*2.1. Model*

The central section of the tooth, with and without taking into account the NCCL, is shown in Figure 1. The tooth model includes the volume of enamel (1) and dentine (2). The tooth pulp (3) is not modeled but is taken into account when parameterizing the NCCL. When deepening the NCCL in the tooth tissue, it is taken into account that it should not penetrate into the pulp.

**Figure 1.** The central section of the tooth, taking into account (**a**) and without taking into account (**b**) an NCCL: 1 is enamel; 2 is dentine; 3 is pulp; I is defect. **Figure 1.** The central section of the tooth, taking into account (**a**) and without taking into account (**b**) an NCCL: 1 is enamel; 2 is dentine; 3 is pulp; I is defect.

The tooth geometry without taking into account the root system is often used in practice [47]. Such models make it possible to quickly obtain qualitative results on the unit deformation. The tooth models do not take into account the root system. This decision was made to qualitative assessment of tooth deformation in the first approximation. The tooth geometry without taking into account the root system is often used in practice [47]. Such models make it possible to quickly obtain qualitative results on the unit deformation. The tooth models do not take into account the root system. This decision was made to qualitative assessment of tooth deformation in the first approximation.

Parameterization of the tooth geometry is performed according to its main parameters: height *h* , length l , and thickness of the enamel *e l* . *e l* is the parameter of the enamel's maximum possible thickness. The actual enamel thickness in the model can be more or less by 10-15%. Figure 1 shows the geometrical configuration of a tooth with *h* 7.2 , *l* 9.44 , and 1.5 *<sup>e</sup> l* mm. Overall dimensions of the tooth correspond to premolars and molars. Static boundary conditions are set on the tooth surface 1 *S* and kinematic ones on the surface 2 *S* . The boundary conditions for all models are the same. The load varies from 100 to 1000 N. The NCCL is parameterized. Parameterization is based on the Parameterization of the tooth geometry is performed according to its main parameters: height *h*, length *l*, and thickness of the enamel *l<sup>e</sup>* . *l<sup>e</sup>* is the parameter of the enamel's maximum possible thickness. The actual enamel thickness in the model can be more or less by 10–15%. Figure 1 shows the geometrical configuration of a tooth with *h* ≈ 7.2, *l* ≈ 9.44, and *l<sup>e</sup>* ≈ 1.5 mm. Overall dimensions of the tooth correspond to premolars and molars. Static boundary conditions are set on the tooth surface *S*<sup>1</sup> and kinematic ones on the surface *S*2. The boundary conditions for all models are the same. The load varies from 100 to 1000 N. The NCCL is parameterized. Parameterization is based on the position and coordinates of the defect. As a result of modeling, an NCCL (I) 2*l<sup>w</sup>* × *h<sup>w</sup>* × *b<sup>w</sup>* is obtained. Figure 1 shows the NCCL (I) with parameters 5.38 × 0.73 × 1.3 mm.

position and coordinates of the defect. As a result of modeling, an NCCL (I) <sup>2</sup>*l h b w w w* is obtained. Figure 1 shows the NCCL (I) with parameters 5.38 0.73 1.3 mm. A cavity is created in the tooth for a prosthetic inlay when creating a new type of A cavity is created in the tooth for a prosthetic inlay when creating a new type of restoration. Figure 2 shows the geometry of the cavity central section of the tooth model prosthetic inlay.

restoration. Figure 2 shows the geometry of the cavity central section of the tooth model prosthetic inlay. An original new method of treatment is proposed. The formed cavity to fix the inlay (II) includes the main part obtained by expanding the lesion, with an additional retention point in the form of a cavity passing to the proximal surface of the tooth, an additional platform at the top of the cavity for fixing the veneer part of the inlay, and a gingival fold (III) located more apically than the lesion.

Element (III) was introduced into the construct to recreate the dentogingival attachment. Often the NCCL is combined with a gingival margin recession. The reconstruction of the periodontal attachment between the artificial material and the gum is not possible.

The inlay cavity was parameterized using 3 parameters:


A geometric configuration of the inlay cavity is shown in Figure 3 for parameter values *h*<sup>1</sup> = 0.3, *h*<sup>2</sup> = 0.2, and *h*<sup>3</sup> = 0.5 mm. The central section of the cavity extends over the

entire length of the NCCL. The inlay's final appearance is formed with the geometry of the veneer part. *Materials* **2022**, *14*, x FOR PEER REVIEW 5 of 21

**Figure 2.** Modeling a cavity for a prosthetic inlay: 1 is enamel; 2 is dentine; 3 is pulp; 4 is inlay; II is cavity to fix the inlay; III is gingival fold. **Figure 2.** Modeling a cavity for a prosthetic inlay: 1 is enamel; 2 is dentine; 3 is pulp; 4 is inlay; II is cavity to fix the inlay; III is gingival fold. *Materials* **2022**, *14*, x FOR PEER REVIEW 6 of 21

Figure 3 shows the tooth geometry with the NCCL restoration using a new prosthetic inlay, as well as the view of the inlay in the tooth cavity. Model 1 is enamel, 2 is dentin,

The inlay is quite streamlined on all sides. The inlay model is parameterized. The thickness, veneer part, and cavity area can change. The figure shows one of the options for the veneer part geometry of the inlay. Given inlay geometry will be used in a numerical

The prosthetic inlay maintains the aesthetics of the dentition. The inlay restores the aesthetics of the tooth and increases the contact area of the tooth and the prosthetic struc-






The main limitations of the model at the moment:

sources and a detailed study of the tooth-inlay contact zone;

refine the behavior model of the system materials in the future;

cracks due to the complexity of such mechanical models.

experiment series.

reality sliding is possible;

ture.

Figure 3 shows the tooth geometry with the NCCL restoration using a new prosthetic inlay, as well as the view of the inlay in the tooth cavity. Model 1 is enamel, 2 is dentin, and 4 is a new restoration of an NCCL using different materials. The pulp of the tooth (3) is not modeled but is taken into account when creating a cavity for a prosthetic inlay.

The inlay is quite streamlined on all sides. The inlay model is parameterized. The thickness, veneer part, and cavity area can change. The figure shows one of the options for the veneer part geometry of the inlay. Given inlay geometry will be used in a numerical experiment series.

The prosthetic inlay maintains the aesthetics of the dentition. The inlay restores the aesthetics of the tooth and increases the contact area of the tooth and the prosthetic structure.

The main limitations of the model at the moment:

