Fabrication of self-rolling geodesic objects and photonic crystal tubes

Danescu, Alexandre; Régreny, P.; Cremillieu, Pierre; Leclercq, Jean‐Louis

doi:10.1088/1361-6528/aabf54

Cited by 9 publications

(6 citation statements)

References 25 publications

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“…One possibility is to directly prescribe the functions G(x ) on the growth surface. Three of its "incompatible" components will then describe the accumulated defects and acquired residual stresses, while the other three "compatible" components will characterize the shape of the body at the end of the deposition process; the latter is relevant in many biological problems [50] and in engineering problems related to residual actuation [58].…”

Section: Deposition Protocolsmentioning

confidence: 99%

Nonlinear elasticity of incompatible surface growth

Truskinovsky

Zurlo

2019

Phys. Rev. E

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Surface growth is a crucial component of many natural and artificial processes from cell proliferation to additive manufacturing. In elastic systems surface growth is usually accompanied by the development of geometrical incompatibility leading to residual stresses and triggering various instabilities. In a recent paper (PRL, 119, 048001, 2017) we developed a linearized elasticity theory of incompatible surface growth which quantitatively linked deposition protocols with post-growth states of stress. Here we extend this analysis to account for both physical and geometrical nonlinearities of an elastic solid. The new development reveals the shortcomings of the linearized theory, in particular, its inability to describe kinematically confined surface growth and to account for growth-induced elastic instabilities.

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Section: Deposition Protocolsmentioning

confidence: 99%

Nonlinear elasticity of incompatible surface growth

Truskinovsky

Zurlo

2019

Phys. Rev. E

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“…where we introduced ξ = h 1 ∕ h 2 . The result in (4.9) can also be obtained [31, 32] from classical Love–Kirchhoff theory of plates in plane-stress. This is expected since for a small diameter domain the linearized small-perturbation theory applies.…”

Section: Applications To Some Classical Designed Surfacesmentioning

confidence: 95%

“…Right, top: Experimental evidence of a a = 10 μ m length square plate with an isotropic in-plane pre-stress that relaxes into a shape close to a spherical cap (reprinted with permission from IOP [32]). Right, bottom: 3D finite-element computations of the relaxation of the same finite elastic square plate with the same pre-stress.…”

Section: Applications To Some Classical Designed Surfacesmentioning

confidence: 99%

Shell design from planar pre-stressed structures

Danescu

Ionescu

2020

Mathematics and Mechanics of Solids

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The interplay between mechanics and geometry is used to construct a theoretical framework able to describe the class of three-dimensional objects that can be fabricated from suitable planar designs by using relaxation of pre-strains/stress in ultra-thin films. Small deformations and large rotations are used here to model the elastic relaxation into various three-dimensional shapes. Over the kinematics associated with the designed mid-surface, a small perturbation of Love–Kirchhoff type is considered in order to deduce the design plate-to-shell equations for orthotropic materials with an important pre-stress/strain heterogeneity. The resulting equations for the efforts average and efforts moments provide the supplementary equations to compute the in-plane pre-strain/stress. In particular, for materials with a weak material transversal heterogeneity the moments equations involve only the thickness, the curvature tensor, and the pre-strain/stress moments. Special attention is devoted to materials that can be obtained by layer-by-layer crystal growth (molecular beam epitaxy), which posses an in-plane isotropic pre-strain. We have found that a rectangular plate could relax both into a cylindrical surface or on a part of a sphere in which case it should have a small diameter with respect to the sphere radius. In both cases, the theoretical estimates have been compared with the experimental realizations and finite-element numerical computations and we found very good agreement among all of them. In addition, for the cone geometry we found that the design is not possible from an isotropic pre-stress with an in-plane homogeneity. However, the 3D finite-element computation of the relaxed surface with a (necessary) non-isotropic pre-stress obtained from the theoretical estimates matches remarkably well the designed conical surface.

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“…For example, as for the currently popular helical materials, such as chiral ceramics [15] and elastic metal springs, [16] their spiral walls can obviously not play the role of an equivalent F-P unit and so does a multihole tube with the mesh-structured cladding. [17][18][19] Moreover, as for the self-rolled-up 2D material, [20,21] the cladding is usually too thin for internal oscillations and resonances of the interested EM bands. In view of the earlier facts, resolving this ARR capability could provide more tubular materials with a new perspective on strengthening the interactions with light and extending related applications.…”

Section: Introductionmentioning

confidence: 99%

Cladding‐Free Antiresonance in Tubular Structures

Zhao

Yan

Dong

et al. 2022

Advanced Photonics Research

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Antiresonance reflection (ARR) effectively turns tubular structures into functional devices ranging from waveguides to spectrometers and sensors, thus attracting a growing number of interests in recent years. Yet, ARRs are generally enabled inside the designed tube cladding with certain structural properties, which essentially acts as a quasi‐Fabry–Pérot (F–P) cavity. This limits the application of the ARR effect on popular tubular entities in non‐F–P cladding morphology, such as the chiral helical material or the self‐rolled‐up ultrathin/meshy membrane. Here, the scheme of core‐antiresonant reflection (core‐ARR or CARR) based on the leaky F–P effect is proposed, which validates ARRs inside the central core rather than the cladding of hollow tubes, hence expanding the optional scope of materials and constructions for tubular substances. Briefly, the CARR behavior is demonstrated in cylindrical, polyhedral, spiral, meshy, and notched hollow tubes with either transparent or opaque cladding materials. More importantly, tubular structures with CARR modes can be flexibly tuned in terms of the resonant frequency, which is used herein for sensitive detection of the environmental pressure, humidity, and thermal influence. As the CARR effect promotes interactions between light and various tubular structures, it holds promise for future opportunities in fields of physics, biophotonics, and material science.

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Fabrication of self-rolling geodesic objects and photonic crystal tubes

Cited by 9 publications

References 25 publications

Nonlinear elasticity of incompatible surface growth

Nonlinear elasticity of incompatible surface growth

Shell design from planar pre-stressed structures

Cladding‐Free Antiresonance in Tubular Structures

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