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Instability investigation on fluid-loaded pre-stretched cylindrical membranes
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, Structural Mechanics.ORCID iD: 0000-0002-5819-4544
2015 (English)In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 471, no 2177, 20150016Article in journal (Refereed) Published
Abstract [en]

This paper discusses the evaluation of instabilities on the quasi-static equilibrium path of fluid-loaded pre-stretched cylindrical membranes and the switching to a secondary branch at a bifurcation point. The membrane is represented by only the in-plane stress components, for which an incompressible, isotropic hyperelastic material model is assumed. The free inflation problem yields governing equations and boundary conditions, which are discretized by finite differences and solved by a Newton-Raphson method. An incremental arclength-cubic extrapolation method is used to find generalized equilibrium paths, with different parametrizations. Limit points and bifurcation points are observed on the equilibrium path when fluid level is seen as the controlling parameter. An eigen-mode injection method is employed to switch to a secondary equilibrium branch at the bifurcation point. A limit point with respect to fluid level is observed for a partially filled membrane when the aspect ratio (length/radius) is high, whereas for smaller aspect ratios, the limit point with respect to fluid level is observed at over-filling. Pre-stretch is observed to have a stiffening effect in the pre-limit zone and a softening effect in the post-limit zone.

Place, publisher, year, edition, pages
2015. Vol. 471, no 2177, 20150016
Keyword [en]
hydrostatic loading, limit point, bifurcation point, softening, eigen-mode injection method, finite differences
National Category
Applied Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-160730DOI: 10.1098/rspa.2015.0016ISI: 000353352400016Scopus ID: 2-s2.0-84929207245OAI: oai:DiVA.org:kth-160730DiVA: diva2:791204
Note

QC 20150813. Updated from submitted to published.

Available from: 2015-02-27 Created: 2015-02-27 Last updated: 2017-12-04Bibliographically approved
In thesis
1. Inflation Mechanics of Hyperelastic Membranes
Open this publication in new window or tab >>Inflation Mechanics of Hyperelastic Membranes
2015 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

The applications of inflatable membrane structures are increasing rapidly in the various fields of engineering and science. The geometric, material, force and contact non-linearities complicate this subject further, which in turn increases the demand for computationally efficient methods and interpretations of counter-intuitive behaviors noted by the  scientific community. To understand the complex behavior of membranes in biological and medical engineering contexts, it is necessary to understand the mechanical behavior of a membrane from a physics point of view. 

The first part of the  present work studies the pre-stretched circular membrane in contact with a soft linear substrate. Adhesive and frictionless contact conditions are considered during inflation, while only adhesive contact conditions are considered during deflation. The peeling of membrane during deflation is studied, and a numerical formulation of the energy release rate is proposed. It is observed that the pre-stretch is having a considerable effect on the variation of the energy release rate.

In the second part, free and constrained inflation of a cylindrical membrane is investigated. Adhesive and frictionless contact conditions are considered between the membrane and substrate. It is observed that the continuity of principal stretches and stresses depend on contact conditions and the inflation/deflation phase. The adhesive traction developed during inflation and deflation arrests the axial movement of material points, while an adhesive line force created at the contact boundary is responsible for a jump in stretches and stresses at the contact boundary. The pre-stretch produces a softening effect in free and constrained inflation of cylindrical membranes.

The third part of the thesis discusses the instabilities observed for fluid containing cylindrical membranes. Both limit points and bifurcation points are observed on equilibrium branches. The secondary branches emerge from bifurcation points, with their directions determined by an eigen-mode injection method. The occurrence of critical points and the stability of equilibrium branches are determined by perturbation techniques. The relationship between eigenvalue analysis and symmetry is highlighted in this part of the thesis.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2015. xii, 24 p.
Series
TRITA-MEK, ISSN 0348-467X ; 2015:01
Keyword
Membrane Mechanics, Inflation, Adhesive Contact, Instabilities, Bifurcation, Limit Point
National Category
Applied Mechanics
Research subject
Engineering Mechanics
Identifiers
urn:nbn:se:kth:diva-160707 (URN)978-91-7595-447-9 (ISBN)
Presentation
2015-03-05, E2, Lindstedtsvägen 3, KTH Main campus, Stockholm, 10:15 (English)
Opponent
Supervisors
Note

QC 20150227

Available from: 2015-02-27 Created: 2015-02-26 Last updated: 2015-02-27Bibliographically approved
2. 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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Patil, AmitEriksson, Anders

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