The article investigates the biomechanics of masticatory loading on a dental implant with a ZrO2 crown. Various loading conditions are analyzed to ensure the reliability of dental implant performance.

• Implant; Bone; Cancellous bone; Cortical bone; Load; Osseointegration; Cx`rown

It is well known that after implant placement into bone, an interaction occurs between the implant surface and the bone, resulting in osseointegration. Osseointegration is defined as a direct structural connection between living, organized bone and the surface of an implant subjected to functional loading. Achieving osseointegration requires compliance with several conditions: the use of a biocompatible material, appropriate macrodesign, a suitable surface, correct surgical technique, and adequate loading of the implant [1-3].

Objective of the study

To analyze the stress-strain state during the interaction of bone and an implant with a zirconium dioxide crown

Geometric model

During the study, the following components were designed: cortical bone, abutment, implant, cancellous bone, and crown. All dimensions and physical properties of the bone tissues were taken from CT scan results and implemented in the Solid Edge software. The cancellous bone is surrounded by cortical bone with a thickness of 2 mm. A molar crown made of zirconium dioxide was also designed and assigned the corresponding material properties. The overall dimensions of the assembly are approximately 43.5 mm in height and 16 mm in width. Holes were created in the bone tissue models for implant placement. In addition, a tetrahedral mesh with an element size of 1.37 mm was applied to the entire assembly to perform the calculations (Table 1).

Table 1: Material dimensions.

Object	Material	Mass, kg	Volume, mm3	Weight, ?
Cortical bone	Cortical tissue	0,022	12664	0,216
Implant	Titanium	0,001	146	0,006
Abutment	Titanium	0,001	112	0,005
Cancellous bone	Cancellous bone	0,036	44000	0,350
Crown	Zirconium dioxide	0,004	629	0,035

To ensure correct calculation of masticatory loading and the accuracy of the results, surface contacts between the crown and the implant and between the implant and the bone surface were taken. A one-stage (immediate) load of 200–400 N is a safe, measured pressure on the implant with a temporary crown immediately after surgery. This load stimulates healing, prevents bone atrophy, and allows chewing soft foods without overloading the structure [4].. The application algorithm generates conditional stresses at each contacting surface, providing idealized conditions for simulating their interaction. For the accuracy of the experiment, it was assumed that the surfaces of the cancellous and cortical bone were 100% osseointegrated and free of gaps. In order to conduct a reliable load experiment, it is necessary to study the material properties as well as the implant placement process (Figure 1, Table 2 and 3).

Figure 1 Dimensions of the modeled assembly components, where: 1 – abutment 2 – implant 3 – cancellous bone 4 – cortical bone 5 – ZrO? crown.

Table 2: Contact modeling

Contact name	Contact type	Search distance
Crown–abutment	Bonding	0,04 mm
Abutment–implant	Bonding	0,04 mm
Implant–cancellous bone	Bonding	0,04 mm
Cancellous bone–cortical bone	Bonding	0,04 mm

Table 3: Number of elements and nodes analyzed

Object	Nodes	Elements
Crown	126 346	80562
Abutment	31586	25014
Implant	33000	21587
Cancellous bone	84656	52346
Cortical bone	108545	77458

Material properties

The total displacement under all applied forces remains within the same minimum and maximum ranges, which may indicate the stability of the system under increasing load. Previously [2], a calculation without a crown was performed, in which the displacements were slightly greater than those under the same load with the crown present. These results demonstrate a relationship between the applied force and the maximum displacement of the object, which may be useful for further analysis of the stability and strength of both configurations (Table 4-Table 8) (Figure 2-Figure 5).

Table 4: Titanium

Attribute	Value
Density	4511,000 kg/m^3
Coefficient of thermal expansion	8,2·10?? 1/°C
Thermal conductivity	0,016 kW/(m·K)
Specific heat capacity	519,000 J/(kg•K)
Elastic modulus	102731,879 MPa
Poisson’s ratio	0,340
Yield strength	172,369 MPa
Ultimate strength	241,316 MPa

Table 5: Cancellous bone.

Attribute	Value
Density	800,000 kg/m^3
Coefficient of thermal expansion	4,3 ·10??/°C
Thermal conductivity	0,000 kW/(m·K)
Specific heat capacity	0,000 J/(kg•K)
Elastic modulus	1400,000 MPa
Poisson’s ratio	0,300
Yield strength	10,000 MPa
Ultimate strength	12,000 MPa

Table 6: Cortical bone

Attribute	Value
Density	1740,000 kg/m^3
Coefficient of thermal expansion	5,1 ·10??/°C
Thermal conductivity	0,001 kW/(m·K)
Specific heat capacity	1,000 J/(kg•K)
Elastic modulus	14000,000 MPa
Poisson’s ratio	0,300
Yield strength	100,000 MPa
Ultimate strength	150,000 MPa

Table 7: Zirconium dioxide

Attribute	Value
Density	5680,000 kg/m^3
Coefficient of thermal expansion	10,3 ·10??/°C
Thermal conductivity	3,000 kW/(m·K)
Specific heat capacity	400,000 J/(kg•K)
Elastic modulus	210000,000 MPa
Poisson’s ratio	0,300
Yield strength	195,000 MPa
Ultimate strength	1400,000 MPa
Elongation, %	4,000

Table 8: Loads.

Load name	Load type	Load value	Load distribution	Load direction	Load direction parameter
Force 1	Force	200 ?	On the crown	( 0,20, 0,00, 0,98 )	Along the vector
Force 2	Force	300 ?	On the crown	( 0,20, 0,00, 0,98 )	Along the vector
Force 3	Force	400 ?	On the crown	( 0,20, 0,00, 0,98 )	Along the vector

Figure 2 Displacements under a force of 200 N (normal masticatory load).

Figure 3 Displacements under a force of 300 N (increased masticatory load).

Figure 4 Displacements under a force of 400 N (maximum masticatory load).

Figure 5 Graph of displacement and coordinate dependence on load.

Stress analysis results

Safety margin results (Figure 6-Figure 12) (Table 9-Table 17)

Figure 6 von Mises stresses (Force 200 N).

Figure 7 von Mises stresses (Force 300 N).

Figure 8 von Mises stresses (Force 400 N).

Figure 9 Graph of safety factor dependence on load.

Figure 10 Safety factor results (Force 200 N).

Figure 11 Safety factor results (Force 300 N).

Figure 12 Safety factor results (Force 400 N).

Table 9: Force 200 N.

Results component: total displacement
Range	Value	X	Y	Z
Minimum	0 mm	-12,596 µm	-7,778 µm	27,966 µm
Maximum	0,000764 mm	3,872 µm	-2,661 µm	45,171 µm

Table 10: Force 300 N.

Results component: total displacement
Range	Value	X	Y	Z
Minimum	0 mm	-12,596 µm	-7,778 µm	27,966 µm
Maximum	0,00115 mm	3,872 µm	-2,661 µm	45,171 µm

Table 11: Force 400 N

Results component: total displacement
Range	Value	X	Y	Z
Minimum	0 mm	-12,596 µm	-7,778 µm	27,966 µm
Maximum	0,00153 mm	3,872 µm	-2,661 µm	45,171 µm

Table 12: Force 200 N

Results component: von Mises
Range	Value	X	Y	Z
Minimum	2,63e-27 MPa	11,771 µm	20,000 µm	4,849 µm
Maximum	29,7 MPa	3,948 µm	-5,738 µm	33,352 µm

Table 13: Force 300 N.

Results component: von Mises
Range	Value	X	Y	Z
Minimum	4,55e-28 MPa	11,771 µm	20,000 µm	4,849 µm
Maximum	44,5 MPa	3,948 µm	-5,738 µm	33,352 µm

Table 14: Force 400 N.

Results component: von Mises
Range	Value	X	Y	Z
Minimum	3,81e-27 MPa	11,771 µm	20,000 µm	4,849 µm
Maximum	59,4 MPa	3,948 µm	-5,738 µm	33,352 µm

Table 15: Force 200 N.

Results component: safety factor / coordinates
Range	Value	X	Y	Z
Minimum	6,57	3,948 µm	-5,738 µm	33,352 µm
Maximum	6,19e+14	9,726 µm	20,000 µm	-6,969 µm

Table 16: Force 300 N

Results component: safety factor / coordinates
Range	Value	X	Y	Z
Minimum	4,38	3,948 µm	-5,738 µm	33,352 µm
Maximum	4,4e+14	8,409 µm	20,000 µm	-2,848 µm

Table 17: Force 400 N

Results component: safety factor / coordinates
Range	Value	X	Y	Z
Minimum	3,28	3,948 µm	-5,738 µm	33,352 µm
Maximum	3,53e+23	-3,901 µm	20,000 µm	-16,762 µm

1. The minimum stress values for all three applied forces remain insignificant. It can be noted that the crown helps to reduce stress values [2],
2. the maximum stress values increase with the applied force from 29.7 to 59.4 MPa. This indicates that as the load increases, the material experiences higher stress levels.
3. displacements along the X, Y, and Z axes remain constant for all load levels, which indicates the stability of the structure.
4. the minimum values of the safety factor under applied forces of 200–400 N range from 6.57 to 3.28, which demonstrates a sufficient safety margin of the structure.

The results of the safety factor analysis show a relationship between the applied force and the safety level of the crown-supported structure. The minimum safety factor values decrease with increasing load, indicating the need for careful monitoring of the structural condition under higher loads.

The comparative analysis of the stress–strain state of the implant without a crown and the implant with a crown and bone showed that the crown–implant system plays a key role in load distribution and in ensuring long- term durability. Applying a load to the occlusal edge of an implant under vertical loading along its axis results in significant splitting stresses along the implant’s vertical axis. Maximum stresses in the implant extend to the area of contact with the cortical plate on the load side, where they are concentrated. Stresses are also recorded on the opposite surface of the implant in the area of its interaction with the bone tissue. When the implant is immersed in bone tissue, the primary stresses in both the implant and the bone tissue are determined at the apex of the implant and the bone and are of a splitting nature. On the pressure side, the maximum stresses vary, and on the opposite side, a compression zone forms, extending to the apex of the implant. The stresses are compensated, but an unevenly applied load at an angle can create fatigue stress nodes in the area of contact between the implant and the bone tissue on the pressure side, which can negatively impact the usability of the implant-supported denture.

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