed., 2001.

3. The metric-restricted inverse design problem;Acharya, Amit;Nonlinearity,2016

4. S. Almi and E. Tasso, Brittle fracture in linearly elastic plates, Preprint, 2020.

5. Homogenization of composite ferromagnetic materials;Alouges, François;Proc. A.,2015

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