Exact Constructions in the (Non-linear) Planar Theory of Elasticity: From Elastic Crystals to Nematic Elastomers

Pierluigi Cesana, Francesco Della Porta, Angkana Rüland, Christian Zillinger, Barbara Zwicknagl

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In this article we deduce necessary and sufficient conditions for the presence of “Conti-type”, highly symmetric, exactly stress-free constructions in the geometrically non-linear, planar n-well problem, generalising results of Conti et al. (Proc R Soc A 473(2203):20170235, 2017). Passing to the limit n→ ∞, this allows us to treat solid crystals and nematic elastomer differential inclusions simultaneously. In particular, we recover and generalise (non-linear) planar tripole star type deformations which were experimentally observed in Kitano and Kifune (Ultramicroscopy 39(1–4):279–286, 1991), Manolikas and Amelinckx (Physica Status Solidi (A) 60(2):607–617, 1980; Physica Status Solidi (A) 61(1):179–188, 1980). Furthermore, we discuss the corresponding geometrically linearised problem.

Original languageEnglish
Pages (from-to)383-445
Number of pages63
JournalArchive for Rational Mechanics and Analysis
Volume237
Issue number1
DOIs
Publication statusPublished - Jul 1 2020

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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