**3. Results**

The crown part of the tooth is deformed together, i.e., there is no change in the crown geometry. The position and number of the points of load application from the antagonist tooth has little effect on the stress-strain state of the tooth-inlay system.

The stress-strain state of a tooth without defect was considered in advance (Figure 4). The nature of the distribution of the intensity of stresses and strains is shown on the example of the load of 500 N from the antagonist tooth.

**Figure 4.** Stress and strain intensity of the tooth without NCCL: (**a**) is stress intensity; (**b**) is strain intensity.

The maximum stress and strain intensity is observed in the zone of kinematic boundary conditions. The maximum intensity of stresses and strains is observed in the tooth enamel near the cervical area. The maximum stress level in dentine is 85% lower than in enamel and reaches 28.8 MPa. The maximum level of strains in dentine does not exceed 0.2%. The intensity of stresses and strains in the zone where the NCCL will be modeled reaches the level of approximately 70 MPa and 0.1%, respectively.

The stress and strain intensity of the tooth with NCCL at a load of 500 N are shown in Figure 5.

intensity.

in Figure 5.

reaches the level of approximately 70 MPa and 0.1%, respectively.

**Figure 5.** Stress and strain intensity of the tooth with NCCL: (**a**) is stress intensity; (**b**) is strain intensity. **Figure 5.** Stress and strain intensity of the tooth with NCCL: (**a**) is stress intensity; (**b**) is strain intensity.

**Figure 4.** Stress and strain intensity of the tooth without NCCL: (**a**) is stress intensity; (**b**) is strain

The maximum stress and strain intensity is observed in the zone of kinematic boundary conditions. The maximum intensity of stresses and strains is observed in the tooth enamel near the cervical area. The maximum stress level in dentine is 85% lower than in enamel and reaches 28.8 MPa. The maximum level of strains in dentine does not exceed 0.2%. The intensity of stresses and strains in the zone where the NCCL will be modeled

The stress and strain intensity of the tooth with NCCL at a load of 500 N are shown

The maximum level of stress and strain in the tooth model with NCCL is observed in the "wedge" zone. The maximum stress intensity is observed at the edge of the NCCL in the enamel and reaches 181 MPa. The maximum stress intensity is higher more than 2.5 times than in the tooth without NCCL. The maximum strain intensity is also observed in the NCCL in the dentine and reaches 0.32%, which is 1.6 times higher than in the model The maximum level of stress and strain in the tooth model with NCCL is observed in the "wedge" zone. The maximum stress intensity is observed at the edge of the NCCL in the enamel and reaches 181 MPa. The maximum stress intensity is higher more than 2.5 times than in the tooth without NCCL. The maximum strain intensity is also observed in the NCCL in the dentine and reaches 0.32%, which is 1.6 times higher than in the model without defects.

without defects. The next stage of the study is analyzing the effect of the prosthetic inlay in the NCCL by changing the "wedge" geometry. Figures 6 and 7 show the stress intensity distribution The next stage of the study is analyzing the effect of the prosthetic inlay in the NCCL by changing the "wedge" geometry. Figures 6 and 7 show the stress intensity distribution in the biomechanical tooth-inlay system under the load of 500 N from the antagonist tooth. The qualitative view of the distribution of the deformation behavior parameters of the tooth-inlay system does not depend on the inlay material. The main difference between the solutions is in quantitative values. Stress and strain intensities are shown in the example of a model with an inlay from material 1.

The level of the stress intensity in the area of the prosthetic inlay is comparable to the stresses in the tooth without defects. The maximum stress intensity in the tooth-inlay system has shifted to the cervical area of the tooth.

The stress intensity in the inlay is 60.2% lower than in the tooth. At the lower boundary from the outside, local stress concentrators are observed at the level of 77 MPa. The distribution of stress fields in dentine corresponds to the loading conditions. The main stresses from the antagonist tooth action are realized in the enamel and in the inlay. The stress intensity on the outer surface inlay is lower than on the inner one.

The dependences of the maximum values of stress intensities in the biomechanical system elements on the applied load value are shown in Figure 8.

The inlay material does not significantly affect the values of maximum stresses in the enamel. The more uniform distribution of the stress intensity in the biomechanical tooth-inlay system is observed by the use of material 1. A significant increase of stress intensity in the tooth dentin is observed in this case. The max*σ*int in dentine when inlay material 1 is 2.5 and 1.2 times higher than in the tooth model without and with an NCCL, respectively. A decrease max*σ*int in enamel and an increase in dentine were also observed when using prosthetic inlays from materials 2 and 3. A comparison of the stress level with models without and with NCCL is shown in Table 3.

ple of a model with an inlay from material 1.

*Materials* **2022**, *14*, x FOR PEER REVIEW 9 of 21

**Figure 6.** Stress intensity of the biomechanical assembly: (**a**,**b**) are tooth-inlay system; (**c**) is enamel; (**d**) is dentine. **Figure 6.** Stress intensity of the biomechanical assembly: (**a**,**b**) are tooth-inlay system; (**c**) is enamel; (**d**) is dentine. **Figure 6.** Stress intensity of the biomechanical assembly: (**a**,**b**) are tooth-inlay system; (**c**) is enamel; (**d**) is dentine.

in the biomechanical tooth-inlay system under the load of 500 N from the antagonist tooth. The qualitative view of the distribution of the deformation behavior parameters of the tooth-inlay system does not depend on the inlay material. The main difference between the solutions is in quantitative values. Stress and strain intensities are shown in the exam-

in the biomechanical tooth-inlay system under the load of 500 N from the antagonist tooth. The qualitative view of the distribution of the deformation behavior parameters of the tooth-inlay system does not depend on the inlay material. The main difference between the solutions is in quantitative values. Stress and strain intensities are shown in the exam-

**Figure 7.** Stress intensity of the inlay: (**a**) is general view, (**b**) is outer side. **Figure 7.** Stress intensity of the inlay: (**a**) is general view, (**b**) is outer side.

**Figure 7.** Stress intensity of the inlay: (**a**) is general view, (**b**) is outer side.

The level of the stress intensity in the area of the prosthetic inlay is comparable to the

The level of the stress intensity in the area of the prosthetic inlay is comparable to the stresses in the tooth without defects. The maximum stress intensity in the tooth-inlay sys-

tem has shifted to the cervical area of the tooth.

stress intensity on the outer surface inlay is lower than on the inner one.

system elements on the applied load value are shown in Figure 8.

The stress intensity in the inlay is 60.2% lower than in the tooth. At the lower boundary from the outside, local stress concentrators are observed at the level of 77 MPa. The distribution of stress fields in dentine corresponds to the loading conditions. The main stresses from the antagonist tooth action are realized in the enamel and in the inlay. The

The dependences of the maximum values of stress intensities in the biomechanical

**Figure 8.** Dependence of the maximum values of the biomechanical assembly stress intensity on the load: (**a**) is enamel; (**b**) is dentine; (**c**) is inlay; black (solid line) is model without defect; black (dotted line) is model with defect; green is model with material 1 inlay, red is model with material 2 inlay, blue is model with material 3 inlay. **Figure 8.** Dependence of the maximum values of the biomechanical assembly stress intensity on the load: (**a**) is enamel; (**b**) is dentine; (**c**) is inlay; black (solid line) is model without defect; black (dotted line) is model with defect; green is model with material 1 inlay, red is model with material 2 inlay, blue is model with material 3 inlay.


The inlay material does not significantly affect the values of maximum stresses in the **Table 3.** Comparison max*σ*int (%) in the biomechanical assembly elements of different models.

A decrease in the stress intensity in the tooth enamel when using a restoration in the form of a prosthetic inlay by 12–16% can be noted. An increase in the maximum intensity of stresses in the dentine and the inlay near of the gingival fold is observed due to the contact gluing. The stress intensity in the model with a prosthetic inlay made of material 1 is more than two times lower on the main volume of materials. The influence of the geometry of the cavity for the inlay and veneer part on the deformation behavior of the biomechanical assembly must be studied.

*Materials* **2022**, *14*, x FOR PEER REVIEW 11 of 21

max int

biomechanical assembly must be studied.

**Table 3.** Comparison

Not taking into account the NCCL

Taking into account the NCCL

Let us consider the nature of the strain intensity distribution in the biomechanical tooth-inlay assembly (Figure 9). Let us consider the nature of the strain intensity distribution in the biomechanical tooth-inlay assembly (Figure 9).

**Model Element Model Accounting for Prosthetic Inlay**

A decrease in the stress intensity in the tooth enamel when using a restoration in the form of a prosthetic inlay by 12–16% can be noted. An increase in the maximum intensity of stresses in the dentine and the inlay near of the gingival fold is observed due to the contact gluing. The stress intensity in the model with a prosthetic inlay made of material 1 is more than two times lower on the main volume of materials. The influence of the geometry of the cavity for the inlay and veneer part on the deformation behavior of the

(%) in the biomechanical assembly elements of different models.

Enamel <by 16.00% <by 11.86% <by 12.93%

Dentine >by 154.62% >by 15.17% >by 38.83%

Enamel <by 10.65% <by 6.24% <by 7.38% Dentine >by 23.39% <by 44.19% <by 32.72%

**Material 1 Material 2 Material 3**

**Figure 9.** Strain: (**a**) is tooth-inlay system; (**b**) is enamel; (**c**) is dentine; (**d**) is inlay. **Figure 9.** Strain: (**a**) is tooth-inlay system; (**b**) is enamel; (**c**) is dentine; (**d**) is inlay.

The maximum strain intensity is observed in the dentine near the edge of the contact interaction zone with the prosthetic inlay. The strain intensity is lower by two or more times on the rest of the dentine volume. The max int in the enamel is observed near the cervical area of the tooth. The max int in the prosthetic inlay is located on the lower sur-The maximum strain intensity is observed in the dentine near the edge of the contact interaction zone with the prosthetic inlay. The strain intensity is lower by two or more times on the rest of the dentine volume. The max*ε*int in the enamel is observed near the cervical area of the tooth. The max*ε*int in the prosthetic inlay is located on the lower surface near the edge of the contact zone. This effect can be eliminated by: changing the geometry of the prosthetic inlay; the selection of material and refinement of the finite element model.

A dependence of the strain maximum intensity on the load level is shown in Figure 10.

face near the edge of the contact zone. This effect can be eliminated by: changing the The strain intensity in the enamel is lower in the models with a prosthetic inlay in the NCCL. The maximum influence on the nature of the distribution and the level of strain intensity is observed in the tooth dentine. The strain increase in the dentine and a shift of the maximum level *ε*int to the "wedge" area in model with a defect can be noted. The max*ε*int dentine in the model with an NCCL is 1.7 times more than in the tooth without a defect.

The use of a new NCCL restoration in the form of a prosthetic inlay makes it possible to reduce the strain intensity in the dentine when using materials 2 and 3. An increase max*ε*int in dentine is observed in the model with an inlay made of material 1 by 2.1 times than in the tooth without defect. The maximum level zone *ε*int is localized near the inlay-tooth contact border near the area of the gingival fold. The level of strain intensity is comparable to the strains of the tooth without defect on the main volume of dentine.

ment model.

10.

max int

**Figure 10.** Dependence of the maximum values of the strain intensity of the biomechanical assembly on the load: (**a**) is enamel; (**b**) is dentine; (**c**) is inlay; black (solid line) is model without defect; black (dotted line) is model with defect; green is model with material 1 inlay, red is model with material 2 inlay, blue is model with material 3 inlay. **Figure 10.** Dependence of the maximum values of the strain intensity of the biomechanical assembly on the load: (**a**) is enamel; (**b**) is dentine; (**c**) is inlay; black (solid line) is model without defect; black (dotted line) is model with defect; green is model with material 1 inlay, red is model with material 2 inlay, blue is model with material 3 inlay.

geometry of the prosthetic inlay; the selection of material and refinement of the finite ele-

A dependence of the strain maximum intensity on the load level is shown in Figure

The strain intensity in the enamel is lower in the models with a prosthetic inlay in the NCCL. The maximum influence on the nature of the distribution and the level of strain intensity is observed in the tooth dentine. The strain increase in the dentine and a shift of The minimum value max*ε*int is observed in the inlay from material 1. The maximum strain level of the inlay from materials 2 and 3 is comparable to the tooth enamel. This can adversely affect the service life of the prosthetic structure.

the maximum level int to the "wedge" area in model with a defect can be noted. The max int dentine in the model with an NCCL is 1.7 times more than in the tooth without a defect. The use of a new NCCL restoration in the form of a prosthetic inlay makes it possible to reduce the strain intensity in the dentine when using materials 2 and 3. An increase It is important to evaluate the dependence of the contact parameters because of the problem statement. The interface zone parameters are indicators of the strain behavior of the tooth-inlay system: contact pressure *P<sup>K</sup>* and contact tangential stress *τK*. A dependence of the maximum (max) and average (∆) levels of contact parameters on the tooth-inlay mating surface for three inlay materials are shown in Figure 11.

tooth contact border near the area of the gingival fold. The level of strain intensity is com-

parable to the strains of the tooth without defect on the main volume of dentine.

in dentine is observed in the model with an inlay made of material 1 by 2.1 times

int

is localized near the inlay-

than in the tooth without defect. The maximum level zone

max int

This can adversely affect the service life of the prosthetic structure.

) and average (

inlay mating surface for three inlay materials are shown in Figure 11.

mum strain level of the inlay from materials 2 and 3 is comparable to the tooth enamel.

*K P*

It is important to evaluate the dependence of the contact parameters because of the problem statement. The interface zone parameters are indicators of the strain behavior of

is observed in the inlay from material 1. The maxi-

) levels of contact parameters on the tooth-

*K*

. A depend-

and contact tangential stress

The minimum value

ence of the maximum (

the tooth-inlay system: contact pressure

max

**Figure 11.** Dependence of contact parameters in the inlay on the load: (**a**) is contact pressure; (**b**) is tangential contact stress; solid lines is the maximum; points is the average; green is model with material 1 inlay, red is model with material 2 inlay, blue is model with material 3 inlay. **Figure 11.** Dependence of contact parameters in the inlay on the load: (**a**) is contact pressure; (**b**) is tangential contact stress; solid lines is the maximum; points is the average; green is model with material 1 inlay, red is model with material 2 inlay, blue is model with material 3 inlay.

The maximum contact parameters are observed near the edge of the tooth-inlay contact zone near the gingival fold, similar to stresses and strains. The average level of contact pressure and contact tangential stress is 3–4 and 7–8.9 times lower than the maximum values of the parameters respectively. The max *<sup>K</sup>* and *<sup>K</sup>* are 7-9 and 15-19 times lower than max *<sup>K</sup> P* and *<sup>K</sup> P* . The study of the influence values of the friction coefficient The maximum contact parameters are observed near the edge of the tooth-inlay contact zone near the gingival fold, similar to stresses and strains. The average level of contact pressure and contact tangential stress is 3–4 and 7–8.9 times lower than the maximum values of the parameters respectively. The max*τ<sup>K</sup>* and ∆*τ<sup>K</sup>* are 7–9 and 15–19 times lower than max*P<sup>K</sup>* and ∆*PK*. The study of the influence values of the friction coefficient on the biomechanical assembly deformation is required.

on the biomechanical assembly deformation is required. The obtained estimates give an idea of the qualitative patterns of the influence of the new restoration type and its materials on tooth deformation.
