DOI:

10.37988/1811-153X_2026_2_158

Numerical study of the stress-strain state of an individual titanium mesh designed for targeted bone regeneration and fixation of fixed dentures

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Authors

  • A.G. Stepanov 1, Doctor of Science in Medicine, professor of the Institute of Digital Dentistry
    ORCID: 0000-0002-6543-0998
  • S.V. Apresyan 1, Doctor of Science in Medicine, professor, director of the Institute of Digital Dentistry
    ORCID: 0000-0002-3281-707X
  • P.A. Mossakovsky 2, PhD in Physics and Mathematics, leading researcher of the Institute of Mechanics
    ORCID: 0009-0003-5468-1403
  • M.V. Dzhalalova 2, PhD in Physics and Mathematics, senior researcher of the Institute of Mechanics
    ORCID: 0009-0004-8866-2937
  • M.V. Kopylov 1, dentist, assistant at the Institute of Digital Dentistry
    ORCID: 0000-0001-8567-2225
  • Z.A. Avetisyan 1, dentist, postgraduate of the Institute of Digital Dentistry
    ORCID: 0009-0004-8068-3418
  • O.P. Korolkova 2, research fellow at the Institute of Mechanics
    ORCID: 0000-0001-5559-6014
  • 1 RUDN University, 117198, Moscow, Russia
  • 2 Lomonosov Moscow State University, 119991, Moscow, Russia

Abstract

The paper considers a geometrically complex dental structure that promotes directed bone regeneration to eliminate chewing load on the bone regeneration and implants until they are fully engrafted. The design includes the patient’s lower jaw, an individual perforated titanium mesh fixed with screws with two abutment supports, and a fixed bridge-like dental prosthesis with two crowns fixed on these supports. Several loading options were considered: vertical force 100 N on the occlusal surfaces of two crowns (variant 1) and the same load at an angle of 45° in different planes (variants 2, 3 and 4). The results of solving the contact problem showed a minimum displacement of the upper surface of the titanium mesh under vertical load (variant 1) — 10 µm; under angular loads, the displacement values increased more than 4 times. The maximum stresses in the spongy and cortical bones in all variants were insignificant and were within the safe range. The maximum stress in the titanium mesh under vertical load (variant 1) was 411 MPa, under angular loads, the maximum stresses are significantly higher, and their values exceed 1000 MPa and are in the area of plastic deformations. To reduce the stress in the titanium mesh itself, recommendations are given on the thickness of the mesh and a more correct arrangement of the holes in it.

Key words:

individual titanium mesh, targeted bone regeneration, 3D printing, stress-strain state, mathematical modeling

For Citation

[1]
Stepanov A.G., Apresyan S.V., Mossakovsky P.A., Dzhalalova M.V., Kopylov M.V., Avetisyan Z.A., Korolkova O.P. Numerical study of the stress-strain state of an individual titanium mesh designed for targeted bone regeneration and fixation of fixed dentures. Clinical Dentistry (Russia).  2026; 29 (2): 158—166. DOI: 10.37988/1811-153X_2026_2_158

References

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Received

June 24, 2025

Accepted

April 24, 2026

Published on

July 4, 2026