Finite element analysis of membrane wrinkling

Lu, Kun; Accorsi, Michael L.; Leonard, John W.

doi:10.1002/1097-0207(20010220)50:5<1017::aid-nme47>3.0.co;2-2

Cited by 93 publications

(60 citation statements)

References 12 publications

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“…Wrinkling is a phenomenon commonly observed in everyday life, such as in ageing human skin or ripening fruits, and has been studied extensively both theoretically [1][2][3][4] and experimentally.…”

Section: Introductionmentioning

confidence: 99%

Wrinkling and strain localizations in polymer thin films

2012

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Wrinkles and strain localized features are observed in many natural systems and are useful surface patterns for a wide range of applications, including optical gratings and microfluidic devices. However, the transition from sinusoidal wrinkles to more complex strain localized features, such as delaminations or folds, is not well understood. In this paper, we investigate the onset of wrinkling and strain localizations in a model system of a glassy polymer film attached to a surface of an elastomeric substrate. We show that careful measurement of feature amplitude as a function of applied strain allows not only the determination of wrinkle, fold, or delamination onset but also allows clear distinction between each type of feature. We observe that amplitude increases discontinuously as delamination occurs; whereas, the amplitude for a fold deviates gradually compared to the amplitude for a nearby wrinkle as a function of applied strain. The folds observed in these experiments have an outward morphology from the surface, in contrast to folds that form into the plane for a film floating on a liquid substrate. A deformation mode map is presented, where the measured critical strain for localization is compared for films with thickness ranging from 5 nm to 180 nm.

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Section: Introductionmentioning

confidence: 99%

Wrinkling and strain localizations in polymer thin films

2012

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“…A generalized version of this algorithm for isotropic and anisotropic membranes was subsequently published by Roddeman et al [18,19]. Muttin [14] derived a quadrilateral finite element that is based on Roddeman's work and Lu et al [8] extended Muttin's work by deriving explicit equations for the force vector and tangent stiffness matrix. Further publications that emerged from the paper by Wu and Canfield are, for example, Kang and Im [5], Schoop et al [21], Raible et al [16] and Mosler [13].…”

Section: Literature Reviewmentioning

confidence: 99%

Simulation of tension fields with in-plane rotational degrees of freedom

Pagitz

Abdalla

2010

Comput Mech

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This paper introduces a novel multigrid approach for the geometric non-linear simulation of tension fields on the basis of a three-node membrane finite element. The element possesses, in addition to the nodal displacement degrees of freedom, an in-plane rotational degree of freedom inside the element domain that controls the direction of the tension field. This rotational degree of freedom allows the enforcement of continuity and tension field boundary conditions on the basis of a coarser mesh with varying size.

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“…As these formulations relate to the deformed configuration, their application in a FE-code can be quite complicated. Seokwoo and Seyoung [8], Lu et al [11] and Schoop et al [12] formulated the wrinkling conditions by means of the 2nd Piola-Kirchhoff stress tensor.…”

Section: Introductionmentioning

confidence: 99%

“…Some authors used stress based criterions to determine in which state the membrane is, other used strain based criterions. We in this paper use a mixed stressstrain-criterion proposed in [11] for linear material behaviour.A membrane is taut when both the principal stresses are positive. We use the usual membrane theory.…”

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Wrinkling of nonlinear membranes

Schoop

Taenzer

Hornig

2002

Computational Mechanics

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Membranes are stiff under tension but switch over to wrinkling when compression occurs. Roddeman proposed a kinematic model to handle this phenomenon under finite deformation conditions. The wrinkling conditions of Roddeman are transformed into the reference configuration. This results in a more simple nonlinear formulation. For application in a finite element code a consistent linearization was carried out. Numerical examples for linear and nonlinear orthotropic constitutive equations are discussed. IntroductionMembrane structures are widely used. Airships, sails and airbags are examples of such structures. Therefore a growing interest of numerical simulation of membranes exists.Usually numerical analysis is performed by means of the Finite Element Method. We make use of a FE-formulation described in [1]. Thereby a spatial membrane is related to a plane reference (dressmaker's pattern). A nonlinear FE algorithm requires the determination of the state of stress in the integration points of each element. How to determine the state of stress in an integration point in case of wrinkling is the topic in this paper.Membranes are very suitable for carrying tensile loads, but they fail partially or completely if compressive in-plane loads occur. Since membranes do not possess any flexural stiffness they can not carry compressive in-plane loads. In this case membranes wrinkle. The wrinkling phenomenon was treated by authors in the past. In this field pioneer work was done by Reissner [2] in 1938, followed by many authors as for instance Mansfield [3], Wu [4], Miller, Hedgepeth [5] and Pipkin [6]. This paper is based on the work of Roddeman [7], who propose a kinematic approach. Taenzer gave a formulation of this kinematic model, suitable for spatial membrane elements with a plane reference (see [1] and [10]). However, Roddeman and Taenzer elaborated the theory in terms of the Cauchy stress tensor. As these formulations relate to the deformed configuration, their application in a FE-code can be quite complicated. Seokwoo and Seyoung [8], Lu et al. [11] and Schoop et al. [12] formulated the wrinkling conditions by means of the 2nd Piola-Kirchhoff stress tensor.In this paper the wrinkling conditions of Roddeman are transformed into the reference configuration. This results in simpler nonlinear equations, valid for linear and nonlinear anisotropic elastic materials. For application in a FE algorithm consistent linearization was performed. Different states of a membraneThere are three possibilities: A membrane or regions of a membrane can be taut, regularly wrinkled or slack. In a FE-calculation we decide this question in all integration points. Some authors used stress based criterions to determine in which state the membrane is, other used strain based criterions. We in this paper use a mixed stressstrain-criterion proposed in [11] for linear material behaviour.A membrane is taut when both the principal stresses are positive. We use the usual membrane theory. If a membrane is not taut, it is regularly wrinkled if one princi...

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Finite element analysis of membrane wrinkling

Cited by 93 publications

References 12 publications

Wrinkling and strain localizations in polymer thin films

Wrinkling and strain localizations in polymer thin films

Simulation of tension fields with in-plane rotational degrees of freedom

Wrinkling of nonlinear membranes

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