Objective To enhance the long-term service safety and design reliability of solid wood furniture shelves, this study investigates the creep behavior of black walnut (Juglans nigra) edge-glued boards under sustained loading and develops a creep constitutive model and performance prediction methodology suitable for shelf durability design and deformation forecasting.

Method We conducted a 42-day three-point bending creep test to examine the viscoelastic response of the material under characteristic stress levels of 2%f_m, 6%f_m, and 10%f_m (f_m is the average modulus of rupture). Using nonlinear fitting, we comparatively evaluated the goodness-of-fit of the power-law model, the standard linear solid model, and the Burgers model. Based on parameter evolution analysis, we established a generalized creep constitutive equation that accounts for stress dependence and proposed an optimized structural parameter design method for solid wood shelves grounded in long-term deformation control thresholds.

Result (1) The Burgers model emerged as the optimal constitutive model (R² > 0.992; RMSE ranging from 1.88 × 10⁻⁶ to 7.71 × 10⁻⁶), effectively capturing instantaneous elasticity, delayed elasticity, and steady-state viscous flow. (2) Model parameters exhibited pronounced stress dependence: the delayed elastic modulus increased exponentially with stress, while the relaxation time decayed following a power law, indicating a transition from quasi-linear creep at low stress to nonlinear creep at high stress. The proposed generalized constitutive model accurately predicted long-term deformation across the stress range of 2%f_m to 10%f_m. (3) The parameter optimization method derived from this model enables scientific determination of critical dimensions-such as thickness and span-for furniture shelves based on target service life and allowable deformation, thereby facilitating performance-driven precision design.

Conclusion This study establishes a mapping framework from material-level creep parameters to component-level design parameters. The proposed model and optimization methodology offer theoretical tools for the durability design and safety assessment of solid wood furniture shelves, supporting a paradigm shift in furniture engineering from empirical practices toward predictive performance-based design.