Fig. 3: Programming the fracture resisting features in mechanical metamaterial.

a Artificial toughening units inspired by nature (middle), micro-scale fracture toughening events observed using X-ray computed tomography (XCT) scanning (left), and their experimentally captured macroscale crack-resisting behaviors (right). Crack bowing (CB, red) phase is designed with type-1 DP cells, while crack deflection (CD, blue) phase is developed with a combination of type-1 and type-2 DP cells. Negative shielding (NS, yellow on the middle/left) and positive shielding (PS, purple on the middle/left) layers of the shield units (gradient purple on the right) are developed by type-3 DP cells. Light blue boxes on the right and dark gray structures on middle/left indicate reinforcement bridges, and light gray represent conventional cells without damage programming. Refer to Supplementary Note 3 for detailed design rationales of the toughening units and crack-resisting mechanisms. The images of metamaterial samples (right) are captured by camera during the fracture experiments. The red gradient arrows indicate the crack propagations according to XCT-scanned micro-scale fracture toughening events (left), schematic crack propagations of micro-scale fracture toughening events (middle), and the overall macroscopic fracture paths of the metamaterial samples (right). b The theoretical curves and experimentally validated fracture energies normalized by densities of conventional metamaterials and DP metamaterials with CB phases, CD phases, shield units, and reinforcement bridges, respectively. \({\theta }_{s}\), \({d}_{B}\), \(\rho\), \({\rho }_{{CB}}\), and \({d}_{{CD}}\) represent shield angle, distance between adjacent reinforcement fibers, density of conventional metamaterials, density of CB phases, distance between the adjacent CD phases, respectively. The error bars are calculated based on the standard deviations from the results of three repetitive experiments. Note that certain error bars were small, making them almost indiscernible. c Quantification of normalized fracture energy per propagation unit associated with individual toughening mechanisms. Source data are provided as a Source Data file.