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We study the stability of ghost force-free energy-basedatomistic-to-continuum coupling methods. In 1D we essentially complete thetheory by introducing a universally stable a/c coupling as well as astabilisation mechanism for unstable coupling schemes.  We then present a comprehensive study of a two-dimensional scalar planarinterface setting, as a step towards a general 2D/3D vectorial analysis. Ourresults point out various new challenges. For example, we find that none of theghost force-free methods known to us are universally stable (i.e., stable undergeneral interaction and general loads). We then explore to what extent our 1Dstabilisation mechanism can be extended.

(In-)Stability and Stabilisation of QNL-Type Atomistic-to-Continuum Coupling Methods