Things fall apart: the universal geometry of failure
Cracks are everywhere. These ubiquitous signatures of brittle failure can be found from micron to kilometer scales in natural and human-made systems alike. When things fall apart, they encode the mechanisms of their failure in their geometry. In this dissertation, I implement a novel geometric framework and dynamical cracking model, coupled with laboratory experimentation, to first categorize thin fractured films across the solar system, and then to validate these categorizations by creating simple but tunable experiments in analog materials. In doing so, I demonstrate that nature preferentially forms mosaics that are statistically equivalent to a "brick-wall" pattern, and that outliers to this preference -- hexagonal and grid patterns -- are formed via crack twisting or overprinting respectively. These behaviors are universal; they operate independently of system initial conditions or material composition. This work connects the fields of mathematics, geophysics, and planetary science with the aim of introducing and validating a novel method for use by the broader scientific community that can improve our understanding of crack mechanics and pattern evolution through time.
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