Numerical-continuation-enhanced flexible boundary condition scheme applied to mode-I and mode-III fracture

Motivated by the inadequacy of conducting atomistic simulations crack propagation using static boundary conditions that do not reflect movement tip, we extend Sinclair's flexible condition algorithm [J. E. Sinclair, Philos. Mag. 31, 647 (1975)] and propose a numerical-continuation-enhanced scheme, enabling full solution paths for cracks to be computed with pseudo-arclength continuation, present method incorporating more detailed far-field information into model next no additional computational cost. The algorithms are ideally suited study details lattice trapping barriers brittle fracture can incorporated density functional theory multiscale quantum classical mechanics molecular calculations. We demonstrate our approach mode-III 2D toy employ it conduct 3D mode-I silicon realistic interatomic potentials, highlighting superiority over employing corresponding condition. In particular, inclusion numerical continuation enables converged results obtained systems containing few thousand atoms, very iterations required compute each new solution. also introduce estimate range admissible stress intensity factors ${K}_{\ensuremath{-}}<K<{K}_{+}$ cheaply its utility on both systems.