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A programmable environment for shape optimization and shapeshifting problems

Nature Computational Science (2024)Cite this article

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A preprint version of the article is available at arXiv.

Abstract

Soft materials underpin many domains of science and engineering, including soft robotics, structured fluids, and biological and particulate media. In response to applied mechanical, electromagnetic or chemical stimuli, such materials typically change shape, often dramatically. Predicting their structure is of great interest to facilitate design and mechanistic understanding, and can be cast as an optimization problem where a given energy function describing the physics of the material is minimized with respect to the shape of the domain and additional fields. However, shape-optimization problems are very challenging to solve, and there is a lack of suitable simulation tools that are both readily accessible and general in purpose. Here we present an open-source programmable environment, Morpho, and demonstrate its versatility by showcasing a range of applications from different areas of soft-matter physics: swelling hydrogels, complex fluids that form aspherical droplets, soap films and membranes, and filaments.

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Fig. 1: Soap films and membranes.
Fig. 2: Nematic liquid-crystal tactoids.
Fig. 3: Modeling swelling hydrogels under confinement using tetrahedral meshes and level-set constraints.
Fig. 4: Filament on a spherical substrate.
Fig. 5: Level-set methods.

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Data availability

All data were generated by Morpho from input scripts provided in a separate repository at https://doi.org/10.5281/zenodo.14193815 (ref. 83). Source data are provided with this paper.

Code availability

The Morpho code used for this study is archived with Zenodo at https://doi.org/10.5281/zenodo.14179515 (ref. 43). Updated versions will be available from GitHub at https://github.com/Morpho-lang/morpho. Source code for all examples shown in this publication is provided in a separate repository at https://doi.org/10.5281/zenodo.14193814 (ref. 83). All code is released under an open-source MIT license.

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Acknowledgements

This material is based on work supported by the National Science Foundation under grant no. ACI-2003820. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript. T.J.A. thanks the many people who have used various versions of the program or otherwise contributed to the project: C. Moseley, K. Vohra, P. Navarro, H. Ramirez, R. Ong, S. Wufeng, A. Wilson, A. Culbert, A. DeBenedictis, B. Mbanga, C. Burke, I. Hunter, M. Giso, M. S. E. Peterson, Z. Xie, J. E. Flores-Calderón and students from the Tufts Computational Physics course who patiently tried early versions of the code.

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Authors and Affiliations

  1. Department of Physics and Astronomy, Tufts University, Medford, MA, USA

    Chaitanya Joshi, Daniel Hellstein, Cole Wennerholm, Eoghan Downey, Emmett Hamilton & Timothy J. Atherton

  2. Department of Mathematics, Tufts University, Medford, MA, USA

    Emmett Hamilton, Samuel Hocking, Anca S. Andrei & James H. Adler

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  1. Chaitanya Joshi
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Contributions

T.J.A. designed the overall architecture for the Morpho code. T.J.A., C.J. and D.H. contributed to implementation. A.S.A., S.H. and J.H.A. advised on optimization algorithms. C.W. and E.D. developed the tactoid analysis example. E.H. devised the tubule pulling example. C.J. developed the filament and hydrogel examples. All authors prepared the paper.

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Correspondence to Timothy J. Atherton.

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Nature Computational Science thanks the anonymous reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Jie Pan, in collaboration with the Nature Computational Science team.

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Supplementary information

Supplementary Information

Supplementary Video 1

Membrane tether at increasing indentation.

Supplementary Video 2

Swelling hydrogel bead between confining spheres.

Supplementary Video 3

Coiling transition of an elastic filament confined to a curved surface.

Supplementary Video 4

Two-dimensional minimal surface problem solved by a level-set method with finite differences.

Supplementary Video 5

Two-dimensional minimal surface problem solved by a variational level-set method.

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Source Data Fig. 1

Statistical source data.

Source Data Fig. 2

Statistical source data.

Source Data Fig. 3

Statistical source data.

Source Data Fig. 4

Statistical source data.

Source Data Fig. 5

Statistical source data.

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Joshi, C., Hellstein, D., Wennerholm, C. et al. A programmable environment for shape optimization and shapeshifting problems. Nat Comput Sci (2024). https://doi.org/10.1038/s43588-024-00749-7

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