Nonlinear Viscoelastic‐Viscoplastic Coupled Behavior and Mechanical Model for Substrates of Flexible Solar Array

ABSTRACT In 2021, following the successful launch of the Tianhe‐Core‐Module, the large‐scale flexible solar array was deployed smoothly in orbit, marking China's first application of flexible solar arrays and subsequently establishing them as a prominent research focus. The substrate of the flexible solar array is composed of polyimide composites, a typical polymer material that exhibits viscoelastic‐viscoplastic behavior under on‐orbit fluctuating thermal‐mechanical action, thereby influencing the long‐term structural performance. This study begins by investigating the nonlinear viscoelastic‐viscoplastic behavior of the flexible substrate through creep‐unloading‐recovery experiments under varying temperatures and stress levels. Subsequently, a coupled viscoelastic‐viscoplastic constitutive model is proposed. For the viscoelastic component, a novel generalized double hereditary integral model is developed based on the microelement method. For the viscoplastic component, a nonlinear time‐dependent evolution model, independent of the yield surface, is formulated to account for the unique characteristics of the substrate. A detailed methodology for calibrating all nonlinear parameters through experimental data is provided. Furthermore, leveraging the finite element incremental approach, an innovative dual‐recursive numerical scheme and a nonlinear iterative‐correction computational scheme are implemented, incorporating the model's distinctive features. The nonlinear viscoelastic‐viscoplastic Jacobian tensor is rigorously derived, and a user‐defined material subroutine ( UMAT ) is developed to facilitate large‐scale numerical simulations. Finally, the accuracy, reliability, and generality of the proposed method are validated through comparative analyses with experimental data, published literature, the linear Boltzmann hereditary integral model, and the nonlinear Schapery hereditary integral model. The findings of this study will contribute to the evaluation of the long‐term in‐orbit behavior of flexible solar arrays.