The deformation of copper with grain size less than 10 nm is investigated using a 2D continuum model incorporating atomistically-based constitutive relations. The local constitutive response of a series of symmetric and asymmetric tilt grain boundaries is obtained using an atomistic quasicontinuum method under tension and shear. The atomistic results show that it is possible to associate a constant maximum stress with each deformation mechanism triggered in the GB vicinity, i.e. GB sliding and decohesion, atom shuffling and partial dislocation emission. The GB strength is always found weaker in shear than in tension. This information is incorporated into a continuum polycrystalline model tested under compression. This model provides useful insights, in the absence of intragranular plasticity, into the onset of macroscopic quasi-plasticity, which results from GB sliding and collective grain rotation mechanisms.