Transient analysis of viscoelastic graphene origami-enabled auxetic metamaterial plates

Graphene origami-enabled auxetic metamaterial plates have demonstrated highly tunable stiffness and multifunctional mechanical performance under static, buckling, and vibration conditions. However, their time-dependent transient behavior considering viscoelastic effects remains largely unexplored, despite its critical importance in aerospace panels, protective structures, and flexible devices subjected to short-duration dynamic loads. This study addresses this gap by developing and implementing three higher-order finite element models for the transient viscoelastic analysis of graphene origami-enabled auxetic metamaterial plates, incorporating the Kelvin–Voigt constitutive model to capture rate-dependent stiffness and internal damping effects. The main contribution of this study is the development of a higher-order finite element models for the transient viscoelastic analysis of graphene origami-enabled auxetic metamaterial plates, enabling systematic evaluation of time-dependent dynamic behaviour under short-duration loading. Within this study, the influences of graphene origami distribution patterns, hydrogen coverage, graphene origami weight fraction, layer configuration, boundary conditions, aspect ratio, and internal damping are rigorously quantified under step and blast loads. Model verification against benchmark solutions from the open literature demonstrates excellent agreement, confirming the robustness and accuracy of the proposed finite element models. The results establish clear structure–property–dynamics relationships, showing that optimized graphene origami–hydrogen coverage configurations significantly enhance effective stiffness, reduce dimensionless dynamic central deflections, and increase oscillation frequency, while hydrogenation weakens stiffness and amplifies transient amplitudes. The study further demonstrates that boundary restraint and viscoelastic damping govern response magnitude and decay rate, with fully clamped plates minimizing deflections and higher viscosity accelerating oscillation attenuation. Collectively, these findings provide a computational basis for tailoring the transient performance of graphene origami-enabled auxetic metamaterial plates through material grading and damping design.