A creep deformation prediction model for shelf boards in furniture engineering design

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.