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Contact mechanics of a circular membrane inflated against a deformable substrate
KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.ORCID iD: 0000-0003-3716-8520
KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.ORCID iD: 0000-0002-5819-4544
2015 (English)In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 67-68, 250-262 p.Article in journal (Refereed) Published
Abstract [en]

Finite inflation of a hyperelastic flat circular membrane against a deformable adhesive substrate and peeling upon deflation are analyzed. The membrane material is considered to be a homogeneous, isotropic and incompressible Mooney-Rivlin solid. The deformable substrate is assumed to be a distributed linear stiffness in the direction normal to the undeformed surface. The adhesive contact is considered to be perfectly sticking with no tangential slip between the dry surfaces of the membrane and the substrate. The inflation mechanics problem in the variational form yields the governing equations and boundary conditions, which are transformed to a nonlinear two-point boundary value problem by a careful choice of field variables for efficient computation. It is found that during inflation (deflation) with adhesive contact, the meridional stretch exhibits continuity up to C0 (C-1) at the contact junction, while the circumferential stretch remains continuous up to C1 (C0). Interestingly, stretch locking in an adhesive contact is found to give a higher indentation on the substrate than in a frictionless contact. Peeling at the contact junction has been studied, and numerical formulations for the energy release rate are proposed.

Place, publisher, year, edition, pages
2015. Vol. 67-68, 250-262 p.
Keyword [en]
Adhesive contact, Constrained inflation, Contact peeling, Deformable substrate, Energy release rate
National Category
Other Engineering and Technologies
URN: urn:nbn:se:kth:diva-170316DOI: 10.1016/j.ijsolstr.2015.04.025ISI: 000357243900020ScopusID: 2-s2.0-84930757627OAI: diva2:827670

QC 20150629

Available from: 2015-06-29 Created: 2015-06-29 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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