# An Attempt to Model the Surface Pressures of Apples Using the Finite Element Method
## 1 Introduction
### FEM Load Assessment of Biological Material  
Forecasts of areas of influence, deformation, and distribution of surface pressure in fruit are important issues in post-harvest research. There are many methods for fruit damage assessment, i.e., by means of surface pressure and stress distribution [20]. Developments in computer technology, with the use of finite element methods (FEM, enable the use of this system to predict the mechanical behaviours of fruits under loading. It is used to solve complex problems with the use of computer engineering techniques, without the need to perform experimental studies. It is a particularly important technique used in the design and construction of engineering structures [21]. [PERSON] et al. [22] described a mechanical behaviour of seeds that were exposed to external linear loading. Thanks to the tests carried out, the researchers identified seed sites that were particularly vulnerable to changes in the structure of biological material [22; 23]. [PERSON] et al. [24] examined the behaviour of the structure of the biological material using the example of a nut that was squeezed between two parallel plates until the shell and grain began to crack [24]. The behaviour of a biological material in individual layers of beans was also studied using the example of beans and peas. The maximum deformation that occurred during the external load application was determined. The finite element method was used to model the deformation [25]. Similar studies were conducted by [PERSON] et al. [26], who, under external loading, studied the behaviour of interacting rapeseeds in the stack [26]. Theoretical aspects of computer integration--in regard to the method--were solved in the 1960s and 1970s. Research and development from the European Union's research base in the 1990s resulted in extensive scientific output in various fields of engineering [27]. This method also proved useful in agricultural engineering research, in the context of deformation of agricultural products. Many tests were carried out to estimate the complex stress field of organic materials under different boundary conditions [28; 29; 30; 31; 32; 33; 34]. It should be stressed that most of these tests were carried out considering static or quasi-static load cases--small deformation and linear contacts with the linear assumptions of the elastic material model through implicit solvers. The consideration of non-linearity in partial contact and ductility in material models (especially in cases of impact loads) in such tests were absent or very limited [27]. Many experimental methods can measure the level of damage, stress distribution, surface pressure, and the reaction of the fruit to external forces. Works involving damage measurements, surface pressure using the finite element method are beginning to appear [21; 22; 23]. For example, the extent of deformation of the tomato fruit because of hard surface contact, between tomatoes, has been mapped [35]. In this study, a 3D model of the tomato was generated in CATIA, and then the compression tests were simulated using MES to determine the mechanical properties of the tomato. The comparison of experimental data with the conducted finite element simulation confirmed that the two sets of results were consistent [5]. The tests in which the Golden Delicious apple variety was tested also used a 3D scanner, a high-speed digital camera, and the FEM technique mentioned above; the aim of the tests was to determine the degree of deformation of these fruits arranged in a box. The experimentally validated FEM model in this study will be used to determine the appropriate conditions related to the transport, storage, and processing of apples. In this way, the authors confirmed the results of a simulation using SolidWorks during the fruit drop, where they also used a high-speed camera, and consequently noticed that the results of visual tests and simulations were very similar [35]. The susceptibility of pears to different impact conditions was determined experimentally and implemented using FEM [21].