The use of multi-scale procedures is encouraged by the continuous increase of computational capacity, but it is still a challenge performing a non-linear analysis of real composite structures without the aid of large computers. This work proposes a strategy to conduct non-linear multi-scale analysis in an efficient way. The proposed method considers that in a large structure, in general, material non-linear processes only take place in a localized region (or in a reduced number of finite elements, if a FE method is used). The strategy determines the elements that require a non-linear analysis defining of a non-linear activation function that accounts for the failure of the most critical point in the microstructure. The procedure conserves the dissipated energy through the scales, being mesh independent as the mesh objectivity concept is extended to the microstructure. The validity of the strategy proposed is proved with the analysis of academic examples showing not only the mesh independency but also the reduction of computational cost. Finally, an industrial composite component is solved using a standard computer, showing that the proposed strategy is capable of reducing the computational cost from 32 days and 14 hours (required by a classical multi-scale method) to less than 12 hours.