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 editors: Iwaniec, Tadeusz; Onninen, Jani; Pankka, Pekka; Radice, Teresa

Journal or series: SIAM Journal on Mathematical Analysis

ISSN: 0036-1410

eISSN: 1095-7154

Publication year: 2021

Volume: 53

Issue number: 1

Pages range: 509-529

Publisher: Society for Industrial and Applied Mathematics

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1137/20M1329305

Publication open access: Not open

Publication channel open access:

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

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

Abstract

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.

Keywords: partial differential equations; mathematical models; elasticity (physical properties)

Free keywords: neohookean materials; minimizers; monotone mappings; the principle of non-interpenetration of matter

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2021

JUFO rating: 2