Crumples as a Generic Stress-Focusing Instability in Confined Sheets

Timounay, Yousra; De, Raj; Stelzel, Jessica L.; Schrecengost, Zachariah S.; Ripp, Monica; Paulsen, Joseph D.

doi:10.1103/physrevx.10.021008

Cited by 14 publications

(13 citation statements)

References 64 publications

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“…Spherical stamping of a flat sheet provides a model example of wrinkles localizing into sharp folds with increased confinement. This wrinkle-to-crumple transition has been studied experimentally [70], and detailed simulations could further shed light on stress localization in this process. Furthermore, the general framework for modeling nonzero rest curvature enables us to explore the complementary system of a curved shell pressed to a flat substrate, which has seen recent experimental and theoretical development [71,72,73].…”

Section: Representative Examplesmentioning

confidence: 93%

Simulation of crumpled sheets via alternating quasistatic and dynamic representations

Andrejevic¹,

Rycroft²

2021

Preprint

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In this work, we present a method for simulating the large-scale deformation and crumpling of thin, elastoplastic sheets. Motivated by the physical behavior of thin sheets during crumpling, we adopt two different formulations of the governing equations of motion: a quasistatic formulation that effectively describes smooth deformations, and a fully dynamic formulation that captures large changes in the sheet's velocity. The former is a differential-algebraic system solved implicitly, while the latter is a purely differential system solved explicitly, using a hybrid integration scheme that adaptively alternates between the two representations. We demonstrate the capacity of this method to effectively simulate a variety of crumpling phenomena. Finally, we show that statistical properties, notably the accumulation of creases under repeated loading, as well as the area distribution of facets, are consistent with experimental observations.

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Section: Representative Examplesmentioning

confidence: 93%

Simulation of crumpled sheets via alternating quasistatic and dynamic representations

Andrejevic¹,

Rycroft²

2021

Preprint

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“…We did not investigate neither the selected wavelength of the wrinkles nor the impact of curvature on those. Numerous recent studies have been tackling these challenges in slightly different configurations [15,31,32,33].…”

Section: Morphology Of Mylar Balloonsmentioning

confidence: 99%

Geometry and mechanics of inextensible curvilinear balloons

Siéfert

Bico

Reyssat

et al. 2020

Journal of the Mechanics and Physics of Solids

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Mylar balloons are popular in funfairs or birthday parties. Their conception is very simple: two pieces of flat thin sheets are cut and sealed together along their edges to form a flat envelope. Inflation tends to deform this envelope in order to maximize its inner volume. However, although thin sheets are easy to bend and hardly resist compressive loads, they barely stretch, which imposes non-trivial geometrical constraints. Such thin sheets are generally described under the framework of "tension field theory" where their stiffness is considered as infinite under stretching and vanishes under compression or bending. In this study, we focus on the shape after inflation of flat, curved templates of constant width. Counter-intuitively, the curvatures of the paths tend to increase upon inflation, which leads to out of plane buckling of non-confined closed structures. After determining the optimal cross section of axisymmetric annuli, we predict the change in local curvature induced in open paths. We finally describe the location of wrinkled and smooth areas observed in inflated structures that correspond to compression and tension, respectively.

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“…The CM model [1] attracted a remarkable level of interest and provoked research activity that far exceeded its original realm of application. Specifically, the proposal that wrinkle patterns in thin solid bodies should be considered far-from-threshold phenomena and correspondingly be analyzed through a theoretical framework that is sharply distinct from traditional post-buckling methods inspired a multitude of experimental and theoretical studies in ultarthin sheets subjected to confinement by capillary effects or other forces [23][24][25][26][27][28][29][30][31][32][33][34][35][36]. In particular, these studies provided strong support to the reasoning underlying CM principle (1a) that determines the wrinkle wavelength: a balance between the bending modulus and the stiffness of an effective substrate, which may be an actual foundation, or induced by a boundary load or curved topography that imply tension perpendicularly to the compressed axis [19,37].…”

Section: Introductionmentioning

confidence: 99%

Stretching Hookean ribbons Part II: from buckling instability to far-from-threshold wrinkle pattern

Xin¹,

Davidovitch²

2020

Preprint

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We address the fully-developed wrinkle pattern formed upon stretching a Hookean, rectangularshaped sheet, when the longitudinal tensile load induces transverse compression that far exceeds the stability threshold of a purely planar deformation. At this "far from threshold" parameter regime, which has been the subject of the celebrated Cerda-Mahadevan (CM) model [1], the wrinkle pattern expands throughout the length of the sheet and the characteristic wavelength of undulations is much smaller than its width. Employing Surface Evolver simulations over a range of sheet thicknesses and tensile loads we elucidate the theoretical underpinnings of the far-from-threshold framework in this set-up. We show that the evolution of wrinkles comes in tandem with collapse of transverse compressive stress, rather than vanishing transverse strain (which was hypothesized in [1]), such that the stress field approaches asymptotically a compression-free limit, describable by tension field theory. We compute the compression-free stress field by simulating a Hookean sheet that has finite stretching modulus but no bending rigidity, and show that this singular limit encapsulates the geometrical nonlinearity underlying the amplitude-wavelength ratio of wrinkle patterns in physical, highly bendable sheets, even though the actual strains may be so small that the local mechanics is perfectly Hookean. Finally, we revisit the balance of bending and stretching energies that gives rise to a favorable wrinkle wavelength, and study the consequent dependence of the wavelength on the tensile load as well as the thickness and length of the sheet.

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Crumples as a Generic Stress-Focusing Instability in Confined Sheets

Cited by 14 publications

References 64 publications

Simulation of crumpled sheets via alternating quasistatic and dynamic representations

Simulation of crumpled sheets via alternating quasistatic and dynamic representations

Geometry and mechanics of inextensible curvilinear balloons

Stretching Hookean ribbons Part II: from buckling instability to far-from-threshold wrinkle pattern

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