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  • 1.
    Eriksson, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Nordmark, Arne
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Patil, Amit
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Zhou, Yang
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Parametric stability investigations for hydro-statically loaded membranes2016In: Computers & structures, ISSN 0045-7949, E-ISSN 1879-2243, Vol. 174, p. 33-41Article in journal (Refereed)
    Abstract [en]

    This paper discusses instabilities occurring in thin pressurized membranes, important in biological as well as in engineering contexts. The membranes are represented by only their in-plane stress components, for which an incompressible isotropic hyper-elastic behavior can be assumed. A hydro-static pressurization can give instabilities in the form of limit points with respect to a loading parameter, but also bifurcations, and wrinkling. The hyper-elastic material model itself can also, under some circumstances, lead to a bifurcation situation. The instability situations can be included as constraints in a structural optimization. The paper discusses the formulation, the solution methods and some relevant instability situations. Numerical examples considering the pressurization of a flat and a cylindrical pre-stressed membrane illustrate some aspects of instability.

  • 2.
    Patil, Amit
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Inflation and Instabilities of Hyperelastic Membranes2016Doctoral 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.

  • 3.
    Patil, Amit
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Inflation Mechanics of Hyperelastic Membranes2015Licentiate 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.

  • 4.
    Patil, Amit
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Dasgupta, A.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Contact mechanics of a circular membrane inflated against a deformable substrate2015In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 67-68, p. 250-262Article in journal (Refereed)
    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.

  • 5.
    Patil, Amit
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    DasGupta, Anirvan
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Contact Mechanics of a Circular Membrane Inflated Against a Soft Adhesive Substrate2014In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146Article in journal (Other academic)
  • 6.
    Patil, Amit
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Nordmark, Arne
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Free and constrained inflation of a pre-stretched cylindrical membrane2014In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 470, no 2169, p. UNSP 20140282-Article in journal (Refereed)
    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.

  • 7.
    Patil, Amit
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Nordmark, Arne
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Instabilities of wrinkled membranes with pressure loadings2016In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 94, p. 298-315Article in journal (Refereed)
    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.

  • 8.
    Patil, Amit
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Nordmark, Arne
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Instability investigation on fluid-loaded pre-stretched cylindrical membranes2015In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 471, no 2177, article id 20150016Article in journal (Refereed)
    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.

  • 9.
    Patil, Amit
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Nordmark, Arne
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Wrinkling of cylindrical membranes with non-uniform thickness2015In: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 54, p. 1-10Article in journal (Refereed)
    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.

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