Letter

Fracture in sheets draped on curved surfaces

  • Nature Materials volume 16, pages 8993 (2017)
  • doi:10.1038/nmat4733
  • Download Citation
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Abstract

Conforming materials to rigid substrates with Gaussian curvature—positive for spheres and negative for saddles—has proven a versatile tool to guide the self-assembly of defects such as scars, pleats1,2,3,4,5, folds, blisters6,7, and liquid crystal ripples8. Here, we show how curvature can likewise be used to control material failure and guide the paths of cracks. In our experiments, and unlike in previous studies on cracked plates and shells9,10,11, we constrained flat elastic sheets to adopt fixed curvature profiles. This constraint provides a geometric tool for controlling fracture behaviour: curvature can stimulate or suppress the growth of cracks and steer or arrest their propagation. A simple analytical model captures crack behaviour at the onset of propagation, while a two-dimensional phase-field model with an added curvature term successfully captures the crack’s path. Because the curvature-induced stresses are independent of material parameters for isotropic, brittle media, our results apply across scales12,13.

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Acknowledgements

The authors thank E. Efrati, H. Kedia, D. Kleckner, M. Driscoll, S. Nagel, T. Witten and R. Scott for interesting discussions and J. Mazor for assistance with some supplementary experiments. Some simulations were carried out on the Midway Cluster provided by the University of Chicago Research Computing Center. We acknowledge the Materials Research and Engineering Centers (MRSEC) Shared Facilities at The University of Chicago for the use of their instruments. This work was supported by the National Science Foundation MRSEC Program at The University of Chicago (Grant DMR-1420709) and a Packard Fellowship. V.K. and V.V. acknowledge funding from FOM and NWO.

Author information

Affiliations

  1. James Franck Institute and Department of Physics, The University of Chicago, Chicago, Illinois 60637, USA

    • Noah P. Mitchell
    •  & William T. M. Irvine
  2. Instituut-Lorentz for Theoretical Physics, Universiteit Leiden, 2333 CA Leiden, The Netherlands

    • Vinzenz Koning
    •  & Vincenzo Vitelli
  3. Enrico Fermi Institute, The University of Chicago, Chicago, Illinois 60637, USA

    • William T. M. Irvine

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Contributions

W.T.M.I. and V.V. initiated this study. N.P.M. and W.T.M.I. designed experiments. N.P.M. performed and analysed the experiments and simulations. N.P.M. and V.K. constructed the analytical model. All authors interpreted the data. N.P.M., V.V. and W.T.M.I. wrote the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to Noah P. Mitchell or William T. M. Irvine.

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