Title: Mechanical Failure of Disordered Lattices

Abstracts: Many engineering applications require lightweight materials with specific mechanical properties, such as a large deformation before failure or a high load-bearing capacity. Possible materials are lattices, which consist of slender beams intersecting at various points. These are for example truss bridges, the Eiffel tower, or radio towers. These engineered structures are ordered lattices. However, most lattices found in nature, for example, bones, fiber networks or rigid foams are disordered: their geometry is irregular and their response to perturbation becomes complex. To choose the proper structure for mechanical applications, we must identify which parameters affect the failure behavior and understand where failures take place. Ultimately, this will permit the optimization and safe use of structures. In this study, we address these two questions by investigating the mechanical response of 2-dimensional disordered lattices that have geometry set by the force-chain networks of granular packings. First, we show that the mean number of intersecting beams (the mean coordination) affects how the structure degrades (gradually vs. catastrophic collapse). Second, we use rigidity theory and network science tools to forecast failure locations.