Mechanical metamaterials: does toughness characterize fracture?

Abstract: Rapid progress in additive manufacturing methods has created a new class of ultralight and strong architected metamaterials that resemble periodic truss structures. The mechanical performance of these metamaterials with a very large number of unit cells is ultimately limited by their tolerance to damage and defects, but an understanding of this sensitivity has remained elusive. Using a stretching-dominated micro-architecture and metamaterial specimens comprising millions of unit-cells we show that not only is the stress intensity factor, as used in conventional elastic fracture mechanics, insufficient to characterize fracture but also that conventional fracture testing protocols are inadequate. Via a combination of numerical calculations and asymptotic analyses, we extend the ideas of fracture mechanics and develop a general test and design protocol for the failure of metamaterials.