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Crack patterns obtained by unidirectional drying of a colloidal suspension in a capillary tube: experiments and numerical simulations using a two-dimensional variational approach

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Fracture Phenomena in Nature and Technology

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Abstract

Basalt columns, septarias, and mud cracks possess beautiful and intriguing crack patterns that are hard to predict because of the presence of cracks intersections and branches. The variational approach to brittle fracture provides a mathematically sound model based on minimization of the sum of bulk and fracture energies. It does not require any a priori assumption on fracture patterns and can therefore deal naturally with complex geometries. Here, we consider shrinkage cracks obtained during unidirectional drying of a colloidal suspension confined in a capillary tube. We focus on a portion of the tube where the cross-sectional shape cracks does not change as they propagate. We apply the variational approach to fracture to a tube cross-section and look for two-dimensional crack configurations minimizing the energy for a given loading level. We achieve qualitative and quantitative agreement between experiments and numerical simulations using a regularized energy (without any assumption on the cracks shape) or solutions obtained with traditional techniques (fixing the overall crack shape a priori). The results prove the efficiency of the variational approach when dealing with crack intersections and its ability to predict complex crack morphologies without any a priori assumption on their shape.

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Acknowledgments

The work of VL and GG was partially supported by the ANR Program JC-JC ANR-05-JCJC-0029 Morphologies. CM gratefully acknowledges the funding of the French National Research Council (CNRS) for a PICS bilateral exchange program with BB and a grant of the University Pierre et Marie Curie EMERGENCES-UPMC. BB’s work was supported in part by the National Science Foundation under the grant DMS-0909267. Some of the numerical experiments were performed using resources of the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number 0CI-1053575, provided by TACC at the University of Texas under the Resource Allocation TG-DMS060014N and the resources of the Institut du Développement et des Ressources en Informatique Scientifique (IDRIS) under the DARI 2011 allocation 100064.

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Authors and Affiliations

  1. UPMC University of Paris 6, UMR 7190, Institut Jean Le Rond d’Alembert, Boite courrier 161-2, 4 Place Jussieu, Paris, 75005, France

    C. Maurini

  2. CNRS, UMR 7190, Institut Jean Le Rond d’Alembert, Boite courrier 161-2, 4 Place Jussieu, Paris, 75005, France

    C. Maurini

  3. Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, LA, 70803, USA

    B. Bourdin

  4. UPMC University of Paris 6, UMR 7608, FAST, Bat 502, Campus University, Orsay, 91405, France

    G. Gauthier & V. Lazarus

  5. UMR 7608, FAST, Bat 502, University of Paris-Sud, Campus University, Orsay, 91405, France

    G. Gauthier & V. Lazarus

  6. CNRS, UMR 7608, FAST, Bat 502, Campus University, Orsay, 91405, France

    G. Gauthier & V. Lazarus

Authors
  1. C. Maurini
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  2. B. Bourdin
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  3. G. Gauthier
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  4. V. Lazarus
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Corresponding author

Correspondence to V. Lazarus .

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Editors and Affiliations

  1. Dipartimento di Ingegneria Civile, Ambientale e Meccanica, Università di Trento, Trento, Italy

    Davide Bigoni

  2. Dipartimento di Ingegneria Civile, Architettura, Territorio, Ambiente e di Matematica, Università di Brescia, Brescia, Italy

    Angelo Carini

  3. Dipartimento di Ingegneria Civile, Ambientale e Meccanica, Università di Trento, Trento, Italy

    Massimiliano Gei

  4. Dipartimento di Ingegneria Civile, Architettura, Territorio, Ambiente e di Matematica, Università di Brescia, Brescia, Italy

    Alberto Salvadori

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Maurini, C., Bourdin, B., Gauthier, G., Lazarus, V. (2014). Crack patterns obtained by unidirectional drying of a colloidal suspension in a capillary tube: experiments and numerical simulations using a two-dimensional variational approach. In: Bigoni, D., Carini, A., Gei, M., Salvadori, A. (eds) Fracture Phenomena in Nature and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-04397-5_7

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  • DOI: https://doi.org/10.1007/978-3-319-04397-5_7

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