The Geometric Role of Precisely Engineered Imperfections on the Critical Buckling Load of Spherical Elastic Shells

Lee, Anna; Jiménez, Francisco López; Marthelot, Joël; Hutchinson, John W.; Reis, Pedro

doi:10.1115/1.4034431

Cited by 143 publications

(160 citation statements)

References 37 publications

(62 reference statements)

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“…The shape of the dimple is self-selected by the deformation of the outer elastic mold under indentation and can be predicted by FEM simulations as described in Ref. [3] and briefly recalled in Sec. 3.…”

Section: Fabrication Of Shells Containing a Controlled Geometricmentioning

confidence: 99%

“…To fabricate precisely imperfect thin elastic shells (i.e., shells containing a well-defined geometric imperfection), we use a second technique (itself a modification of that of Ref. [9] mentioned earlier), which we had introduced to investigate the effect of the imperfection amplitude on the critical buckling load [3]. We coated the inner side of a thick hemispherical shell of thickness t mold ¼ 975 lm, used as a mold, which was indented by a flat plate attached to a universal testing machine.…”

Section: Fabrication Of Shells Containing a Controlled Geometricmentioning

confidence: 99%

“…In the experiments, the precise shape of the initial dimple is self-selected by the elastic deformations resulting from the fixed indentation of the mold by a rigid plate, at the time of the fabrication process, during curing. In the simulations, to predict the shape of the engineered defect, we used the numerical method that we had developed and experimentally verified previously to study the effect of an imperfection on the critical buckling pressure of the shell [3,8]. The outer elastic mold was modeled as an incompressible Neo-Hookean solid, with reduced hybrid axisymmetric elements CAX4RH, and a thickness t mold ¼ 975 lm.…”

Section: Mimicking the Experimental Procedures In The Femmentioning

confidence: 99%

“…In work of our own [3,8], we have recently demonstrated that the critical buckling load of spherical shells observed in precision experiments can be accurately and deterministically predicted by both finite element modeling (FEM) and a reduced shell theory model. These experiments leveraged a previously developed technique based on a viscous coating mechanism [9] to fabricate thin polymeric shells with significant flexibility and versatility in controlling the underlying parameters.…”

Section: Introductionmentioning

confidence: 99%

“…1 in Ref. [3] for a summary of historical data) can be as low as 20% of the classical prediction for spherical shell buckling derived by Zoelly [4] in 1915…”

Section: Introductionmentioning

confidence: 99%

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Buckling of a Pressurized Hemispherical Shell Subjected to a Probing Force

Marthelot

Jiménez

Lee

et al. 2017

Journal of Applied Mechanics

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We study the buckling of hemispherical elastic shells subjected to the combined effect of pressure loading and a probing force. We perform an experimental investigation using thin shells of nearly uniform thickness that are fabricated with a well-controlled geometric imperfection. By systematically varying the indentation displacement and the geometry of the probe, we study the effect that the probe-induced deflections have on the buckling strength of our spherical shells. The experimental results are then compared to finite element simulations, as well as to recent theoretical predictions from the literature. Inspired by a nondestructive technique that was recently proposed to evaluate the stability of elastic shells, we characterize the nonlinear load-deflection mechanical response of the probe for different values of the pressure loading. We demonstrate that this nondestructive method is a successful local way to assess the stability of spherical shells.

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Section: Fabrication Of Shells Containing a Controlled Geometricmentioning

confidence: 99%

Section: Fabrication Of Shells Containing a Controlled Geometricmentioning

confidence: 99%

Section: Mimicking the Experimental Procedures In The Femmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…1 in Ref. [3] for a summary of historical data) can be as low as 20% of the classical prediction for spherical shell buckling derived by Zoelly [4] in 1915…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Buckling of a Pressurized Hemispherical Shell Subjected to a Probing Force

Marthelot

Jiménez

Lee

et al. 2017

Journal of Applied Mechanics

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Inverse Design of Mechanical Metamaterials with Target Nonlinear Response via a Neural Accelerated Evolution Strategy

et al. 2022

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Materials with target nonlinear mechanical response can support the design of innovative soft robots, wearable devices, footwear, and energy‐absorbing systems, yet it is challenging to realize them. Here, mechanical metamaterials based on hinged quadrilaterals are used as a platform to realize target nonlinear mechanical responses. It is first shown that by changing the shape of the quadrilaterals, the amount of internal rotations induced by the applied compression can be tuned, and a wide range of mechanical responses is achieved. Next, a neural network is introduced that provides a computationally inexpensive relationship between the parameters describing the geometry and the corresponding stress–strain response. Finally, it is shown that by combining the neural network with an evolution strategy, one can efficiently identify geometries resulting in a wide range of target nonlinear mechanical responses and design optimized energy‐absorbing systems, soft robots, and morphing structures.

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Modeling and Design of Zero‐Stiffness Elastomer Springs Using Machine Learning

Kim

Tawfick

King

2022

Advanced Intelligent Systems

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Architected metamaterials exhibit complex stress–strain responses, such as quasi‐zero stiffness (QZS) plateau response useful in vibration and energy absorption, by exploiting elastic instabilities such as buckling. However, the design of metamaterials with prescribed nonlinear mechanical properties is challenging due to the difficulty in accurately predicting nonlinear mechanical responses such as buckling and self‐contact, as well as geometric and material uncertainties. Herein, additive manufacturing (AM) with machine learning (ML) to demonstrate data‐driven modeling and the design of nonlinear elastomeric springs with a broad stress plateau is combined. 243 elastomer chi (χ) spring parts with different design parameters fabricated by AM are tested. A Gaussian process (GP) model is trained on key features of the measured mechanical response and predicts the mechanical response within a 3% error with as few as 97 parts. To account for the geometric and material uncertainties, the GP model to develop an uncertainty‐aware design optimization approach to tailor the mechanical response based on the covariance matrix adaptation evolution strategy (CMA‐ES) is utilized. Excellent agreement is demonstrated between the designed response and measured response over the range of plateau stress considered. The research illustrates the promise of experimental data‐driven approaches and AM in enabling complex material design.

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The Geometric Role of Precisely Engineered Imperfections on the Critical Buckling Load of Spherical Elastic Shells

Cited by 143 publications

References 37 publications

Buckling of a Pressurized Hemispherical Shell Subjected to a Probing Force

Buckling of a Pressurized Hemispherical Shell Subjected to a Probing Force

Inverse Design of Mechanical Metamaterials with Target Nonlinear Response via a Neural Accelerated Evolution Strategy

Modeling and Design of Zero‐Stiffness Elastomer Springs Using Machine Learning

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