A hybrid multiscale framework is presented, which processes the material scales in a concurrent manner, borrowing features from hierarchical multiscale methods. The framework is used for the analysis of nonlinear heterogeneous materials and is capable of tackling strain localization and failure phenomena. Domain decomposition techniques, such as the finite element tearing and interconnecting method, are used to partition the material in a number of non-overlapping domains and adaptive refinement is performed at those domains that are affected by damage processes. This refinement is performed in terms of material scale and finite element size. It is verified that the results are independent of the chosen domain decomposition. Moreover, the multiscale analyses are validated with reference solutions obtained with a full fine-scale solution procedure.