The effect of ghost forces for a quasicontinuum method in three dimension

We study the effect of “ghost forces” for a quasicontinuum method in three dimension with a planar interface. “Ghost forces” are the inconsistency of the quasicontinuum method across the interface between the atomistic region and the continuum region. Numerical results suggest that “ghost forces” may lead to a negilible error on the solution, while lead to a finite size error on the gradient of the solution. The error has a layer-like profile, and the interfacial layer width is of O(ɛ). The error in certain component of the displacement gradient decays algebraically from O(1) to O(ɛ) away from the interface. A surrogate model is proposed and analyzed, which suggests the same scenario for the effect of “ghost forces”. Our analysis is based on the explicit solution of the surrogate model.