Stress-based atomistic/continuum coupling:  a new variant of the quasicontinuum approximation
C. Makridakis, C. Ortner and E. Suli
International Journal for Multiscale Computational Engineering, 10, 51-64 (2012).

ABSTRACT
The force-based quasicontinuum (QCF) approximation is the principle that lies
behind the most commonly used atomistic/continuum hybrid models for crystalline
solids. Recent analyses have shown some potential pitfalls of the QCF method,
particularly the lack of positive definiteness of the linearized QCF operator
and the lack of uniform stability as the number of atoms tends to infinity. We
derive a weak variational representation of the QCF operator and identify the
origin of these difficulties as the lack of a interface condition on the
stresses. This leads us to propose an improved variant of the QCF method that
can be understood as a coupling mechanism based on stresses rather than forces.