Stability of a force-based hybrid method with planar sharp interface
Provides theoretical convergence guarantees for force-based atomistic-to-continuum coupling, a known challenge in multiscale modeling.
The paper identifies stability conditions for a force-based hybrid method coupling atomistic and continuum models, proving second-order convergence to the atomistic solution as lattice parameter vanishes for planar sharp interfaces in defect-free systems.
We study a force-based hybrid method that couples atomistic model with Cauchy-Born elasticity model with sharp transition interface. We identify stability conditions that guarantee the convergence of the hybrid scheme to the solution of the atomistic model with second order accuracy, as the ratio between lattice parameter and the characteristic length scale of the deformation tends to zero. Convergence is established for hybrid schemes with planar sharp interface for system without defects, with general finite range atomistic potential and simple lattice structure. The key ingredient of the proof is regularity and stability analysis of elliptic systems of difference equations. We apply the results to atomistic-to-continuum scheme for a 2D triangular lattice with planar interface.