Authors: Xingjie Helen Li, Mitchell Luskin, Christoph Ortner, Brian Van Koten
University of Minnesota and University of Warwick
The development of consistent and stable atomistic-to-continuum methods for multi-dimensional crystalline solids remains a challenge. For example,the stability of the force-based quasicontinuum (QCF) method remains an open problem. In 1D and 2D, we show that by blending atomistic and Cauchy--Born continuum forces (instead of a sharp transition as in the QCF method) one obtains positive-definite blended force-based quasicontinuum (B-QCF) methods.
We also formulate an energy-based atomistic-to-continuum coupling method based on blending the quasicontinuum method for the simulation of crystal defects. We present optimal choices of approximation parameters (core size, blending function, and finite element mesh) for materials with defects.
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