Convergence of a force-based hybrid method for atomistic and continuum models in three dimension

Abstract

We study a force-based hybrid method that couples atomistic models with nonlinear Cauchy-Born elasticity models. We show that the proposed scheme converges quadratically to the solution of the atomistic model, as the ratio between lattice parameter and the characteristic length scale of the deformation tends to zero. Convergence is established for general short-ranged atomistic potential and for simple lattices in three dimension. The convergence is based on consistency and stability analysis. General tools are developed in the framework of pseudo-difference operators for stability analysis in arbitrary dimension of the multiscale atomistic and continuum coupling methods.

32 pages, (v2: some typos corrected)

References in corpus (1)

• The Spectrum of the Force-Based Quasicontinuum Operator for a Homogeneous Periodic Chain

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• A Posteriori Error Estimate and Adaptive Mesh Refinement Algorithm for Atomistic/Continuum Coupling with Finite Range Interactions in Two Dimensions