Dynamic analysis of aerospace structures typically relies on high-dimensional finite element models. Under large vibration amplitudes, geometrically nonlinear effects become significant and cannot be neglected, leading to nonlinear equations of motion whose time integration is computationally expensive.Model order reduction is therefore essential to accelerate simulations during the design phase, enabling efficient exploration and optimization of structural configurations. Dynamic substructuring techniques provide an effective framework for constructing reduced-order models (ROMs) while supporting a modular representation of structural subcomponents—an important requirement in industrial applications. Although substructuring-based ROMs are well established for linear and locally nonlinear systems, their extension to structures exhibiting global geometric nonlinearities remains limited. In this work, we address this gap by proposing an extension of the Craig–Bampton reduction method to geometrically nonlinear structures. The reduction subspace is first constructed at the substructure level using the classical Craig–Bampton basis, and is then enriched by embedding it in a nonlinear quadratic manifold . This manifold is obtained by statically condensing high frequency fixed interface modes to low frequency modes and interface degrees of freedom. This results in a second order manifold that is used to approximate the dynamic solution. The reduced-order model is then obtained using Galerkin projection of the substructure dynamic equilibrium equations onto the tangent space of this manifold. Numerical results demonstrate that the proposed approach accurately captures the displacement fields induced by dynamic loading while achieving a substantial reduction in computational cost compared to the full-order model.