Tremendous efforts have been put into the study of structural integrity and the understanding of failure mechanisms in composites. Geometric non-linearity, receiving few attention in coupon-level simulations, can play an important role in the design and analysis of larger structures. This paper aims at extending the recently-developed Floating Node Method for damage analysis of laminated composites subjected to large deformations. The kinematics of strong discontinuities including interfacial delamination and matrix cracks are explicitly described in a geometrically nonlinear framework. Interactions between these two kinds of failure patterns are enabled through enriched elements equipped with floating nodes. To verify this proposed method, buckling-induced delamination and low-velocity impact damage are modelled, the results of which show good agreement with results from literature.