*1.2. Problem Context*

Computer modeling and the accumulated experience of describing the behavior of various materials allow them to be used in the field of medical research. Today there are many examples of successful applications of numerical models in dentistry [1,2]. Research of the finite element method (FEM) allows us to expand our understanding of the causes of the occurrence and development of mechanical damage to teeth. Analysis of NCCLs in terms of mechanical behavior seems interesting and promising [3,4].

NCCLs are a fairly common dentition disease in the world [5–7]. This is a non-carious disease of the teeth with tissue degradation near the cervical area. There are four types of NCCLs according to the nature of development in the tooth tissues, as well as two types according to the geometry of the "wedge" section (V and U shaped) [8,9]. It is scientifically substantiated that the shape of the NCCLs affects the load distribution in the tooth. In the area of development of a V-shaped NCCL, the stress concentration is four times higher [9]. Tissue degradation in the defect zone develops without treatment. It has a significant impact on the patient's life quality. Such NCCLs cause a number of inconveniences to the patient: violation of the tooth aesthetics, pain, overload of healthy teeth, etc.

There are many works aimed at studying the causes of the occurrence and development of NCCLs. The hard tooth tissue properties of NCCLs affected are being investigated [10–14]. The biomechanical reasons for the occurrence of abfraction are analyzed [12,15–17]; Occlusal loads and resulting stress-strain states of teeth are being studied [16,18–20]. It is found that the enamel strength decreases in the direction from the outer surface to the dentine-enamel junction [21]. The axial load is 30% more strongly distributed in the enamel. The response to axial load is 30% higher in the enamel than in the rest of the tooth tissues. Multiple multidirectional loads cause reactions that are five times higher than the reactions to the axial load of the same level [17,18]. At the same time, the enamel-cement border and the cervical part of the vestibular surface experience the maximum load, mainly in the incisors and premolars. Abfraction is considered the main cause of developing tooth NCCLs [12,22,23]. However, Grippo J.O. and Masai J.V. [24] found that the stresses occurring in the cervical region on the vestibular surface are similar to those on the oral one, where NCCLs are extremely rare. The combination of acids and internal stresses on tooth enamel is the reason for this effect according to scientists [24,25]. A relationship is also established between parafunctions, such as bruxism, and the occurrence of tooth NCCLs [26,27].

The loss of restoration of NCCL is a serious problem that dentists face daily. This is due to many factors, for example, high loads on the tooth crown part [11,12,28]. Part of modern research is aimed at analyzing the effect of the material on the strain of the tooth-restoration system [29–31]. Other authors consider the influence of different mechanisms of inelastic strain on the restorations' performance [32,33]. The modification of the restorations' geometric configuration and new treatment technologies is another research area [34,35]. Science-intensive approaches in dentistry have made it possible to study the processes occurring in the tooth tissues [10,15,19,36–39]. The influence of occlusal and parafunctional loads is researched. An analysis of change in the properties of hard tooth tissues is performed. The pattern of the stress distribution in healthy and affected teeth is investigated. However, to date, the information obtained on the etiology and pathogenesis of abfractions is still insufficient to provide quality care to patients with NCCLs.

This problem requires new effective solutions. The modern level of providing highly qualified medical care makes high demands in the treatment of dental system pathologies. The methods of biomechanical modeling and mathematical analysis acquire a special role in the planning stage of dental treatment [11]. FEM is used for the modeling and analysis of complex systems, including biomechanical ones [9,18,32–35]. The numerical model will allow planning options for the formation of a cavity for optimal long-term restoration. Changing the defect geometry during preparation can change or transfer the load vector to stronger areas. The prediction of the impact of loading for various restoration options will help to assess the possible effectiveness of orthopedic treatment. A reasonable choice of treatment tactics will prevent or reduce the rate of progression of the disease.
