Conical instabilities on paper

DOI10.1088/1751-8113/45/1/015203zbMATH Open1337.74030arXiv1107.5008OpenAlexW3099003188MaRDI QIDQ3118743

Martin Müller, Pablo Vázquez-Montejo, Jemal Guven

Publication date: 5 March 2012

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Abstract: The stability of the fundamental defects of an unstretchable flat sheet is examined. This involves expanding the bending energy to second order in deformations about the defect. The modes of deformation occur as eigenstates of a fourth-order linear differential operator. Unstretchability places a global linear constraint on these modes. Conical defects with a surplus angle exhibit an infinite number of states. If this angle is below a critical value, these states possess an n-fold symmetry labeled by an integer, n geq 2. A nonlinear stability analysis shows that the 2-fold ground state is stable, whereas excited states possess 2(n - 2) unstable modes which come in even and odd pairs.

Full work available at URL: https://arxiv.org/abs/1107.5008

Mathematics Subject Classification ID

Membranes (74K15) Optimization of shapes other than minimal surfaces (49Q10) Applications of variational problems in infinite-dimensional spaces to the sciences (58E50)

Related Items (3)

Isometric bending requires local constraints on free edges ⋮ Equilibrium shapes with stress localisation for inextensible elastic Möbius and other strips ⋮ First integrals for elastic curves: twisting instabilities of helices

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