Role of topology in dictating the fracture toughness of mechanical metamaterials

The systemic comparison between sheet-based triply minimal surfaces (TPMS), strut-based ordered lattice to-pologies and plate-based lattice topologies offer insights into designs for damage tolerant and tough structures. In this work, we explore the topology-fracture toughness relationship of several classes of periodic cellular materials via a series of finite element simulations in mode I, mode II and combined loading. Results showed that sheet lattices are the toughest at higher densities, and their performance tends to degrade faster at lower relative densities & PROP;rho 3 due to plate buckling as opposed to rho(2) for their strut counterparts in mode I. In a low-density regime, TPMS sheet-based topologies lattices present a better alternative than plate-based topologies for their near-linear scaling with density for fracture toughness. Crack propagation paths for 3D cellular structures depend on fracture geometry. In center-crack fracture geometries, 3D lattices exhibit a straight crack path that is topology independent in mode I. On the other hand, crack propagation paths are topology dependent for edge -crack fracture geometries due to the T-stresses' contribution: T-13 and T-11 arising from topology discreteness. Our results shed new light on the structure-property relationship that will facilitate the design of tougher and better crack-resistant 3D cellular structures.