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Instabilities of wrinkled membranes with pressure loadings
KTH, School of Engineering Sciences (SCI), Mechanics. (Structural Mechanics)ORCID iD: 0000-0003-3716-8520
KTH, School of Engineering Sciences (SCI), Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics.ORCID iD: 0000-0002-5819-4544
2016 (English)In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782Article in journal (Refereed) Epub ahead of print
Abstract [en]

Wrinkling can affect the functionality of thin membranes subjected to various loadings or boundary conditions. The concept of relaxed strain energy was studied for isotropic, hyperelastic, axisymmetric membranes pressurized by gas or fluid. Non-intuitive instabilities were observed when axisymmetric wrinkled membranes were perturbed with angle dependent displacement fields. A linearized theory showed that static equilibrium states of pressurized membranes, modelled by a relaxed strain energy formulation, are unstable, when the wrinkled surface is subjected to pressure loadings. The theory is extended to the non-axisymmetric membranes and it is shown that these instabilities are local phenomena. Simulations for the pressurized cylindrical membranes with non-uniform thickness and hemispherical membranes support the claims in both theoretical and numerical contexts including finite element simulations.

Place, publisher, year, edition, pages
Elsevier, 2016.
Keyword [en]
Wrinkling; Relaxed strain energy; Instability; Wave number; Tension field theory
National Category
Applied Mechanics
Research subject
Engineering Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-187039DOI: 10.1016/j.jmps.2016.05.014OAI: oai:DiVA.org:kth-187039DiVA: diva2:928667
Funder
Swedish Research Council
Note

QC 20160518

Available from: 2016-05-16 Created: 2016-05-16 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.
Series
TRITA-MEK, ISSN 0348-467X ; 2016-09
Keyword
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
Identifiers
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)
Opponent
Supervisors
Funder
Swedish Research Council
Note

QC 20160518

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

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