Fracturing of topological Maxwell lattices

Abstract: We present fracturing analysis of topological Maxwell lattices when they are stretched by applied stress. Maxwell lattices are mechanical structures containing equal numbers of degrees of freedom and constraints in the bulk and are thus on the verge of mechanical instability. Recent progress in topological mechanics led to the discovery of topologically protected floppy modes and states of self stress at edges and domain walls of Maxwell lattices. When normal brittle materials are being stretched, stress focuses on crack tips, leading to catastrophic failure. In contrast, we find that when topological Maxwell lattices are being stretched, stress focuses on states of self stress domain walls instead, and bond-breaking events start at these domain walls, even in presence of cracks. Remarkably, we find that the stress-focusing feature of the self-stress domain walls persists deep into the the failure process, when a lot of damages already occurred at these domain walls. We explain the results using topological mechanics theory and discuss the potential use of these topological Maxwell lattice structures as mechanical metamaterials that exhibit high strength against fracturing and well controlled fracturing process.