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By performing extensive simulations with unprecedentedly large system sizes,we unveil how rigidity influences the fracture of disordered materials. Weobserve the largest damage in networks with connectivity close to the isostaticpoint and when the rupture thresholds are small. However, regardless of networkand spring properties, a more brittle fracture is observed upon increasingsystem size. Differently from most of the fracture descriptors, the maximumstress drop, a proxy for brittleness, displays a universal non-monotonicdependence on system size. Based on this uncommon trend it is possible toidentify the characteristic system size $L^*$ at which brittleness kicks in.The more the disorder in network connectivity or in spring thresholds, thelarger $L^*$. Finally, we speculate how this size-induced brittleness isinfluenced by thermal fluctuations.

Athermal Fracture of Elastic Networks: How Rigidity Challenges the Unavoidable Size-Induced Brittleness