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Multi-layered folding with voids.
MedLine Citation:
PMID:  22431755     Owner:  NLM     Status:  PubMed-not-MEDLINE    
Abstract/OtherAbstract:
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.
Authors:
T J Dodwell; G W Hunt; M A Peletier; C J Budd
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Publication Detail:
Type:  Journal Article    
Journal Detail:
Title:  Philosophical transactions. Series A, Mathematical, physical, and engineering sciences     Volume:  370     ISSN:  1364-503X     ISO Abbreviation:  Philos Trans A Math Phys Eng Sci     Publication Date:  2012 Apr 
Date Detail:
Created Date:  2012-03-20     Completed Date:  2012-07-05     Revised Date:  2013-04-24    
Medline Journal Info:
Nlm Unique ID:  101133385     Medline TA:  Philos Trans A Math Phys Eng Sci     Country:  England    
Other Details:
Languages:  eng     Pagination:  1740-58     Citation Subset:  -    
Affiliation:
Department of Mechanical Engineering, University of Bath, UK. tjd20@bath.ac.uk
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