**3. Results**

The influence of the mouthguard geometry on the stress–strain state and the parameters of the occlusion region was considered in our findings.

Figures 3 and 4 show the stress intensity distributions in the hard tissues of the teeth with an indentation force of 250 N for the upper and lower teeth. As expected, the use of a mouthguard leads to a significant decrease in the level of stress intensity. *Materials* **2021**, *14*, x FOR PEER REVIEW 6 of 12

**Figure 3.** The stress intensity in the upper dentition tooth at 250 N: (**a**) case a; (**b**) case b; (**c**) case c-A; (**d**) case c-B; (**e**) case c-C; I—zone of maximum stress intensity. **Figure 3.** The stress intensity in the upper dentition tooth at 250 N: (**a**) case a; (**b**) case b; (**c**) case c-A; (**d**) case c-B; (**e**) case c-C; I—zone of maximum stress intensity.

When using a mouthguard, the dependence of the maximal stress intensity on the indentation force was found to be close to linear. With an increase in the force of indentation, an increase in the effect of reducing the intensity of stresses in the hard tissues of the teeth was observed when using all types of mouthguards. In the tooth of the upper dentition, the greatest decrease in the level of stress intensity was observed when using a In the case of teeth contact without a mouthguard, the maximal stress intensity was observed near the occlusion region. When using mouthguards, a significant decrease in the level of stress intensity was observed. In most cases, the maximum stresses are distributed over a larger area. For the multilayer EVA case, the mouthguard shifted the zone of maximum stresses towards the neck of the tooth.

mouthguard with an interlayer adjusted to the geometry of the elements of the dentition. The mouthguard use was shown to have a significant impact on the parameters of contact interaction. With the contact of antagonist teeth without a mouthguard, the max-

an indentation force of 250 N. Figure 6 shows a comparison of the maximum level of the parameters of the contact zones when using individual dental mouthguards of different

A significant decrease in the maximum level of contact pressure can be noted for all types of dental mouthguards. The maximum level of contact shear stress decreased less than the contact pressure in the zone of contact with the tooth of the upper dentition.

The maximum contact pressure was higher in the tooth of the lower dentition, and the maximum contact shear stress was in the tooth of the upper dentition (Figure 6). As in the case of stress intensity, the maximum decrease in the level of contact interaction parameters was observed when using a mouthguard with an interlayer adjusted to the ge-

The dependence of the level of plastic deformations in the mouthguard was not linear

ometry of the elements of the dentition (case c-C).

and did not exceed 30% at a maximum load.

geometric configurations.

**Figure 4.** The stress intensity in the lower dentition tooth at 250 N: (**a**) case a; (**b**) case b; (**c**) case c-A; (**d**) case c-B; (**e**) case c-C; I, II—zone of maximum stress intensity. **Figure 4.** The stress intensity in the lower dentition tooth at 250 N: (**a**) case a; (**b**) case b; (**c**) case c-A; (**d**) case c-B; (**e**) case c-C; I, II—zone of maximum stress intensity.

For multilayer mouthguards with an A-silicon interlayer, the maximum stress intensity was observed in the contact zones, but removed from the tooth occlusion zone. When using individual mouthguards, the intensity of stresses in the tooth of the upper dentition decreased by 3.6 times when using a multilayer EVA mouthguard and on average by 6.2 times when using multilayer mouthguards with an A-silicon interlayer.

The greatest decrease in the level of stress intensity was observed when using a mouthguard with an interlayer adjusted to the geometry of the elements of the dentition (Figure 3e), maximal stress intensity was less by more than eight times.

The decrease in the maximum level of stress intensity in the hard tissues of the tooth of the lower dentition when using a multilayer individual EVA mouthguard was found to be much less than for the tooth of the upper dentition (Figure 4). The maximum stress intensity decreased by only 1.9 times. In this case, the maximum stress intensity when using a multilayer EVA mouthguard was localized near the edge of the contact area with the mouthguard.

**Figure 5.** Dependence of maximal stress intensity on indentation force for the teeth of the upper (**a**) and lower (**b**) dentition: 1—case a; 2—case b; 3—case c-A; 4—case c-B; 5—case c-C. When using multilayer mouthguards in the tooth of the lower dentition, the greatest decrease in the maximum level of stress intensity was observed on average four times more without their localization near the contact surface. Of particular interest is the analysis of the influence of the geometric characteristics of the mouthguard on the deformation behavior of the elements of the dentition. Within the framework of a series of numerical

experiments, the dependences of the maximum level of stress intensity on the force of indentation in hard tissues of teeth were established for all variants of design schemes (Figure 5). As expected, the dependence of the maximum level of stress intensity on the indentation force between a pair of antagonist teeth without mouthguard usage was linear. **Figure 4.** The stress intensity in the lower dentition tooth at 250 N: (**a**) case a; (**b**) case b; (**c**) case c-A; (**d**) case c-B; (**e**) case c-C; I, II—zone of maximum stress intensity.

*Materials* **2021**, *14*, x FOR PEER REVIEW 7 of 12

**Figure 5.** Dependence of maximal stress intensity on indentation force for the teeth of the upper (**a**) and lower (**b**) dentition: 1—case a; 2—case b; 3—case c-A; 4—case c-B; 5—case c-C. **Figure 5.** Dependence of maximal stress intensity on indentation force for the teeth of the upper (**a**) and lower (**b**) dentition: 1—case a; 2—case b; 3—case c-A; 4—case c-B; 5—case c-C.

When using a mouthguard, the dependence of the maximal stress intensity on the indentation force was found to be close to linear. With an increase in the force of indentation, an increase in the effect of reducing the intensity of stresses in the hard tissues of the teeth was observed when using all types of mouthguards. In the tooth of the upper dentition, the greatest decrease in the level of stress intensity was observed when using a mouthguard with an interlayer adjusted to the geometry of the elements of the dentition.

The mouthguard use was shown to have a significant impact on the parameters of contact interaction. With the contact of antagonist teeth without a mouthguard, the maximum level of contact pressure and contact shear stress reached 78.6 and 7.19 MPa with an indentation force of 250 N. Figure 6 shows a comparison of the maximum level of the parameters of the contact zones when using individual dental mouthguards of different geometric configurations. *Materials* **2021**, *14*, x FOR PEER REVIEW 8 of 12

Within the framework of the study, the models of materials and objects of the study

When modeling the EVA behavior model, it is possible to consider the viscosity of the material. Additional studies of the deformation material and further clarification of the constitutive relations are required. Friction coefficients of EVA-tooth material and EVA-A-silicone are constant at 0.3; the coefficient of friction was taken from the reference literature. Investigation of the friction of materials requires specialized equipment and an original test procedure. Considering the experimentally obtained frictional properties of materials will make it possible to obtain a better picture of deformation of the elements of

Within the framework of the task, the multilayered teeth were not considered, which introduces an additional error into the model. The tooth is a composite structure. In further studies, it is planned to consider the multilayered tooth with different properties of

The 2D FEA problem was solved. The contact between the layers of the mouthguard was considered, but the level of the parameters of the EVA-A-silicon contact zone was a lower order of magnitude than in the occlusion area. No delamination of the interlayer was observed during the simulation. Frictional contact with a previously unknown contact area, and the nature of the distribution of contact state status zones was realized in

The study of the influence of the geometry of the mouthguards on the deformation of the elements of the dentition was carried out in the first approximation. Researchers



Mouthguard thickness has a significant impact on the patient's comfort. Recent studies considered an influence of the mouthguard's thickness on its performance [22–24]. Westerman et al. [22] revealed that the rational thickness for an EVA mouthguard is 4


mechanical unit in flat and axisymmetric formulations;

**Figure 6.** Maximal values of contact parameters: (**a**) max PK; (**b**) max τK. **Figure 6.** Maximal values of contact parameters: (**a**) max PK; (**b**) max τK.

**4. Discussion** 

the dentition.

the materials of the layers.

the zone of teeth closing.

have a number of challenges that follow:


the biomechanical unit;

*4.1. Limitation Statement* 

A significant decrease in the maximum level of contact pressure can be noted for all types of dental mouthguards. The maximum level of contact shear stress decreased less than the contact pressure in the zone of contact with the tooth of the upper dentition.

The maximum contact pressure was higher in the tooth of the lower dentition, and the maximum contact shear stress was in the tooth of the upper dentition (Figure 6). As in the case of stress intensity, the maximum decrease in the level of contact interaction parameters was observed when using a mouthguard with an interlayer adjusted to the geometry of the elements of the dentition (case c-C).

The dependence of the level of plastic deformations in the mouthguard was not linear and did not exceed 30% at a maximum load.
