Multi-layered folding with voids

T. J. Dodwell, G. W. Hunt, M. A. Peletier, C. J. Budd

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

In the deformation of layered materials such as geological strata, or stacks of paper, mechanical properties compete with the geometry of layering. Smooth, rounded corners lead to voids between the layers, while close packing of the layers results in geometrically induced curvature singularities. When voids are penalized by external pressure, the system is forced to trade off these competing effects, leading to sometimes striking periodic patterns. In this paper, we construct a simple model of geometrically nonlinear multi-layered structures under axial loading and pressure confinement, with non-interpenetration conditions separating the layers. Energy minimizers are characterized as solutions of a set of fourth-order nonlinear differential equations with contact-force Lagrange multipliers, or equivalently of a fourth-order free-boundary problem. We numerically investigate the solutions of this free-boundary problem and compare them with the periodic solutions observed experimentally.
Original languageEnglish
Pages (from-to)1740-1758
Number of pages19
JournalPhilosophical Transactions of the Royal Society A - Mathematical Physical and Engineering Sciences
Volume370
Issue number1965
DOIs
Publication statusPublished - Apr 2012

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Voids
Folding
folding
voids
free boundaries
Free Boundary Problem
Fourth Order
Lagrange multipliers
Differential equations
Contact Force
strata
Minimizer
Mechanical properties
Nonlinear Differential Equations
Packing
Mechanical Properties
Geometry
Periodic Solution
differential equations
Trade-offs

Cite this

Multi-layered folding with voids. / Dodwell, T. J.; Hunt, G. W.; Peletier, M. A.; Budd, C. J.

In: Philosophical Transactions of the Royal Society A - Mathematical Physical and Engineering Sciences, Vol. 370, No. 1965, 04.2012, p. 1740-1758.

Research output: Contribution to journalArticle

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