Open AccessModeling Crack Patterns by Modified STIT Tessellations
Author(s) -
Roberto León,
Werner Nagel,
Joachim Ohser,
S. Arscott
Publication year - 2020
Publication title -
image analysis and stereology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.237
H-Index - 27
eISSN - 1854-5165
pISSN - 1580-3139
DOI - 10.5566/ias.2245
Subject(s) - tessellation (computer graphics) , parametric statistics , division (mathematics) , fracture (geology) , planar , voronoi diagram , computer science , development (topology) , geology , geometry , mathematics , computer graphics (images) , statistics , geotechnical engineering , mathematical analysis , arithmetic
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.