The hierarchical, multiscale character of composite materials still poses a severe challenge for efficient structural-scale simulation: the strong separation between microstructural and structural dimensions usually requires resolving hundreds of millions of microstructural features. Once these multiscale features are combined with nonlinear elastoplastic responses, traditional concurrent multiscale schemes rapidly become computationally very demanding. To address these challenges, this paper proposes a data-driven concurrent multiscale reduced-order model approach for the elastoplastic nonlinear mechanical response of large-scale composite structures. At the microscale, the local response and effective stress of the RVEs are computed efficiently using the previously proposed FCA method [1-3], driven by the strain histories transferred from the macroscale structure at different load steps. The resulting effective stresses are then passed back to the corresponding Gauss integration points of the macroscale structural model. At the macroscale, a nonlinear finite element analysis is carried out using these effective stresses to obtain structural responses. The overall approach, referred to as the FE–FCA method, is formulated within a unified finite element framework, which allows the use of unstructured meshes and RVEs with strong material property contrast, such as porous materials. In addition, an incremental FCA scheme is introduced to accurately capture the loading and unloading behaviour of the macroscale structure, thereby extending the method from a purely microscale tool to a fully concurrent macro–micro analysis framework. Moreover, in the FE–FCA formulation the RVEs associated with all integration points are solved in parallel within each structural load step, and a four-step judgment strategy is adopted to further accelerate the RVE computations, which leads to a substantial increase in the overall computational efficiency. Compared to the traditional concurrent multiscale FE2 method, the proposed FE-FCA method significantly improves computational efficiency while maintaining accuracy. Furthermore, the method is equally applicable to the prediction of nonlinear mechanical behaviour of large-scale composite structures, significantly reducing storage requirements during computation, highlighting the flexibility of the method.