Simulating capillary folding of thin elastic sheets with pinned contact lines
We consider the capillary folding of thin elastic sheets with pinned contact lines in three dimensions. The folding occurs due to the interaction between the elastic sheet and a droplet deposited on top of it. Firstly, we derive the equilibrium equations by minimizing the total energy of the system....
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| Published in | Journal of computational physics Vol. 511; p. 113124 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
15.08.2024
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0021-9991 1090-2716 |
| DOI | 10.1016/j.jcp.2024.113124 |
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| Abstract | We consider the capillary folding of thin elastic sheets with pinned contact lines in three dimensions. The folding occurs due to the interaction between the elastic sheet and a droplet deposited on top of it. Firstly, we derive the equilibrium equations by minimizing the total energy of the system. This energy comprises the interfacial energies and the elastic energy, which is described by the nonlinear Koiter's model. Then we develop a time-splitting numerical scheme to solve the gradient flow dynamics. Following this dynamics, the system evolves towards the equilibrium state. At each time step, we first determine the droplet surface with a constant mean curvature by minimizing a squared area functional, subject to the boundary condition at the pinned contact line. The elastic sheet, discretized by the C1-conforming subdivision element method, is then evolved by taking into account the fluid pressure and the capillary force. We propose a novel remeshing strategy to avoid the need for interpolating the capillary force on the sheet boundary and to prevent simulations from breakdown due to distorted meshes. We perform numerical tests to demonstrate the accuracy of the numerical method, as well as its ability to predict folded structures for various types of sheets.
•Introduced a 3D model for the capillary folding of thin elastic sheets.•Developed a time-splitting numerical scheme for the gradient flow dynamics.•Proposed a novel remeshing strategy to avoid distorted meshes.•Obtained numerical results in good agreements with experimental results. |
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| AbstractList | We consider the capillary folding of thin elastic sheets with pinned contact lines in three dimensions. The folding occurs due to the interaction between the elastic sheet and a droplet deposited on top of it. Firstly, we derive the equilibrium equations by minimizing the total energy of the system. This energy comprises the interfacial energies and the elastic energy, which is described by the nonlinear Koiter's model. Then we develop a time-splitting numerical scheme to solve the gradient flow dynamics. Following this dynamics, the system evolves towards the equilibrium state. At each time step, we first determine the droplet surface with a constant mean curvature by minimizing a squared area functional, subject to the boundary condition at the pinned contact line. The elastic sheet, discretized by the C1-conforming subdivision element method, is then evolved by taking into account the fluid pressure and the capillary force. We propose a novel remeshing strategy to avoid the need for interpolating the capillary force on the sheet boundary and to prevent simulations from breakdown due to distorted meshes. We perform numerical tests to demonstrate the accuracy of the numerical method, as well as its ability to predict folded structures for various types of sheets.
•Introduced a 3D model for the capillary folding of thin elastic sheets.•Developed a time-splitting numerical scheme for the gradient flow dynamics.•Proposed a novel remeshing strategy to avoid distorted meshes.•Obtained numerical results in good agreements with experimental results. |
| ArticleNumber | 113124 |
| Author | Li, Zhixuan Ren, Weiqing |
| Author_xml | – sequence: 1 givenname: Zhixuan surname: Li fullname: Li, Zhixuan email: zhixuanli@u.nus.edu – sequence: 2 givenname: Weiqing orcidid: 0000-0001-5730-867X surname: Ren fullname: Ren, Weiqing email: matrw@nus.edu.sg |
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| Cites_doi | 10.1063/1.2646754 10.1016/j.jcp.2004.01.029 10.1103/PhysRevE.102.062803 10.1090/mcom/3584 10.1103/PhysRevE.89.043011 10.1017/jfm.2022.1083 10.1016/j.jcp.2006.05.023 10.1002/smll.201601147 10.1002/nme.182 10.1137/140981058 10.1137/18M1210277 10.4208/cicp.OA-2017-0210 10.1016/j.jcp.2016.06.035 10.1063/1.3501317 10.1146/annurev-fluid-122316-050130 10.1137/17M1143034 10.1088/0960-1317/19/8/083001 10.1016/j.cad.2015.10.007 10.1016/0167-8396(94)00007-F 10.1109/JMEMS.2003.811724 10.1002/(SICI)1097-0207(20000430)47:12<2039::AID-NME872>3.0.CO;2-1 10.1051/m2an/2017037 10.1016/j.jcp.2005.07.020 10.1017/jfm.2023.1051 10.1137/21M1416631 10.1137/140972275 10.1137/18M1166961 10.1103/PhysRevLett.98.156103 |
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| Keywords | Koiter's energy Capillary folding Elastic sheet Subdivision element Contact line |
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| Snippet | We consider the capillary folding of thin elastic sheets with pinned contact lines in three dimensions. The folding occurs due to the interaction between the... |
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| SubjectTerms | Capillary folding Contact line Elastic sheet Koiter's energy Subdivision element |
| Title | Simulating capillary folding of thin elastic sheets with pinned contact lines |
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