The coupled strength and toughness of interconnected and interpenetrating multi-material gyroids

The growth of additive manufacturing technologies has spurred interest in examining multi-material micro-architected materials for filling the so-called white spaces in the Ashby strength versus toughness plots. We investigate this problem using interconnected and interpenetrating double gyroids comprising ductile and brittle phases as an exemplar. Both strength and toughness at the initiation of crack growth are shown to vary non-monotonically with the volume fraction of the two phases and multi-material double gyroids significantly outperform their single material counterparts. However, we establish that at a given relative density, the strength and toughness cannot be simultaneously enhanced for architecture designs, which include varying gyroid orientations, phase volume fractions, and the unit cell length scales of the two phases. Intriguingly, even crack flank bridging by the ductile phase during crack growth is insufficient to overcome this inherent property of the interpenetrating gyroids. Our conclusion is that multi-material interpenetrating micro-architected solids are unlikely to outperform single material non-interpenetrating lattices from a strength–toughness perspective but rather become optimal when multi-functionality is required. Impact statement The integration of materials and architectural features at multiple scales into structural mechanics gave us structural designs such as the Eiffel Tower. The explosion of additive manufacturing methods has opened new avenues for the invention of multi-material micro-architected materials that simultaneously possess high strength and toughness at a low density, and thereby can fill the so-called “white spaces” in the Ashby strength–toughness space. The idea is to construct three-dimensional materials with a network of crack arrestors like in rip-stop nylon and break the link between toughness and strength. We use interconnected and interpenetrating double gyroids comprising ductile and brittle phases as an exemplar to investigate the opportunities of such designs. Intriguingly, from a perspective based solely on strength and toughness, we show that multi-material micro-architectures cannot outperform their single material counterparts at a given relative density. In fact, in most designs the coupling between the two phases is non-synergistic. Rather, we argue that multi-material designs such as those used in rip-stop nylon are driven by multi-functional considerations beyond mechanical properties. Graphical abstract