# Modeling Shearing and Bending Behavior of Kiwifruit Branches Using the Discrete Element Method
## 1 Introduction  
The forestry and fruit industries are integral components of the agricultural production system. In China, orchard areas have expanded rapidly, from 1657 thousand hectares in 1978 to 13,010 thousand hectares in 2022. In fruit production, pruning is essential for bearing fruit the following year. This practice generates substantial quantities of pruned branches, estimated at 3750 kg per hectare annually [1; 2; 3]. A significant portion of these pruned branches is either discarded arbitrarily or burned in the open air. Such practices create serious safety hazards and environmental pollution, representing a major waste of resources. Multiple approaches have been developed to harness these pruned branches effectively. In China, they are primarily used as fertilizer, raw materials, or energy resources [4]. China leads global kiwifruit production, with an annual yield of up to 3 billion tons [5; 6]. Nearly half of this production comes from Shaanxi Province. Kiwifruit, a vine plant, matures its fruit on the branches during autumn. In winter, long kiwifruit branches are commonly pruned and discarded in orchards. Farmers in Shaanxi Province predominantly use direct branch returning as fertilizer. This practice involves smashing or chopping long branches into smaller pieces with straw-returning machines or dedicated fruit branch shredders. This accelerates decomposition and enhances soil fertility. Increased yields and reduced fertilizer applications lead to higher incomes for farmers. Additionally, avoiding branch burning improves the agricultural ecological environment. During the mechanized branch returning operation, shearing and bending behaviors dominate the branch chopping and smashing processes. Thus, shear and bending properties are extremely important for understanding kiwifruit branch mechanics. Previous research has employed universal testing machines to investigate the bending, shear, and compression characteristics of crops such as corn, wheat, and rice [7; 8; 9]. Physical properties of apple branches and vine branches, along with other fruit branches, have also been determined [10; 11; 12]. However, little research has been conducted on the smashing process of fruit branches. The study of the bending and shearing process could help to understand the failure mechanism of maximum breaking force, destructional form, and deformation extent, and then help to design high-quality branch-returning machines to improve branch-returning quality, but little research has been conducted to deeply investigate the processes. This is due to a lack of proper methods. Moreover, the bending and shearing behavior were not easily observed in detail in traditional field and laboratory experiments. The finite element method (FEM) and discrete element method (DEM) are two main numerical analysis methods that have been applied in agricultural processes to address certain limitations [13; 14; 15; 16]. The FEM is able to study material failure and large-scale deformation and requires mathematical continuity, while the DEM shows an advantage in the research of discrete objects. When a fruit branch or crop straw breaks in the bending or shearing process, the branch will transition from a continuous medium to a discontinuous medium. With the bonding model of the DEM, bonds break and particles separate when the stress surpasses the predefined thresholds of tensile strength or cohesion; thus, the branch's breaking behavior could be simulated with high accuracy [17]. The visual similarity is better with the DEM than the FEM, as can been found in the previous literature, especially that referring to the simulation of failure and fracture behaviors [18]. In addition, it is more convenient to quantitatively analyze the fracture and deformation characteristics with the bonding keys built into the DEM model [19]. In recent studies, the tensile behavior of plant fiber, the bending behavior of wheat straw, and the shearing behavior of banana straw have been studied [20; 21].