### Abstract

We develop a three-dimensional model for capillary origami systems in which a rectangular plate has finite thickness, is allowed to stretch and undergoes small deflections. This latter constraint limits our description of the encapsulation process to its initial folding phase. We first simplify the resulting system of equations to two dimensions by assuming that the plate has infinite aspect ratio, which allows us to compare our approach to known two-dimensional capillary origami models for inextensible plates. Moreover, as this two-dimensional model is exactly solvable, we give an expression for its solution in terms of its parameters. We then turn to the full three-dimensional model in the limit of small drop volume and provide numerical simulations showing how the plate and the drop deform due to the effect of capillary forces.

Original language | English (US) |
---|---|

Article number | 20150169 |

Journal | Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 374 |

Issue number | 2066 |

DOIs | |

State | Published - Apr 28 2016 |

### Fingerprint

### Keywords

- Capillary origami
- Elasto-capillary system
- Energy minimization
- Nonlinear membrane

### ASJC Scopus subject areas

- Mathematics(all)
- Physics and Astronomy(all)
- Engineering(all)

### Cite this

**Capillary-induced deformations of a thin elastic sheet.** / Brubaker, N. D.; Lega, Joceline C.

Research output: Contribution to journal › Article

*Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences*, vol. 374, no. 2066, 20150169. https://doi.org/10.1098/rsta.2015.0169

}

TY - JOUR

T1 - Capillary-induced deformations of a thin elastic sheet

AU - Brubaker, N. D.

AU - Lega, Joceline C

PY - 2016/4/28

Y1 - 2016/4/28

N2 - We develop a three-dimensional model for capillary origami systems in which a rectangular plate has finite thickness, is allowed to stretch and undergoes small deflections. This latter constraint limits our description of the encapsulation process to its initial folding phase. We first simplify the resulting system of equations to two dimensions by assuming that the plate has infinite aspect ratio, which allows us to compare our approach to known two-dimensional capillary origami models for inextensible plates. Moreover, as this two-dimensional model is exactly solvable, we give an expression for its solution in terms of its parameters. We then turn to the full three-dimensional model in the limit of small drop volume and provide numerical simulations showing how the plate and the drop deform due to the effect of capillary forces.

AB - We develop a three-dimensional model for capillary origami systems in which a rectangular plate has finite thickness, is allowed to stretch and undergoes small deflections. This latter constraint limits our description of the encapsulation process to its initial folding phase. We first simplify the resulting system of equations to two dimensions by assuming that the plate has infinite aspect ratio, which allows us to compare our approach to known two-dimensional capillary origami models for inextensible plates. Moreover, as this two-dimensional model is exactly solvable, we give an expression for its solution in terms of its parameters. We then turn to the full three-dimensional model in the limit of small drop volume and provide numerical simulations showing how the plate and the drop deform due to the effect of capillary forces.

KW - Capillary origami

KW - Elasto-capillary system

KW - Energy minimization

KW - Nonlinear membrane

UR - http://www.scopus.com/inward/record.url?scp=84962920485&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84962920485&partnerID=8YFLogxK

U2 - 10.1098/rsta.2015.0169

DO - 10.1098/rsta.2015.0169

M3 - Article

AN - SCOPUS:84962920485

VL - 374

JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0962-8428

IS - 2066

M1 - 20150169

ER -