  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.
