  Extreme mechanical processes such as strong lattice distortion and bond
breakage during fracture are ubiquitous in nature and engineering, which often
lead to catastrophic failure of structures. However, understanding the
nucleation and growth of cracks is challenged by their multiscale
characteristics spanning from atomic-level structures at the crack tip to the
structural features where the load is applied. Molecular simulations offer an
important tool to resolve the progressive microstructural changes at crack
fronts and are widely used to explore processes therein, such as mechanical
energy dissipation, crack path selection, and dynamic instabilities (e.g.,
kinking, branching). Empirical force fields developed based on local
descriptors based on atomic positions and the bond orders do not yield
satisfying predictions of fracture, even for the nonlinear, anisotropic
stress-strain relations and the energy densities of edges. High-fidelity force
fields thus should include the tensorial nature of strain and the energetics of
rare events during fracture, which, unfortunately, have not been taken into
account in both the state-of-the-art empirical and machine-learning force
fields. Based on data generated by first-principles calculations, we develop a
neural network-based force field for fracture, NN-F$^3$, by combining
pre-sampling of the space of strain states and active-learning techniques to
explore the transition states at critical bonding distances. The capability of
NN-F$^3$ is demonstrated by studying the rupture of h-BN and twisted bilayer
graphene as model problems. The simulation results confirm recent experimental
findings and highlight the necessity to include the knowledge of electronic
structures from first-principles calculations in predicting extreme mechanical
processes.
