# An Attempt to Model the Surface Pressures of Apples Using the Finite Element Method
## 1 Introduction
### Impact Loads on Biological Material  
Apples are subjected to various static, dynamic, and impact loads during harvesting, handling, transport, sorting, storage and other operations necessary to obtain the final product. Impact loads are a major cause of knock-on effects that cause loss to apple growers, as they significantly affect the deterioration of fruit quality parameters [10]. During the impact, irreversible changes in the structure of the internal tissues occur, most often involving damage to cell walls. The mechanism of changes in the cellular structure of apples under impact loads differs significantly from those occurring under quasi-static loads. Therefore, it is not possible to analyse the mechanism of bruising formation and determination of resistance to apple bruise using simple measurement methods based on the compression test [11; 12]. Under impact loads, the biological material behaves like an elastic material. Liquid and air filling the intercellular spaces do not have time to move to other less loaded areas where there are still free spaces [13]. This results in the release of stresses that exceed the strength of the cells, in the form of cracks and irreversible tissue damage. At low load speeds, biological materials exhibit strong viscoelastic properties. In the initial loading phase, after displacement of gases and filling of cell spaces, the process of liquid migration, causing deformation of cell walls, begins [14]. As a result, this type of load allows higher destructive stress values to be achieved than with impact loading.  
In this situation, it becomes important to determine the critical values of the impact energy, for which the elastic deformation of the apple becomes permanent. It can be assumed that, in the case of elastic deformations, i.e., deformations in which the apple returns to its initial shape after removing the load, there is no damage to the flesh tissue, so there is no danger of bruising. Tissue damage occurs only when permanent deformations appear [15].  
Permanent deformations are caused by contact of the outer layer of the apple skin with a hard surface, e.g., the wall of a box, working elements of machines used in the production process, but also when hitting another fruit. The intensity of the bruising also depends on a number of other factors, including the degree of ripeness, the weather conditions and the time of harvest [16]. The size of the bruising and, consequently, the usefulness of the fruit, depend mainly on the reactions of the biological material to the external load, and the time scale adopted [17; 18].  
[PERSON] et al. [19] conducted research to assess the rheological properties of two apple varieties: Avrolles and Douce Coetligne. Based on the analysis of the tissue properties of the flesh and the juice content of the fruit, the authors assessed the behaviour of the apples during the compression test. Endurance tests were carried out 15 and 30 days after harvesting. In the case of Avrolles, the plasticity of the biological material was noticed, while in the case of Douce Coetligne, the viscoelastic properties were noticed. In the case of Douce Coetligne, the apple skin significantly reduced the formation of bruises and deformities in the flesh.