Energy scaling laws for conically constrained thin elastic sheets

Jeremy Brandman, Robert V. Kohn, Hoai Minh Nguyen

Research output: Contribution to journalArticle

Abstract

We investigate low-energy deformations of a thin elastic sheet subject to a displacement boundary condition consistent with a conical deformation. Under the assumption that the displacement near the sheet's center is of order h|logh|, where hâ‰1 is the thickness of the sheet, we establish matching upper and lower bounds of order h 2|logh| for the minimum elastic energy per unit thickness, with a prefactor determined by the geometry of the associated conical deformation. These results are established first for a 2D model problem and then extended to 3D elasticity.

Original languageEnglish (US)
Pages (from-to)251-264
Number of pages14
JournalJournal of Elasticity
Volume113
Issue number2
DOIs
StatePublished - 2013

Keywords

  • Energy scaling laws
  • Thin elastic sheets
  • d-Cone

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering

Fingerprint Dive into the research topics of 'Energy scaling laws for conically constrained thin elastic sheets'. Together they form a unique fingerprint.

  • Cite this