"THE MATHEMATICS OF THIN STRUCTURES" by Jean François Babadjian, Giovanni Di Fratta et al.
 

THE MATHEMATICS OF THIN STRUCTURES

Document Type

Article

Publication Date

3-1-2023

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.

Identifier

85143278268 (Scopus)

Publication Title

Quarterly of Applied Mathematics

External Full Text Location

https://doi.org/10.1090/qam/1628

e-ISSN

15524485

ISSN

0033569X

First Page

1

Last Page

64

Issue

1

Volume

81

Grant

DMS-2006439

Fund Ref

National Science Foundation

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