Variational convergence of discrete geometrically-incompatible elastic models

Raz Kupferman, Cy Maor*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We derive a continuum model for incompatible elasticity as a variational limit of a family of discrete nearest-neighbor elastic models. The discrete models are based on discretizations of a smooth Riemannian manifold (M, g) , endowed with a flat, symmetric connection ∇. The metric g determines local equilibrium distances between neighboring points; the connection ∇ induces a lattice structure shared by all the discrete models. The limit model satisfies a fundamental rigidity property: there are no stress-free configurations, unless g is flat, i.e., has zero Riemann curvature. Our analysis focuses on two-dimensional systems, however, all our results readily generalize to higher dimensions.

Original languageAmerican English
Article number39
JournalCalculus of Variations and Partial Differential Equations
Volume57
Issue number2
DOIs
StatePublished - 1 Apr 2018

Bibliographical note

Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

Keywords

  • 53Z05
  • 74B20
  • 74Q15

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