A1 Journal article (refereed)
A Neohookean Model of Plates (2021)

Iwaniec, T., Onninen, J., Pankka, P., & Radice, T. (2021). A Neohookean Model of Plates. SIAM Journal on Mathematical Analysis, 53(1), 509-529. https://doi.org/10.1137/20M1329305

JYU authors or editors

Publication details

All authors or editorsIwaniec, Tadeusz; Onninen, Jani; Pankka, Pekka; Radice, Teresa

Journal or seriesSIAM Journal on Mathematical Analysis



Publication year2021


Issue number1

Pages range509-529

PublisherSociety for Industrial and Applied Mathematics

Publication countryUnited States

Publication languageEnglish


Publication open accessNot open

Publication channel open access

Publication is parallel publishedhttps://helda.helsinki.fi/handle/10138/328644

Web address of parallel published publication (pre-print)https://arxiv.org/abs/2004.03381


This article is about hyperelastic deformations of plates (planar domains) which minimize a neohookean-type energy. Particularly, we investigate a stored energy functional introduced by J. M. Ball [Proc. Roy. Soc. Edinb. Sect. A, 88 (1981), pp. 315--328]. The mappings under consideration are Sobolev homeomorphisms and their weak limits. They are monotone in the sense of C. B. Morrey. One major advantage of adopting monotone Sobolev mappings lies in the existence of the energy-minimal deformations. However, injectivity is inevitably lost, so an obvious question to ask is, what are the largest subsets of the reference configuration on which minimal deformations remain injective? The fact that such subsets have full measure should be compared with the notion of global invertibility, which deals with subsets of the deformed configuration instead. In this connection we present a Cantor-type construction to show that both the branch set and its image may have positive area. Another novelty of our approach lies in allowing the elastic deformations to be free along the boundary, known as frictionless problems.

Keywordspartial differential equationsmathematical modelselasticity (physical properties)

Free keywordsneohookean materials; minimizers; monotone mappings; the principle of non-interpenetration of matter

Contributing organizations

Ministry reportingYes

Reporting Year2021

JUFO rating2

Last updated on 2024-03-04 at 20:15