Modeling Crack Patterns by Modified STIT Tessellations


  • Roberto León Universidad Andres Bello, Facultad de Ingeniería, Quillota 980, Vina del Mar, Chile
  • Werner Nagel University of Jena, Institute of Mathematics, 07737 Jena, Germany
  • Joachim Ohser University of Applied Sciences, Department of Mathematics and Natural Sciences, Schöfferstr. 3, 64295 Darmstadt, Germany
  • Steve Arscott Institut d'Electronique, de Microélectronique et de Nanotechnologie (IEMN), CNRS, The University of Lille, Cité Scientifique, 59652 Villeneuve d'Ascq, France



fracture pattern, geometry-statistics, Monte Carlo simulation, random tessellation, STIT tessellation


Random planar tessellations are presented which are generated by subsequent division of their polygonal cells. The purpose is to develop parametric models for crack patterns appearing at length scales which can change by orders of magnitude in areas such as nanotechnology, materials science, soft matter, and geology. Using the STIT tessellation as a reference model and comparing with phenomena in real crack patterns, three modifications of STIT are suggested. For all these models a simulation tool, which also yields several statistics for the tessellation cells, is provided on the web. The software is freely available via a link given in the bibliography of this article. The present paper contains results of a simulation study indicating some essential features of the models. Finally, an example of a real fracture pattern is considered which is obtained using the deposition of a thin metallic film onto an elastomer material – the results of this are compared to the predictions of the model.


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How to Cite

León, R., Nagel, W., Ohser, J., & Arscott, S. (2020). Modeling Crack Patterns by Modified STIT Tessellations. Image Analysis and Stereology, 39(1), 33–46.



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