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

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

2011-02-12

arxiv.org/abs/1102.2523v2

Mathematics

Numerical Analysis

32 pages, (v2: some typos corrected)

Scientific paper

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.

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