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Networks of interconnected materials permeate throughout nature, biology, and
technology due to exceptional mechanical performance. Despite the importance of
failure resistance in network design and utility, no existing physical model
effectively links strand mechanics and connectivity to predict bulk fracture.
Here, we reveal a universal scaling law that bridges these levels to predict
the intrinsic fracture energy of diverse networks. Simulations and experiments
demonstrate its remarkable applicability to a breadth of strand constitutive
behaviors, topologies, dimensionalities, and length scales. We show that local
strand rupture and nonlocal energy release contribute synergistically to the
measured intrinsic fracture energy in networks. These effects coordinate such
that the intrinsic fracture energy scales independent of the energy to rupture
a strand; it instead depends on the strand rupture force, breaking length, and
connectivity. Our scaling law establishes a physical basis for understanding
network fracture and a framework for fabricating tough materials from networks
across multiple length scales.
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