Beam network model for fracture of materials with hierarchical microstructure

We introduce a beam network model for hierarchically patterned materials. In these materials, load-parallel gaps intercept stress transmission in the load perpendicular direction in such a manner that damage is confined within hierarchically nested, load-carrying ‘modules’. We describe the morphological characteristics of such materials in terms of deterministically constructed, hierarchical beam network (DHBN) models and randomized variants thereof. We then use these models to analyse the process of damage accumulation (characterized by the locations and timings of beam breakages prior to global failures, and the concomitant avalanche statistics) and of global failure. We demonstrate that, irrespective of the degree of local disorder, failure of hierarchically (micro)structured materials is characterized by diffuse local damage nucleation which ultimately percolates on the network, but never by stress-driven propagation of a critical crack. Failure of non hierarchical reference networks, on the other hand, is characterized by the sequence of damage nucleation, crack formation and crack propagation. These differences are apparent at low and intermediate degrees of material disorder but disappear in very strongly disordered materials where the local failure strengths exhibit extreme scatter. We furthermore demonstrate that, independent of material disorder, the different modes of failure lead to significant differences in fracture surface morphology.