**1. Introduction**

The dentofacial system is vital as its elements maintain various physiological processes,

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

*1.1. Problem Context*

such as respiration, digestion and speech [1]. Dental biomechanics issues have increased in number over the past decade. These issues include the study of the heterogeneity of dental tissues [2], modeling the teeth stress–strain state under orthodontic loads [3], orthodontics problems to correct the occlusion [4] and numerical simulation of contact between teeth and dental implants or mouthguards [5]. Furthermore, the condition of the dentofacial system has a significant influence on physiological processes due to tooth injuries during sports and hard physical labor as well psychoemotional stress [6,7].

Today, one of the most effective ways to avoid dental injuries is the use of a mouthguard [8]. As various mouthguard designs exist on the market, there is a need for computer modeling of biomechanical behavior, both of the structures themselves and of the materials from which they are made [9].

Research has been carried out on the following:

175

• Biomechanical analysis of the effect of the properties of mouthguard materials on the deformation behavior of dental hard tissues [10,11];

**Citation:** Kamenskikh, A.; Kuchumov, A.G.; Baradina, I. Modeling the Contact Interaction of a Pair of Antagonist Teeth through Individual Protective Mouthguards of Different Geometric Configuration. *Materials* **2021**, *14*, 7331. https://

Academic Editor: Giovanni Vozzi

doi.org/10.3390/ma14237331

Received: 10 November 2021 Accepted: 28 November 2021 Published: 30 November 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

• Mathematical modeling of the contact interaction of mouthguards of different geometric configurations with a wide range of physiological loads [12,13]; • A comprehensive interdisciplinary study of the patterns of change in the stress–strain state of the human dentofacial system when using mouthguards [14];

• Biomechanical analysis of the effect of the properties of mouthguard materials on the

• Mathematical modeling of the contact interaction of mouthguards of different geo-

metric configurations with a wide range of physiological loads [12,13];


Currently, there is a particular interest in studying the structural features of mouthguards on the elements of the dentofacial system in order to identify qualitative and quantitative patterns of deformation behavior of teeth. and quantitative patterns of deformation behavior of teeth. *1.2. Research Objectives* 

The study objectives were formulated to evaluate the practical application of multi-

### *1.2. Research Objectives* layer Eva mouthguards with an A-silicone interlayer. The research objectives are:

The study objectives were formulated to evaluate the practical application of multilayer Eva mouthguards with an A-silicone interlayer. The research objectives are: - To solve the problem of deformation of teeth during occlusion for a specific clinical case, with/without mouthguards;


*Materials* **2021**, *14*, x FOR PEER REVIEW 2 of 12

deformation behavior of dental hard tissues [10,11];


## *1.3. Problem Description 1.3. Problem Description*  Analysis of the influence of the geometric configuration of protective mouthguards

Analysis of the influence of the geometric configuration of protective mouthguards on their performance during teeth contact is presented in this study. In this case, the load of the jaw compression is considered as the indentation force with consideration of the friction between the contacting surfaces. on their performance during teeth contact is presented in this study. In this case, the load of the jaw compression is considered as the indentation force with consideration of the friction between the contacting surfaces. The paper presents a comparative analysis of the deformation behavior of a pair of

The paper presents a comparative analysis of the deformation behavior of a pair of antagonist teeth during frictional contact interaction through mouthguards of different geometric configurations. antagonist teeth during frictional contact interaction through mouthguards of different geometric configurations. The task was carried out on the basis of the clinical case data. The patients practiced

The task was carried out on the basis of the clinical case data. The patients practiced sports professionally. Figure 1 shows the components of a biomechanical unit for one of the clinical cases: the upper jaw cast and CT (Computer tomography) image. sports professionally. Figure 1 shows the components of a biomechanical unit for one of the clinical cases: the upper jaw cast and CT (Computer tomography) image.

**Figure 1.** Geometry of the clinical cases: (**a**) CT image; (**b**) the gypsum model of an upper jaw. **Figure 1.** Geometry of the clinical cases: (**a**) CT image; (**b**) the gypsum model of an upper jaw.

Improving the performance of protective mouthguards by introducing additional layers of materials has been considered by many scientific groups [16–18]. In [16], the novel

idea of introducing an additional layer of A-silicone into the design of an ethylene–vinyl acetate (EVA) mouthguard was proposed. vinyl acetate (EVA) mouthguard was proposed. The influence of the geometric characteristics of mouthguards on the stress–strain

Improving the performance of protective mouthguards by introducing additional layers of materials has been considered by many scientific groups [16–18]. In [16], the novel idea of introducing an additional layer of A-silicone into the design of an ethylene–

*Materials* **2021**, *14*, x FOR PEER REVIEW 3 of 12

The influence of the geometric characteristics of mouthguards on the stress–strain state of the hard tissues was carried out in Reference [19]. When analyzing the results, it was found that the geometric configuration of the A-silicone interlayer of the mouthguard has a significant effect on the deformation behavior of the dentition. However, in that work, the canonical geometries of the teeth were considered in contact through an individually adaptable mouthguard. state of the hard tissues was carried out in Reference [19]. When analyzing the results, it was found that the geometric configuration of the A-silicone interlayer of the mouthguard has a significant effect on the deformation behavior of the dentition. However, in that work, the canonical geometries of the teeth were considered in contact through an individually adaptable mouthguard.

## **2. Materials and Methods 2. Materials and Methods**  *2.1. Design of the Experiment*
