Nonlocality and its Influence on the Fracture of Architected Solids
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Architected solids exhibit non-classical mechanical behaviour that emerges primarily from their internal geometry. While such architectures enable exceptional strength-to-weight ratios through geometry-driven mechanisms, they also manifest rich, strongly geometry-dependent fracture responses that challenge conventional continuum descriptions and failure criteria. Detailed numerical resolution of these materials is often prohibitively expensive, motivating homogenised descriptions. However, classical homogenisation relies on local constitutive assumptions, erasing the intrinsic nonlocal interactions that govern crack initiation, propagation, and stiffness evolution. This work introduces a nonlocal, mechanics-driven homogenised continuum framework for fracture that explicitly incorporates a finite interaction horizon representing the crackâs sensing distance ahead of its tip. Nonlocality is embedded through a stochastic gradient estimator (SGE), which reimagines balance laws using a projection-based derivative operator with an intrinsic radius of influence. This approach captures deformation and damage evolution without higher-order gradients or auxiliary fields, while ensuring stress regularisation at crack tips and preserving the classical structure and physical interpretability of the governing equations. The framework reveals how nonlocal stress redistribution couples fracture behaviour to microstructural and geometric features that are invisible to local models. Through benchmark fracture problems and elastically equivalent architected microstructures, the study demonstrates that nonlocal interactions govern stiffness degradation, crack nucleation sites, and consequent damage evolution. Increasing the interaction length produces expected strain-energy nonlocalisation, but also leads to non-intuitive, geometry-induced effects, including reversals in apparent stiffness trends driven by geometry-assisted stress redistribution. These behaviours cannot be reproduced by local homogenisation. Overall, the study establishes that fracture in architected solids is inherently nonlocal, controlled by geometry over a finite interaction horizon, and that a homogenised continuum endowed with an appropriate nonlocal length scale is essential for capturing both standard and emergent fracture phenomena without explicit microstructural resolution.
