TY - JOUR
T1 - THE MATHEMATICS OF THIN STRUCTURES
AU - Babadjian, Jean François
AU - Di Fratta, Giovanni
AU - Fonseca, Irene
AU - Francfort, Gilles A.
AU - Lewicka, Marta
AU - Muratov, Cyrill B.
N1 - Funding Information:
Received February 15, 2022, and, in revised form, July 1, 2022. 2020 Mathematics Subject Classification. Primary 49J45, 74B20, 74K20, 74K35, 53A35. The second author was supported by the Austrian Science Fund (FWF) through the project Analysis and Modeling of Magnetic Skyrmions (grant P-34609). The third author’s research was partially funded by the NSF grant DMS-1906238. The fourth author’s research is partially funded by the NSF Grant DMREF-1921969. The fifth author was partially supported by the NSF award DMS-2006439. The work of the last author was supported, in part, by NSF via grants DMS-0908279, DMS-1313687, DMS-1614948 and DMS-1908709. Email address: jean-francois.babadjian@universite-paris-saclay.fr Email address: giovanni.difratta@unina.it Email address: fonseca@andrew.cmu.edu Email address: gilles.francfort@univ-paris13.fr, gilles.francfort@cims.nyu.edu Email address: lewicka@pitt.edu Email address: muratov@njit.edu
Publisher Copyright:
© 2022 Brown University
PY - 2023/3
Y1 - 2023/3
N2 - 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.
AB - 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.
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U2 - 10.1090/qam/1628
DO - 10.1090/qam/1628
M3 - Article
AN - SCOPUS:85143278268
SN - 0033-569X
VL - 81
SP - 1
EP - 64
JO - Quarterly of Applied Mathematics
JF - Quarterly of Applied Mathematics
IS - 1
ER -