Positive-Definiteness of the Blended Force-Based Quasicontinuum Method

Xingjie Helen Li
Brown University
Applied Mathematics

The development of consistent and stable atomistic-to-continuum coupling models for multi-dimensional crystalline solids remains a challenge. For example, proving stability of the force-based quasicontinuum
(QCF) model 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) models. We establish sharp conditions on the required blending width.

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