Snap-induced morphing: From a single bistable shell to the origin of shape bifurcation in interacting shells

Mingchao Liu; Lucie Domino; Iris Dupont de Dinechin; Matteo Taffetani; Dominic Vella

doi:10.1016/j.jmps.2022.105116

Snap-induced morphing: From a single bistable shell to the origin of shape bifurcation in interacting shells

Mingchao Liu, Lucie Domino, Iris Dupont de Dinechin, Matteo Taffetani, Dominic Vella^*

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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Abstract

The bistability of embedded elements provides a natural route through which to introduce reprogrammability to elastic meta-materials. One example of this is the soft morphable sheet, in which bistable elements that can be snapped up or down, are embedded within a soft sheet. The state of the sheet can then be programmed by snapping particular elements up or down, resulting in different global shapes. However, attempts to leverage this programmability have been limited by the tendency for the deformations induced by multiple elastic elements to cause large global shape bifurcations. We study the root cause of this bifurcation in the soft morphable sheet by developing a detailed understanding of the behaviour of a single bistable element attached to a flat ‘skirt’ region. We study the geometrical limitations on the bistability of this single element, and show that the structure of its deformation can be understood using a boundary layer analysis. Moreover, by studying the compressive strains that a single bistable element induces in the surrounding skirt we show that the shape bifurcation in the soft morphable sheet can be delayed by an appropriate design of the lattice on which bistable elements are placed.

Original language	English
Article number	105116
Number of pages	15
Journal	Journal of the Mechanics and Physics of Solids
Volume	170
Early online date	25 Oct 2022
DOIs	https://doi.org/10.1016/j.jmps.2022.105116
Publication status	Published - 1 Jan 2023

Bibliographical note

Funding Information:
The research leading to these results has received funding from the Royal Society through a Newton International Fellowship (ML), the European Research Council under the European Union's Horizon 2020 Programme/ERC Grant Agreement no. 637334 (DV) and the Leverhulme Trust through a Philip Leverhulme Prize (DV). MT is a member of the Gruppo Nazionale di Fisica Matematica (GNFM) of the Istituto Nazionale di Alta Matematica (INdAM). We are grateful to Y. Zhang for discussions on FEA simulations, and to S. Koot for his help on 3D printing samples.

Funding Information:
The research leading to these results has received funding from the Royal Society through a Newton International Fellowship (ML), the European Research Council under the European Union’s Horizon 2020 Programme/ERC Grant Agreement no. 637334 (DV) and the Leverhulme Trust through a Philip Leverhulme Prize (DV). MT is a member of the Gruppo Nazionale di Fisica Matematica (GNFM) of the Istituto Nazionale di Alta Matematica (INdAM). We are grateful to Y. Zhang for discussions on FEA simulations, and to S. Koot for his help on 3D printing samples.

Publisher Copyright:
© 2022 The Authors

Keywords

Dimpled sheet
Shape morphing
Shell buckling

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title = "Snap-induced morphing: From a single bistable shell to the origin of shape bifurcation in interacting shells",

abstract = "The bistability of embedded elements provides a natural route through which to introduce reprogrammability to elastic meta-materials. One example of this is the soft morphable sheet, in which bistable elements that can be snapped up or down, are embedded within a soft sheet. The state of the sheet can then be programmed by snapping particular elements up or down, resulting in different global shapes. However, attempts to leverage this programmability have been limited by the tendency for the deformations induced by multiple elastic elements to cause large global shape bifurcations. We study the root cause of this bifurcation in the soft morphable sheet by developing a detailed understanding of the behaviour of a single bistable element attached to a flat {\textquoteleft}skirt{\textquoteright} region. We study the geometrical limitations on the bistability of this single element, and show that the structure of its deformation can be understood using a boundary layer analysis. Moreover, by studying the compressive strains that a single bistable element induces in the surrounding skirt we show that the shape bifurcation in the soft morphable sheet can be delayed by an appropriate design of the lattice on which bistable elements are placed.",

keywords = "Dimpled sheet, Shape morphing, Shell buckling",

author = "Mingchao Liu and Lucie Domino and {Dupont de Dinechin}, Iris and Matteo Taffetani and Dominic Vella",

note = "Funding Information: The research leading to these results has received funding from the Royal Society through a Newton International Fellowship (ML), the European Research Council under the European Union's Horizon 2020 Programme/ERC Grant Agreement no. 637334 (DV) and the Leverhulme Trust through a Philip Leverhulme Prize (DV). MT is a member of the Gruppo Nazionale di Fisica Matematica (GNFM) of the Istituto Nazionale di Alta Matematica (INdAM). We are grateful to Y. Zhang for discussions on FEA simulations, and to S. Koot for his help on 3D printing samples. Funding Information: The research leading to these results has received funding from the Royal Society through a Newton International Fellowship (ML), the European Research Council under the European Union{\textquoteright}s Horizon 2020 Programme/ERC Grant Agreement no. 637334 (DV) and the Leverhulme Trust through a Philip Leverhulme Prize (DV). MT is a member of the Gruppo Nazionale di Fisica Matematica (GNFM) of the Istituto Nazionale di Alta Matematica (INdAM). We are grateful to Y. Zhang for discussions on FEA simulations, and to S. Koot for his help on 3D printing samples. Publisher Copyright: {\textcopyright} 2022 The Authors",

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AU - Domino, Lucie

AU - Dupont de Dinechin, Iris

AU - Taffetani, Matteo

AU - Vella, Dominic

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N2 - The bistability of embedded elements provides a natural route through which to introduce reprogrammability to elastic meta-materials. One example of this is the soft morphable sheet, in which bistable elements that can be snapped up or down, are embedded within a soft sheet. The state of the sheet can then be programmed by snapping particular elements up or down, resulting in different global shapes. However, attempts to leverage this programmability have been limited by the tendency for the deformations induced by multiple elastic elements to cause large global shape bifurcations. We study the root cause of this bifurcation in the soft morphable sheet by developing a detailed understanding of the behaviour of a single bistable element attached to a flat ‘skirt’ region. We study the geometrical limitations on the bistability of this single element, and show that the structure of its deformation can be understood using a boundary layer analysis. Moreover, by studying the compressive strains that a single bistable element induces in the surrounding skirt we show that the shape bifurcation in the soft morphable sheet can be delayed by an appropriate design of the lattice on which bistable elements are placed.

AB - The bistability of embedded elements provides a natural route through which to introduce reprogrammability to elastic meta-materials. One example of this is the soft morphable sheet, in which bistable elements that can be snapped up or down, are embedded within a soft sheet. The state of the sheet can then be programmed by snapping particular elements up or down, resulting in different global shapes. However, attempts to leverage this programmability have been limited by the tendency for the deformations induced by multiple elastic elements to cause large global shape bifurcations. We study the root cause of this bifurcation in the soft morphable sheet by developing a detailed understanding of the behaviour of a single bistable element attached to a flat ‘skirt’ region. We study the geometrical limitations on the bistability of this single element, and show that the structure of its deformation can be understood using a boundary layer analysis. Moreover, by studying the compressive strains that a single bistable element induces in the surrounding skirt we show that the shape bifurcation in the soft morphable sheet can be delayed by an appropriate design of the lattice on which bistable elements are placed.

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KW - Shell buckling

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DO - 10.1016/j.jmps.2022.105116

M3 - Article (Academic Journal)

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JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

M1 - 105116

ER -

Snap-induced morphing: From a single bistable shell to the origin of shape bifurcation in interacting shells

Abstract

Bibliographical note

Keywords

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