Characterization of fracture in topology-optimized bio-inspired networks

Trabecular bone is a flexible, lightweight bone tissue that exhibits an anisotropic microarchitecture resembling a web of interconnected struts (trabeculae). We simulate trabecular bone architectures with multi-objective topology optimization, effectively reverse-engineering trabecular structure by optimizing biologically-motivated objectives. Starting from an identical volume, we generate different topologies by varying the objective weights for compliance, surface area, and stability. We model these topologies as disordered, spatially-embedded networks where edges represent trabeculae and nodes represent branch points where trabeculae meet. We simulate mechanical loading on finite-element models where each edge is replaced by a beam, enabling direct comparison of mechanics and topology at multiple scales ranging from that of individual edges/beams to the network at large. We compare the mechanical response of the various topology-optimized networks and identify mechanisms of crack propagation. We characterize and predict crack pathways with community detection methods inspired by similar applications in the study of granular materials.