Topology optimization of micro-architected materials to maximize effective fracture energy

Optimizing fracture resistance in micro-architected materials remains challenging due to the complex interaction of microstructure-induced toughening mechanisms and the inherently history-dependent nature of crack propagation. In this work, we develop a gradient-based topology optimization framework to enhance the fracture resistance of micro-architected materials by maximizing effective fracture energy, defined as the maximum J-integral attained during crack growth. The framework couples a heterogeneous domain, where crack propagation and microstructure-induced toughening mechanisms are explicitly resolved, with an effective homogeneous domain to evaluate a path-independent J-integral serving as the optimization objective. A reverse adjoint formulation is derived to compute history-dependent sensitivities associated with crack irreversibility. Mechanism-guided strategies are incorporated through tailored initial configurations and optimization constraints. The results demonstrate that substantial enhancement of effective fracture energy can be achieved through the synergistic activation of multiple toughening mechanisms, including crack blunting, branching, deflection, and distributed microcracking. An intermediate relative-density regime ((Formula presented)) is identified, within which multiple mechanisms coexist and fracture energy significantly exceeds that of both the base material and canonical lattices. Experimental validation using additively manufactured specimens shows close agreement between predicted and measured crack paths, peak loads, and fracture energies. Notably, the optimized architectures exhibit strong geometric similarity to deep-sea glass sponge skeletons, highlighting the capability of the proposed framework to rediscover evolution-inspired toughening strategies through a purely mechanics-driven optimization process.