Prediction of Drop-Impact Damage Volume in Cucumber (Cucumis sativus L. cv. Zhongnong Cuiyu No. 3) Using a Three-Layer Viscoelastic Finite Element Model and Response Surface Methodology

To support the design of low-damage harvesting and transportation equipment, clarify the damage-formation mechanism under drop impact, and quantitatively predict impact-induced damage volume, this study investigated the cucumber cultivar “Zhongnong Cuiyu No. 3”. Mechanical and creep tests were conducted to determine the biomechanical parameters of the peel, flesh, and core. Based on the distinct internal tissue structure of the cucumber, a three-layer viscoelastic finite element (FE) model was developed. Tissue-specific damage thresholds were applied to calculate the dynamic damage volume throughout the entire impact process. Using a Box–Behnken design, a quadratic response surface model was established to analyze the effects of drop angle, drop height, and logarithmic contact stiffness on the log-transformed damage volume. The framework was subsequently validated through physical drop tests, tissue staining, and sliced-image analysis. Simulation results indicated that as drop height increased from 0.10 to 1.00 m, the maximum von Mises equivalent stress increased from 1.19–1.57 MPa to 2.49–3.30 MPa, with high-stress regions expanding significantly along the longitudinal axis of the fruit. The fitted response surface model yielded an R2, adjusted R2, and predicted R2 of 0.9934, 0.9849, and 0.8943, respectively. Drop height showed the largest contribution to damage-volume variation, followed by a pronounced quadratic effect of drop angle, whereas contact stiffness showed a weaker influence within the tested range. Physical validation showed that the experimental damage volume generally increased with drop height and that the horizontal orientation (0° impact angle) produced lower damage than the inclined postures at medium and high drop heights. The numerical predictions reproduced the overall damage trend and approximate magnitude under several tested conditions, although condition-dependent deviations remained. Larger relative deviations at low damage levels were associated with the small absolute damage volume, biological variability, background micro-damage, staining response, and image-quantification uncertainty. The proposed framework effectively links tissue viscoelasticity, whole-fruit impact response, and three-dimensional damage volume, providing a robust theoretical basis for drop-risk assessment and the optimization of low-damage vegetable mechanization systems.