  The development of consistent and stable quasicontinuum 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.
