+ Site Statistics
+ Search Articles
+ PDF Full Text Service
How our service works
Request PDF Full Text
+ Follow Us
Follow on Facebook
Follow on Twitter
Follow on LinkedIn
+ Subscribe to Site Feeds
Most Shared
PDF Full Text
+ Translate
+ Recently Requested

Confined disclinations: exterior versus material constraints in developable thin elastic sheets

Confined disclinations: exterior versus material constraints in developable thin elastic sheets

Physical Review. E Statistical Nonlinear and Soft Matter Physics 91(2): 022404

We examine the shape change of a thin disk with an inserted wedge of material when it is pushed against a plane, using analytical, numerical, and experimental methods. Such sheets occur in packaging, surgery, and nanotechnology. We approximate the sheet as having vanishing strain, so that it takes a conical form in which straight generators converge to a disclination singularity. Then, its shape is that which minimizes elastic bending energy alone. Real sheets are expected to approach this limiting shape as their thickness approaches zero. The planar constraint forces a sector of the sheet to buckle into the third dimension. We find that the unbuckled sector is precisely semicircular, independent of the angle δ of the inserted wedge. We generalize the analysis to include conical as well as planar constraints and thereby establish a law of corresponding states for shallow cones of slope ε and thin wedges. In this regime, the single parameter δ/ε^{2} determines the shape. We discuss the singular limit in which the cone becomes a plane, and the unexpected slow convergence to the semicircular buckling observed in real sheets.

Please choose payment method:

(PDF emailed within 0-6 h: $19.90)

Accession: 057489318

Download citation: RISBibTeXText

PMID: 25768515

DOI: 10.1103/physreve.91.022404

Related references

Möbius bands, unstretchable material sheets and developable surfaces. Proceedings. Mathematical Physical and Engineering Sciences 472(2192): 20160459, 2016

Cracking sheets: oscillatory fracture paths in thin elastic sheets. Chaos 18(4): 041108, 2008

Elastic building blocks for confined sheets. Physical Review Letters 106(7): 074301, 2011

Tearing of thin sheets: cracks interacting through an elastic ridge. Physical Review. E Statistical Nonlinear and Soft Matter Physics 90(6): 062406, 2014

Spontaneous formation of stringlike clusters and smectic sheets for colloidal rods confined in thin wedgelike gaps. Langmuir 29(33): 10529-10538, 2013

Measuring the Elastic Modulus of Thin Polymer Sheets by Elastocapillary Bending. Acs Applied Materials and Interfaces 7(27): 14734-14742, 2015

Disclinations, e-cones, and their interactions in extensible sheets. Soft Matter 12(19): 4457-4462, 2016

Thin vulcanized rubber sheets as covering material in silo management. Archives of Animal Nutrition 38(11): 1031, 1988

Elastic medium confined in a column versus the Janssen experiment. European Physical Journal. E Soft Matter 16(4): 421-438, 2005

Developable modes in vibrated thin plates. Physical Review Letters 99(25): 254301, 2007

Argentaffin staining of elastic material in semi thin sections. Mikroskopie 39(9-10): 263-271, 1982

Measurements of elastic constants in thin films of colossal magnetoresistance material. Physical Review Letters 90(3): 036103, 2003

Frank elastic-constant anisotropy measured from transmission-electron-microscope images of disclinations. Physical Review Letters 62(17): 1993-1996, 1989

Apparatus and method for forming thin-walled elastic components from an elastomeric material. Official Gazette of the United States Patent & Trademark Office Patents 1255(4), 2002

Possible evidence for on-going volcanism on Mars as suggested by thin, elliptical sheets of low albedo particulate material around pits and fissures close to Cerberus Fossae. Earth, Moon, and Planets 101(1-2): 1-16, 2007