A continuum-atomistic multi-scale technique for nonlinear behavior of nano-materials

•A hierarchical RVE-based continuum-atomistic multi-scale procedure is developed.•The inter-scale kinematic and energetic consistency principals are exploited.•The kinematic compatibility is applied by the atomistic periodic boundary conditions.•The energetic consistency is satisfied by the Hill-Mandel periodic boundary conditions.•Coarse-scale is modeled using the stress tensor and tangent modulus computed from atomistic RVE.