N. D. Morozkin, D. M. Kolonskikh

Ufa University of Science and Technology (Ufa, Russian Federation)

Abstract. The aim of this study is to compute the stress distribution in the temporomandibular joint (TMJ) and its components under various functional occlusal states. Finite element method (FEM) is employed for the computations. An original adaptive triangulation algorithm for a complex three-dimensional domain is proposed, which enables the generation of unstructured tetrahedral meshes with controllable element density in regions of expected stress concentration. The computational efficiency is achieved through a specialized node renumbering algorithm that minimizes the bandwidth of the global stiffness matrix, combined with a compact storage scheme using Cholesky decomposition. Using a model that incorporates anatomical features and different physical and mechanical properties of tissues, simulations are performed for three key phases of the masticatory cycle: central, anterior, and lateral occlusion. Quantitative patterns of principal stress distribution are established. The results obtained correlate with clinical observations regarding high incidence of disc pathologies and TMJ dysfunctions. The computational framework developed in the paper can be applied for practical purposes, including planning of orthopedic and surgical interventions.

Key Words: stress-strain state, finite element method, Delaunay triangulation, adaptive mesh, biomechanics, temporomandibular joint, masticatory cycle, occlusion

For citation: N. D. Morozkin, D. M. Kolonskikh. Numerical simulation of the stress-strain state of the temporomandibular joint based on adaptive finite-element triangulation. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 28:2(2026), 130–144. DOI: https://doi.org/10.15507/2079-6900.28.202602.130-144

Information about the authors:

Nikolay D. Morozkin, D. Sci. (Phys. and Math.), Professor at the Department of Mathematical and Computer Modeling, Ufa University of Science and Technology (32 Zaki Validi St., Ufa, 450076, Russia), ORCID: https://orcid.org/0009-0002-5051-7094, morozkinnd@mail.ru

Denis M. Kolonskikh, Ph. D. (Phys. and Math.), Associate Professor at the Department of Mathematical and Computer Modeling, Ufa University of Science and Technology (32 Zaki Validi St., Ufa, 450076, Russia), ORCID: https://orcid.org/0009-0006-5450-7677, deniskolonskikh@gmail.com