Evolution of critical buckling conditions in imperfect bilayer shells through residual swelling

Lee, Anna; Yan, Dong; Pezzulla, Matteo; Holmes, Douglas P.; Reis, Pedro

doi:10.1039/c9sm00901a

Cited by 16 publications

(6 citation statements)

References 26 publications

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“…In particular, the geometry and placement of a dominant defect prescribe, respectively, the buckling strength and the spot where an instability localizes. Recent extensions of this concept couple geometric defects with differentially swelling [29] or magneto-responsive [30] materials to modify the knockdown factor over time. Relatedly, a more general study showed how a homogeneous natural curvature-which can be a proxy for nonmechanical stimuli like thermal expansion, changes in pH, or differential growth-acts to raise or lower the knockdown factor in spherical shells [31].…”

Section: Introductionmentioning

confidence: 99%

Delayed buckling of spherical shells due to viscoelastic knockdown of the critical load

Stein-Montalvo

Coupier

2021

Proc. R. Soc. A.

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We performed dynamic pressure buckling experiments on defect-seeded spherical shells made of a common silicone elastomer. Unlike in quasi-static experiments, shells buckled at ostensibly subcritical pressures, i.e. below the experimentally determined critical load at which buckling occurs elastically, often following a significant delay period from the time of load application. While emphasizing the close connections to elastic shell buckling, we rely on viscoelasticity to explain our observations. In particular, we demonstrate that the lower critical load may be determined from the material properties, which is rationalized by a simple analogy to elastic spherical shell buckling. We then introduce a model centred on empirical quantities to show that viscoelastic creep deformation lowers the critical load in the same predictable, quantifiable way that a growing defect would in an elastic shell. This allows us to capture how both the deflection at instability and the time delay depend on the applied pressure, material properties and defect geometry. These quantities are straightforward to measure in experiments. Thus, our work not only provides intuition for viscoelastic behaviour from an elastic shell buckling perspective but also offers an accessible pathway to introduce tunable, time-controlled actuation to existing mechanical actuators, e.g. pneumatic grippers.

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Section: Introductionmentioning

confidence: 99%

Delayed buckling of spherical shells due to viscoelastic knockdown of the critical load

Stein-Montalvo

Coupier

2021

Proc. R. Soc. A.

Self Cite

View full text Add to dashboard Cite

show abstract

“…In particular, the geometry and placement of a dominant defect prescribe, respectively, the buckling strength and the spot where an instability localizes. Recent extensions of this concept couple geometric defects with differentially swelling [29] or magneto-responsive [30] materials to modify the knockdown factor over time. Relatedly, a more general study showed how a homogenous natural curvaturewhich can be a proxy for nonmechanical stimuli like thermal expansion, changes in pH, or differential growth -acts to raise or lower the knockdown factor in spherical shells [31].…”

Section: Introductionmentioning

confidence: 99%

Delayed buckling of spherical shells due to viscoelastic knockdown of the critical load

Stein-Montalvo,

Holmes,

Coupier

2021

Preprint

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We performed dynamic pressure buckling experiments on defect-seeded spherical shells made of a common silicone elastomer. Unlike in quasi-static experiments, shells buckled at ostensibly subcritical pressures (i.e. below the experimentally-determined load at which buckling occurs elastically), often following a significant time delay. While emphasizing the close connections to elastic shell buckling, we rely on viscoelasticity to explain our observations. In particular, we demonstrate that the lower critical load may be determined from the material properties, which is rationalized by a simple analogy to elastic spherical shell buckling. We then introduce a model centered on empirical quantities to show that viscoelastic creep deformation lowers the critical load in the same predictable, quantifiable way that a growing defect would in an elastic shell. This allows us to capture how both the critical deflection and the delay time depend on the applied pressure, material properties, and defect geometry. These quantities are straightforward to measure in experiments. Thus, our work not only provides intuition for viscoelastic behavior from an elastic shell buckling perspective, but also offers an accessible pathway to introduce tunable, time-controlled actuation to existing mechanical actuators, e.g. pneumatic grippers.

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“…In these studies, a dimensional reduction procedure was performed on the 3D magneto-elastic energy, assuming a reduced kinematics for the beams and the rods based on the Kirchhoff-Love assumptions. Moreover, we have recently presented a study on magneto-active axisymmetric shells made of hard MREs in (Yan et al, 2020), where the coupling between mechanics and magnetism was leveraged to change the stability onsets of shells undergoing pressure buckling (Hutchinson and Thompson, 2018;Lee et al, 2016Lee et al, , 2019. In this study, experiments were contrasted with a magnetic shell model for axisymmetric deformation and geometrically exact strain measures (Yan et al, 2020).…”

Section: Introductionmentioning

confidence: 99%

A geometrically exact model for thin magneto-elastic shells

Pezzulla,

Yan,

Reis

2021

Preprint

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We develop a reduced model for hard-magnetic, thin, linear-elastic shells that can be actuated through an external magnetic field, with geometrically exact strain measures. Assuming a reduced kinematics based on the Kirchhoff-Love assumption, we derive a reduced two-dimensional magneto-elastic energy that can be minimized through numerical analysis. In parallel, we simplify the reduced energy by expanding it up to the second order in the displacement field and provide a physical interpretation. Our theoretical analysis allows us to identify and interpret the two primary mechanisms dictating the magneto-elastic response: a combination of equivalent magnetic pressure and forces at the first order, and distributed magnetic torques at the second order. We contrast our reduced framework against a three-dimensional nonlinear model by investigating three test cases involving the indentation and the pressure buckling of shells under magnetic loading. We find excellent agreement between the two approaches, thereby verifying our reduced model for shells undergoing nonlinear and non-axisymmetric deformations. We believe that our model for magneto-elastic shells will serve as a valuable tool for the rational design of magnetic structures, enriching the set of reduced magnetic models.

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Evolution of critical buckling conditions in imperfect bilayer shells through residual swelling

Abstract: We propose and investigate a minimal mechanism that makes use of differential swelling to modify the critical buckling conditions of elastic bilayer shells, as measured by the knockdown factor.

Cited by 16 publications

References 26 publications

Delayed buckling of spherical shells due to viscoelastic knockdown of the critical load

Delayed buckling of spherical shells due to viscoelastic knockdown of the critical load

Delayed buckling of spherical shells due to viscoelastic knockdown of the critical load

A geometrically exact model for thin magneto-elastic shells

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