Modeling viscoelasticity–viscoplasticity of high-strain composites for space deployable structures

Space deployable structures made of thin-ply fiber-reinforced composite laminates exhibit significant time-dependent mechanical behaviors, including stress relaxation, shape recovery, and permanent residual deformation throughout their service period. Currently, there is a lack of an appropriate composite laminate model that is able to fully describe these phenomena. Here, we address this gap by proposing an anisotropic viscoelastic–viscoplastic continuum constitutive model to capture the mechanical behavior of composite deployable structures during folding, stowage, deployment, and recovery periods. The model adopts a viscoelastic formulation based on the Boltzmann integral, coupled with a Hill-type rate-dependent viscoplastic formulation. A detailed numerical implementation scheme using fully implicit integration with a two-step viscoelastic predictor and viscoplastic corrector strategy is provided. The accuracy and efficiency of the proposed model are validated against experimental results for both unidirectional and woven laminates. Simulations accurately capture the rate-dependent nonlinear stress–strain response, creep response under constant stress, and hysteresis loops in cyclic loading-unloading tests for single-ply lamina under various off-axis loading directions. Importantly, the proposed method is the first to capture the experimentally observed permanent deformation of real-world composite deployable structures, validated through column bending tests. This advanced modeling and simulation capability significantly enhances the simulation and design of space deployable structures.