The Wrinkling of Thin Membranes: Part I—Theory

Roddeman, DG; Drukker, J.; Oomens, Cwj Cees; Janssen, JD Jan

doi:10.1115/1.3173133

Cited by 179 publications

(82 citation statements)

References 3 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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“…For example, Wu and Canfield [26] developed a method that modifies the deformation gradient for the simulation of isotropic membranes. 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.…”

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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“…The fundamental assumption of this theory is that the compressive stress and the bending stress induced by the out-of-plane deformation are negligible in comparison with the tension stress . Based upon this theory, two major groups of techniques for wrinkling analysis, endowed with a modified constitutive law (Stein and Hedgepeth, 1961;Miller and Hedgepeth, 1985) or deformation gradient tensor (Roddeman et al, 1987a;1987b;Kang and Im, 1997;Shaw and Roy, 2007), have been established to guarantee the absence of compressive stresses. Although these tension field theory approaches may provide efficient predictions for in-plane stress distribution and wrinkling regions, it is impossible for them to provide wrinkle details such as the amplitude, wavelength, and number of wrinkles.…”

Section: Introductionmentioning

confidence: 99%

A vector-form hybrid particle-element method for modeling and nonlinear shell analysis of thin membranes exhibiting wrinkling

Luo

Yang

2014

J. Zheijang Univ.-Sci.

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Abstract:The wrinkling phenomenon is a commonly-known problem in many fields of engineering applications. Using a general structural analysis framework of the vector-form hybrid particle-element method (VHPEM), this paper presents a newly developed shell-based numerical model for the geometrically nonlinear wrinkling analysis of thin membranes. VHPEM is rooted in vector mechanics and physical perspective. It discretizes the analyzed domain into a group of finite particles linked by canonical elements, and the motions of the free particles are governed by Newton's second law while the constrained ones follow the prescribed paths. An adaptive convected material frame is adopted for a general kinematical description. Internal forces related to the non-zero bending rigidity of a membrane can be efficiently evaluated by the rotation deformation in a set of deformation coordinates after eliminating rigid body motions simply by a fictitious reverse motion. To overcome the numerical difficulties associated with wrinkles, a pseudo-dynamic scheme using the explicit time integration is introduced into this method. Structural nonlinearity can be easily handled without iterative operations or any other special modification. The wrinkling behavior can be readily obtained by performing a pseudo bifurcation analysis incorporated into the VHPEM. The numerical results reveal that the VHPEM has good reliability and accuracy on solving the membrane wrinkling problem.

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The Wrinkling of Thin Membranes: Part I—Theory

Cited by 179 publications

References 3 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

A vector-form hybrid particle-element method for modeling and nonlinear shell analysis of thin membranes exhibiting wrinkling

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