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Inflation Mechanics of Hyperelastic Membranes
KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.ORCID iD: 0000-0003-3716-8520
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 [en]
Membrane Mechanics, Inflation, Adhesive Contact, Instabilities, Bifurcation, Limit Point
National Category
Applied Mechanics
Research subject
Engineering Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-160707ISBN: 978-91-7595-447-9 (print)OAI: oai:DiVA.org:kth-160707DiVA: diva2:790954
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
List of papers
1. Contact Mechanics of a Circular Membrane Inflated Against a Soft Adhesive Substrate
Open this publication in new window or tab >>Contact Mechanics of a Circular Membrane Inflated Against a Soft Adhesive Substrate
2014 (English)In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146Article in journal (Other academic) Submitted
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-160729 (URN)
Note

QS 2015

Available from: 2015-02-27 Created: 2015-02-27 Last updated: 2017-12-04Bibliographically approved
2. Free and constrained inflation of a pre-stretched cylindrical membrane
Open this publication in new window or tab >>Free and constrained inflation of a pre-stretched cylindrical membrane
2014 (English)In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 470, no 2169, UNSP 20140282- p.Article in journal (Refereed) Published
Abstract [en]

This paper presents the free and constrained inflation of a pre-stretched hyperelastic cylindrical membrane and a subsequent constrained deflation. The membrane material is assumed as a homogeneous and isotropic Mooney-Rivlin solid. The constraining soft cylindrical substrate is assumed to be a distributed linear stiffness normal to the undeformed surface. Both frictionless and adhesive contact are modelled during the inflation as an interaction between the dry surfaces of the membrane and the substrate. An adhesive contact is modelled during deflation. The free and constrained inflation yields governing equations and boundary conditions, which are solved by a finite difference method in combination with a fictitious time integration method. Continuity in the principal stretches and stresses at the contact boundary is dependent on the contact conditions and inflation-deflation phase. The pre-stretch has a counterintuitive softening effect on free and constrained inflation. The variation of limit point pressures with pre-stretch and the occurrence of a cusp point is shown. Interesting trends are observed in the stretch and stress distributions after the interaction of the membrane with soft substrate, which underlines the effect of material parameters, pre-stretch and constraining properties.

Keyword
contact conditions, soft substrate, Mooney-Rivlin, limit points, deflation, continuity
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-148597 (URN)10.1098/rspa.2014.0282 (DOI)000338717800012 ()
Note

QC 20140811

Available from: 2014-08-11 Created: 2014-08-11 Last updated: 2017-12-05Bibliographically approved
3. Instability investigation on fluid-loaded pre-stretched cylindrical membranes
Open this publication in new window or tab >>Instability investigation on fluid-loaded pre-stretched cylindrical membranes
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.

Keyword
hydrostatic loading, limit point, bifurcation point, softening, eigen-mode injection method, finite differences
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-160730 (URN)10.1098/rspa.2015.0016 (DOI)000353352400016 ()2-s2.0-84929207245 (Scopus ID)
Note

QC 20150813. Updated from submitted to published.

Available from: 2015-02-27 Created: 2015-02-27 Last updated: 2017-12-04Bibliographically approved

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