Abstract In the present work, two-phase integral theory of elasticity developed in Barretta et al. (Phys E 97:13–30, 2018) for nano-beams is generalized to model two-dimensional nano-continua. Notably, a well-posed mixture local/stress-driven nonlocal proposed accurately predict size effects Kirchhoff axisymmetric nanoplates. The key idea express elastic radial curvature as convex combination l...