A nonlocally-informed locally-scaled method for fracture: numerical implementation to model fragmentation of tempered glass

Abstract This contribution presents a new nonlocally-informed locally-scaled (NILS) method for fracture and its finite-element implementation. Referring to volume-approximation of sharp cracks, a modelling strategy is proposed, where a coupled local-nonlocal fracture criterion is formulated. Fracture is referred to as a local process, where a local ground-state fracture criterion is deviated from to formulate a nonlocally-informed counterpart. The formulation tackles discretization-related issues and allows capturing underlying phenomena of brittle fracture, which improves the capability of predicting complex crack-patterns. The main idea of the NILS method is to consider a subdomain-wise fracture criterion in terms of local quantities scaled by nonlocally-informed functions, which carry information about the energy- and fracture-state within a certain neighbourhood surrounding the subdomain, for which the criterion is evaluated. Nonlocally-informed subdomain-wise crack driving and fracture resistance energies are derived referring to volume-approximation of sharp cracks, while addressing mesh-dependency of the predicted crack-paths, the issue of possibly unrealistic crack initiations away from the crack-tip and spatial deviations in the material brittleness, i.e., relatively high brittleness at the tips of sharp cracks. The simulation of crack-initiation and crack-merging is addressed, where the related performance of the NILS method is compared to its counterpart of other approaches. Fracture is referred to in a binary sense, which is similar to the setting of eigenerosion and eigenfracture methods. A parallel finite-element implementation of the NILS method is proposed, where synchronization algorithms are presented. The predictability of the proposed method and the associated fracture criterion is tested through simulating dynamic fragmentation of tempered glass.