Discrete configurational mechanics for the computational study of atomistic fracture mechanics

We formulate discrete configurational mechanics in an atomistic setting, discuss the corresponding computa-tional details, and demonstrate its utility via computational analyses of atomistic fracture mechanics problems. To this end, we first propose a novel Configurational-Force-Criterion (CFC) to predict crack propagation into an atomic crystalline lattice. Thereby, specifically, the CFC relies on comparing discrete configurational forces with a corresponding Crack-Propagation-Threshold (CPT) in the quasi-static approximation of atomistic systems at zero Kelvin. Next, based on the CFC, we introduce a quasi-static computational atomistic crack propagation algorithm. Therein, whenever an atomic pair meets the CFC, we modify the lattice connectivity by deleting the correspond-ing interatomic bond, thus resulting in true irreversibility, i.e. dissipation upon crack extension. Finally, based on different choices for the magnitude of the CPT employed in the CFC, we demonstrate suitability and versatility of discrete configurational mechanics in analyzing atomistic fracture mechanics.