A neohookean model of plates

Tadeusz Iwaniec, Jani Onninen, Pekka Pankka, Teresa Radice

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)509-529
Number of pages21
JournalSIAM Journal on Mathematical Analysis
Volume53
Issue number1
DOIs
StatePublished - 2021

Keywords

  • He principle of non-interpenetration of matter
  • Minimizers
  • Monotone mappings
  • Neohookean materials

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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