The Stabilisation of a Thin Sheet by a Continuous Supporting Medium

Gough, G S; Elam, C. F.; Tipper, G. H.; Bruyne, N.A. de

doi:10.1017/s036839310010495x

Cited by 124 publications

(55 citation statements)

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“…Gough et al (1940) analysed the stability of a thin sheet on an elastic foundation of limited depth with a free or rigid back, or unlimited depth (half-space). They found the buckling wavelength k to be:…”

Section: Figs 8-10mentioning

confidence: 99%

Buckling of inner cell wall layers after manipulations to reduce tensile stress: observations and interpretations for stress transmission

Hejnowicz¹,

Borowska-Wykręt²

2004

Planta

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The inner layer of the cell wall in tissues that are under tensile stress in situ, e.g. epidermis and collenchyma of etiolated sunflower hypocotyls, shows a pattern of transverse folds when the tissues are detached and plasmolysed. This can be observed by Nomarski imaging of inner surfaces of the outer cell walls and electron microscopy of longitudinal sections after peeling the epidermis and bathing it in plasmolysing solutions. The folds are apparently caused by buckling of the inner layer due to the longitudinal compressive force exerted on this layer by the outer wall layer, when it shrinks after the removal of the longitudinal tensile stresses. In these stresses, two components can be distinguished: the tissue stress, disappearing on peeling, and that caused directly by turgor pressure, disappearing in hyperosmotic solution. Investigation of the buckling indicates that the outer layer of the cell wall transmits in situ most of the longitudinal tensile stress in the wall. The common concept that the inner layer of the wall is the region bearing most stress and therefore regulating growth can still be valid with respect to the transverse stress component.

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Section: Figs 8-10mentioning

confidence: 99%

Buckling of inner cell wall layers after manipulations to reduce tensile stress: observations and interpretations for stress transmission

Hejnowicz¹,

Borowska-Wykręt²

2004

Planta

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“…Theoretical studies of surface wrinkling may be traced back to 1940s when wrinkling of face struts was analyzed as a form of local elastic instability in structural sandwich panels (e.g., Gough et al, 1940;Wan, 1947;Goodier and Neou, 1951); an account of the historical development was well documented by Allen (1969). Later, a series of works by Biot extended the wrinkling theory to viscoelastic layers (Biot, 1957) and rubber-like nonlinear elastic media under finite strain (Biot, 1963 and1965).…”

Section: Introductionmentioning

confidence: 99%

Wrinkle patterns of anisotropic crystal films on viscoelastic substrates

Huang

2008

Journal of the Mechanics and Physics of Solids

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This paper presents a nonlinear mathematical model for evolution of wrinkle patterns of an anisotropic crystal film on a viscoelastic substrate layer. The underlying mechanism of wrinkling has been generally understood as a stress-driven instability. Previously, theoretical studies on wrinkling have assumed isotropic elastic properties for the film. Motivated by recent experimental observations of ordered wrinkle patterns in single-crystal thin films, this paper develops a theoretical model coupling anisotropic elastic deformation of a crystal film with viscoelastic deformation of a thin substrate layer. A linear perturbation analysis is performed to predict onset of the wrinkling instability and the initial evolution kinetics; an energy minimization method is adopted to analyze wrinkle patterns at the equilibrium states. For a cubic crystal film under an equi-biaxial compression, orthogonally ordered wrinkle patterns are predicted at both the initial stage and the equilibrium state. This is confirmed by numerical simulations of evolving wrinkle patterns. By varying the residual stresses in the film, numerical simulations show that a variety of wrinkle patterns (e.g., orthogonal, parallel, zigzag, and checkerboard patterns) emerge as a result of the competition between the material anisotropy and the stress anisotropy.

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“…In this plot, the present results (solid curve for BP907 and dashed curve for IM7) are compared with those of two other models. The first one, Gough et al (1939), is obtained by neglecting the presence of the interface shear traction q. In that calculation, instead of the continuity conditions, equations (10) are replaced by the requirement that the surface of the matrix Iv = 0) is constrained to satisfy In the second model (Reissner (1937)) the surface of the matrix is taken to be free from shearing stress.…”

Section: 2mentioning

confidence: 99%

A Mechanical Model for Elastic Fiber Microbuckling

Waas

Babcock

Knauss

1990

Journal of Applied Mechanics

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I Fiber Microbuc kling' A two-dimensional mechanicai model is presented to predict the compressive strength of unidirectional fiber composites using technical beam theory and classical elasticity. First, a single fiber resting on a matrix half-plane is considered. Next, a more elaborate analysis of a uniformly laminated, unidirectional fiber composite halfplane is presented. The model configuration incorporates a free edge which introduces a buckling mode that originates at the free edge and decays into the interior of the half-plane. It is demonstrated that for composites of low volume fraction ( A problem that has received much attention but moderate success is the prediction of compressive strength of fiber composites. Dow and Gruntfest (1960) were apparently the first to identify fiber buckling as a viable mode of compressive failure in composites. Their work was followed by that of Fried and Kaminetsky (1964) and Leventz (1964), who addressed. experimentally and theoretically the question of compressive strength. In these investigations, an empirical factor was used to o b t d~ a ccrrda:im between the experimentally and theoretically predicted values of compressive strength. In 1965, Rosen (1965) presented an analysis addressing the question of microbuckling which was devoid of any empiricism and laid the foundation for much of the work that was to follow. With a few exceptions, noted later, the analytical research work carried out in the past 20 years is based on the model by Rosen (1965). Due to lack of space and because an excpllent literature survey on fiber microbuckling exists @quart (1985)), a discussion of the various contributions that have enhanced our understanding of microbuckling will be omitted here. Instead, the discussion will be limited to those aspects that are fundamental in clarifying the state-of-the-art of the subject. The interested reader is referred to the references at the end of this chapter and the review by Shuart (1985). in particular, for a complete and up-to-date account.The Rosen (1965) model for microbuckling addresses the problem of fiber buckling in glass fiber/epoxy laminates

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The Stabilisation of a Thin Sheet by a Continuous Supporting Medium

Cited by 124 publications

References 1 publication

Buckling of inner cell wall layers after manipulations to reduce tensile stress: observations and interpretations for stress transmission

Buckling of inner cell wall layers after manipulations to reduce tensile stress: observations and interpretations for stress transmission

Wrinkle patterns of anisotropic crystal films on viscoelastic substrates

A Mechanical Model for Elastic Fiber Microbuckling

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