Longitudinally inhomogeneous deformation patterns in isotropic tubes under pure bending

Wadee, M. Ahmer; Bassom, Andrew P.; Aigner, AA

doi:10.1098/rspa.2005.1596

Cited by 32 publications

(19 citation statements)

References 24 publications

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“….) can be determined from a solvability condition imposed on the governing equations for u (2) n and p (2) ; these governing equations are obtained by substituting (3.1)−(3.7) into the nonlinear eigenvalue problem (specified in §2) and equating the coefficients of 2 . However, this approach is algebraically cumbersome.…”

Section: Amplitude Equationsmentioning

confidence: 99%

“…Examples include the cusp-shaped patterns that appear on the inner surface of an axially compressed hollow cylinder [1] or an everted hollow cylinder (A. Juel 2006, personal communication), kinks in a highly deformed solid cylinder or tube [2,3], wrinkling patterns in film/substrate bilayers (e.g. [4,5]), and creases in swollen cellular foams and gels (e.g.…”

Section: Introductionmentioning

confidence: 99%

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Buckling of a coated elastic half-space when the coating and substrate have similar material properties

Ciarletta

2015

Proc. R. Soc. A.

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This study investigates the buckling of a uniaxially compressed neo-Hookean thin film bonded to a neo-Hookean substrate. Previous studies have shown that the elastic bifurcation is supercritical if r ≡ μ f /μ s > 1.74 and subcritical if r < 1.74, where μ f and μ s are the shear moduli of the film and substrate, respectively. Moreover, existing numerical simulations of the fully nonlinear post-buckling behaviour have all been focused on the regime r > 1.74. In this paper, we consider instead a subset of the regime r < 1.74, namely when r is close to unity. Four near-critical regimes are considered. In particular, it is shown that, when r > 1 and the stretch is greater than the critical stretch (the subcritical regime), there exists a localized solution that arises as the limit of modulated periodic solutions with increasingly longer and longer decaying tails. The evolution of each modulated periodic solution is followed as r is decreased, and it is found that there exists a critical value of r at which the deformation gradient develops a discontinuity and the solution becomes a static shock. The semi-analytical results presented could help future numerical simulations of the fully nonlinear post-buckling behaviour.

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Section: Amplitude Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Buckling of a coated elastic half-space when the coating and substrate have similar material properties

Ciarletta

2015

Proc. R. Soc. A.

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“…In 2006, M. Khurram Wadee et al proposed a variational model to formulate the localization of deformation due to buckling under pure bending of thin-walled elastic tubes with circular cross-sections [7]. The results are compared with a number of case studies, including a nanotube, etc., but the model is still an elastic one.…”

Section: Other Approachesmentioning

confidence: 99%

An estimation of critical buckling strain for pipe subjected plastic bending

Ji¹,

Zheng

Chen

et al. 2014

Open Engineering

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An approach for estimating critical buckling strain of pipe subjected plastic bending is established in the present paper. A rigid -perfectly plastic material model and cross section ovalization of pipe during bending are employed for the approach. The energy rates of the ovalised pipe bending and the cross section ovalising are proposed firstly. Furthermore, these energy rates are combined to perform the buckling analysis of pipe bending, an estimation formula of critical buckling strain for pipe subjected plastic bending is proposed. The predicting result of the new critical buckling strain formula is compared with the available experimental data, it shows that the formula is valid. Keywords

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“…The gradual change in the cross section leads to a reduction in the bending stiffness of the cylinder with increasing applied moment. After the bending moment reaches a maximum value, the structure become unstable and so the object suddenly forms a kink [37].…”

Section: A Ovalization Under Pure Bendingmentioning

confidence: 99%

Self-adaptive formation of uneven node spacings in wild bamboo

2016

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Bamboo has a distinctive structure wherein a long cavity inside a cylindrical woody section is divided into many chambers by stiff diaphragms. The diaphragms are inserted at nodes and thought to serve as ring stiffeners for bamboo culms against the external load; if this is the case, the separation between adjacent nodes should be configured optimally in order to enhance the mechanical stability of the culms. Here, we reveal the hitherto unknown blueprint of the optimal node spacings used in the growth of wild bamboo. Measurement data analysis together with theoretical formulations suggest that wild bamboos effectively control their node spacings as well as other geometric parameters in accord with the lightweight and high-strength design concept.

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Longitudinally inhomogeneous deformation patterns in isotropic tubes under pure bending

Cited by 32 publications

References 24 publications

Buckling of a coated elastic half-space when the coating and substrate have similar material properties

Buckling of a coated elastic half-space when the coating and substrate have similar material properties

An estimation of critical buckling strain for pipe subjected plastic bending

Self-adaptive formation of uneven node spacings in wild bamboo

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