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

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 C. Maurini UPMC Univ Paris 6, UMR 7190, Institut Jean Le Rond d’Alembert, Boite courrier 161-2, 4 Place Jussieu, 75005 Paris, France e-mail: [email protected] C. Maurini CNRS, UMR 7190, Institut Jean Le Rond d’Alembert, Boite courrier 161-2, 4 Place Jussieu, 75005 Paris, France B. Bourdin Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, LA 70803, USA e-mail: [email protected] G. Gauthier · V. Lazarus (B) UPMC Univ Paris 6, UMR 7608, FAST, Bat 502, Campus Univ, 91405 Orsay, France e-mail: [email protected] G. Gauthier · V. Lazarus Univ Paris-Sud, UMR 7608, FAST, Bat 502, Campus Univ, 91405 Orsay, France e-mail: [email protected] G. Gauthier · V. Lazarus CNRS, UMR 7608, FAST, Bat 502, Campus Univ, 91405 Orsay, France 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.