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Wrinkling of cylindrical membranes with non-uniform thickness
KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.ORCID iD: 0000-0003-3716-8520
KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.ORCID iD: 0000-0002-5819-4544
2015 (English)In: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 54, 1-10 p.Article in journal (Refereed) Published
Abstract [en]

Thin membranes are prone to wrinkling under various loading, geometric and boundary conditions, affecting their functionality. We consider a hyperelastic cylindrical membrane with non-uniform thickness pressurized by internal gas or fluid. When pre-stretched and inflated, the wrinkles are generated in a certain portion of the membrane depending on the loading medium and boundary conditions. The wrinkling is determined through a criterion based on kinematic conditions obtained from non-negativity of Cauchy principal stresses. The equilibrium solution of a wrinkled membrane is obtained by a specified combination of standard and relaxed strain energy function. The governing equations are discretized by a finite difference approach and a Newton-Raphson method is used to obtain the solution. An interesting relationship between stretch induced softening/stiffening with the wrinkling phenomenon has been discovered. The effects of pre-stretch, inflating medium, thickness variations and boundary conditions on the wrinkling patterns are clearly delineated. (C) 2015 Elsevier Masson SAS. All rights reserved.

Place, publisher, year, edition, pages
2015. Vol. 54, 1-10 p.
Keyword [en]
Wrinkling, Pressure loadings, Relaxed strain energy
National Category
Applied Mechanics
URN: urn:nbn:se:kth:diva-174910DOI: 10.1016/j.euromechsol.2015.05.015ISI: 000361581400001ScopusID: 2-s2.0-84947943118OAI: diva2:865454

QC 20151028

Available from: 2015-10-28 Created: 2015-10-09 Last updated: 2016-05-18Bibliographically approved
In thesis
1. Inflation and Instabilities of Hyperelastic Membranes
Open this publication in new window or tab >>Inflation and Instabilities of Hyperelastic Membranes
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The applications of membranes are increasing rapidly in various fields of engineering and science. The geometric, material, force and contact non-linearities complicate their analysis, which increases the demand for computationally efficient methods and interpretation of counter-intuitive behaviours.

The first part of the present work studies the free and constrained inflation of circular and cylindrical membranes. The membranes are assumed to be in contact with a soft substrate, modelled as a linear spring distribution.Adhesive and frictionless contact conditions are considered during inflation,while only adhesive contact conditions are considered during deflation. For a circular membrane, peeling of the membrane during deflation is studied, and a numerical formulation of the energy release rate is proposed.

The second part of the thesis discusses the instabilities observed for fluid containing cylindrical membranes. Limit points and bifurcation points are observed on primary equilibrium branches. The secondary branches emerge from bifurcation points, with their directions determined by eigenvectors corresponding to zero eigenvalues at the bifurcation point. Symmetry has major implications on stability analysis of the structures, and the relationship between eigenvalue analysis and symmetry is highlighted in this part of the thesis.

In the third part, wrinkling in the pressurized membranes is investigated,and robustness of the modified membrane theory and tension field theory is examined. The effect of boundary conditions, thickness variations, and inflating media on the wrinkling is investigated. It is observed that, with a relaxed strain energy formulation, the obtained equilibrium solutions are unstable due to the occurrence of pressure induced instabilities. A detailed analysis of pressure induced instabilities in the wrinkled membranes is described in the thesis.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2016. 197 p.
TRITA-MEK, ISSN 0348-467X ; 2016-09
Membranes, Constrained inflation, Energy release rate, Adhesive contact condition, Limit point, Bifurcation point, Wrinkling, Tension field theory, Pressure induced instability.
National Category
Applied Mechanics
Research subject
Engineering Mechanics
urn:nbn:se:kth:diva-187041 (URN)978-91-7595-989-4 (ISBN)
Public defence
2016-06-14, Kollegiesalen,, Brinellvagen 8, Stockholm, 13:25 (English)
Swedish Research Council

QC 20160518

Available from: 2016-05-18 Created: 2016-05-16 Last updated: 2016-06-17Bibliographically approved

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Patil, AmitNordmark, ArneEriksson, Anders
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