Cascade unlooping of a low-pitch helical spring under tension

Starostin, E. L.; Heijden, G. H. M. van der

doi:10.1016/j.jmps.2009.02.004

Cited by 11 publications

(3 citation statements)

References 20 publications

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“…Helical microstructures 99 also possess the ‘J-shaped’ stress–strain behavior 100-104 . For a helical ribbon, as shown in Figure 5a, Pham et al 105 gave an analytical expression that captures the non-linear mechanics response under the conditions that the ratio of t / w ≪ 1 and L/ w ≪ 1, i.e.,…”

Section: Helical Designmentioning

confidence: 99%

Design and application of ‘J-shaped’ stress–strain behavior in stretchable electronics: a review

et al. 2017

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A variety of natural biological tissues (e.g., skin, ligaments, spider silk, blood vessel) exhibit ‘J-shaped’ stress-strain behavior, thereby combining soft, compliant mechanics and large levels of stretchability, with a natural ‘strain-limiting’ mechanism to prevent damage from excessive strain. Synthetic materials with similar stress-strain behaviors have potential utility in many promising applications, such as tissue engineering (to reproduce the nonlinear mechanical properties of real biological tissues) and biomedical devices (to enable natural, comfortable integration of stretchable electronics with biological tissues/organs). Recent advances in this field encompass developments of novel material/structure concepts, fabrication approaches, and unique device applications. This review highlights five representative strategies, including designs that involve open network, wavy and wrinkled morphoologies, helical layouts, kirigami and origami constructs, and textile formats. Discussions focus on the underlying ideas, the fabrication/assembly routes, and the microstructure-property relationships that are essential for optimization of the desired ‘J-shaped’ stress-strain responses. Demonstration applications provide examples of the use of these designs in deformable electronics and biomedical devices that offer soft, compliant mechanics but with inherent robustness against damage from excessive deformation. We conclude with some perspectives on challenges and opportunities for future research.

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Section: Helical Designmentioning

confidence: 99%

Design and application of ‘J-shaped’ stress–strain behavior in stretchable electronics: a review

et al. 2017

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“…However, an inextensible strip model is known to have singular issues that could be problematic for numerical simulations [31,32]. On the other hand, anisotropic rod models have been successfully applied to study the shape of a narrow Möbius strip [33], the cascade unlooping of helical strips [34], and bifurcations of buckled narrow strips [31]. In this work, we use the anisotropic rod theory to model elastic strip networks.…”

Section: Geometry Of a Bigon And A Bigon Ringmentioning

confidence: 99%

Numerical modeling of static equilibria and bifurcations in bigons and bigon rings

Yu,

Dreier,

Marmo

et al. 2020

Preprint

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We propose a numerical framework to study mechanics of elastic networks that are made of thin strips. Each strip is modeled as a Kirchhoff rod, and the entire strip network is formulated as a twopoint boundary value problem (BVP) that can be solved by a general-purpose BVP solver. We first study the buckling behavior of a bigon, which consists of two strips initially straight and deformed so as to intersect with each other through a fixed angle at the two ends. Numerical results match with experimental observations in that the intersection angle and aspect ratio of the strip's cross section contribute to make a bigon buckle out of plane. Then we study a bigon ring that is composed of a series of bigons to form a loop. A bigon ring is observed to be multistable, depending on the intersection angle, number of bigon cells, and the anisotropy of the strip's cross section. We find both experimentally and numerically that a bigon ring can fold into a multiply-covered loop, which is similar to the folding of a bandsaw blade. Finally we explore the static equilibria and bifurcations of a 6-bigon ring, and find several families of equilibrium shapes. Our numerical framework captures the experimental configurations of a bigon ring well and further reveals interesting connections among various states. Our framework can be applied to study general elastic strip networks that may contain flexible joints, naturally curved strips of different lengths, etc. The folding and multistable behaviors of a bigon ring may inspire the design of novel deployable and morphable structures.

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“…This kind of structures has been widely studied in the nonlinear framework 2,9,16 since they suffer from geometrical instabilities that can lead to a sudden loss of stiffness as well as extreme deformation shapes, as shown in Figure 1. Moreover their various applications in the aerospace field 11,12 , but also in biophysics, biomechanics or even in micro or nanomechanics 15 are as many motivations to develop robust models 1,14 .…”

Section: Introductionmentioning

confidence: 99%

On the folding and deployment of tape springs: A large displacements and large rotations rod model with highly flexible thin-walled cross-sections.

Picault¹,

Bourgeois²,

Cochelin³

et al. 2012

53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

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Cascade unlooping of a low-pitch helical spring under tension

Cited by 11 publications

References 20 publications

Design and application of ‘J-shaped’ stress–strain behavior in stretchable electronics: a review

Design and application of ‘J-shaped’ stress–strain behavior in stretchable electronics: a review

Numerical modeling of static equilibria and bifurcations in bigons and bigon rings

On the folding and deployment of tape springs: A large displacements and large rotations rod model with highly flexible thin-walled cross-sections.

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