Discrete Element Parameter Calibration for Pruned Apple Branches Using Angle of Repose and Three-Point Bending Tests
Year: 2026
Type: article
Abstract: To establish the fundamental parameter set required for discrete element modeling of pruned apple branches, one-year-old Fuji apple branches collected during winter pruning from a high-density dwarf-rootstock orchard were investigated. Physical experiments and EDEM numerical simulations were combined to calibrate and validate the contact and bonding parameters of the branches. First, basic physical properties, including branch dimensions, moisture content, density, Poisson’s ratio, and elastic modulus, were measured. Restitution, friction, cylinder-lifting angle-of-repose, and three-point bending tests were then conducted to obtain the macroscopic responses required for model calibration. Based on the Hertz–Mindlin (no-slip) model, the angle of repose was selected as the target response. Significant factors were screened using a Plackett–Burman design, and contact parameters were optimized through steepest-ascent tests and central composite design (CCD) response surface methodology. The branch–branch static and rolling friction coefficients were the principal factors affecting the angle of repose; their optimized values were 0.348 and 0.067, respectively. The experimentally measured branch–branch coefficient of restitution was 0.157, while the measured branch–steel coefficient of restitution, static friction coefficient, and rolling friction coefficient were 0.41, 0.42, and 0.08, respectively. The final contact parameter set produced a simulated angle of repose of 28.35°, differing from the experimental mean of 28.57° by 0.77%. Subsequently, bonding parameters were analyzed and optimized using the Hertz–Mindlin with Bonding model, with the maximum failure load in three-point bending as the target response. Response surface optimization yielded a normal contact stiffness per unit area of 2.15 × 1011 N·m−3, a tangential contact stiffness per unit area of 2.00 × 1011 N·m−3, and a critical tangential stress of 5.17 × 107 Pa. Because the effect of critical normal stress was not statistically significant, it was fixed at its center level of 5.00 × 107 Pa; the bond radius was preset to 1.2 mm. Five repeated three-point bending simulations using the final parameter set gave a mean maximum bending failure load of 413.30 ± 23.53 N, a relative difference of 2.50% from the calibration target of 423.9 N. These results indicate that the identified parameter set can adequately characterize the bulk stacking behavior and quasi-static bending load-bearing capacity of apple branches under the present experimental conditions. The calibrated parameters provide a basis for discrete element modeling and equipment optimization in subsequent branch collection, conveying, feeding, and shredding operations.
Source: AgriEngineering
Institution: Hebei Agricultural University
Language: English
Subfield: Mechanical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,930
OpenAlex ID: W7225189735