Issue 67

T. Diburov et alii, Frattura ed Integrità Strutturale, 67 (2024) 259-279; DOI: 10.3221/IGF-ESIS.67.19

where σ ij and ε ij were the stress and strain tensor components, respectively; u i and u j were the displacement vector components; δ was the Kronecker delta; 11 22 33        was volumetric strain;    1 1 2 E        was Lamé's first parameter,   2 1 E     was shear modulus; ν , E were Poisson's ratio and Young's modulus (Tab. 1). The comma before the index meant differentiation by spatial coordinate. The final mesh density as well as the average mesh size was selected based on the convergence of the computational experiment results. For two calculation cases, 3D models are shown in Fig. 2. Boundary conditions were set as follows. The kinematic boundary conditions were the same for all calculations, namely rigid fixation along the surface A (Fig. 2, a): The load boundary conditions were its vertical application to the abutments of each implant alternately for the i numbers of 1, 2, 3 and 4 according to Fig. 2, b for the first case of the calculations:   1 z i F F  , where 50N i F  ; (5) while such boundary conditions were in the form of a distributed compressive load applied orthogonally to the lower surface of the denture base alternately to the segments indicated in Fig. 2, c, simulating various options for redistributing the mastication load from the maxillary prosthesis in the second case:   2 z i F F  (6) where F i =50, 100, 150 N; i was the segment number of the lower surface of the denture base from 1 to 8, numbered from right to left, for the sequential application of the loads in the calculations. For the third case, the load boundary conditions were in the form of a distributed compressive load applied at an α angle of 45  to the lower surface of the denture bases, first alternately but simultaneously then to segments 4 and 5 according to Fig. 2, c, simulating three options for loading the anterior teeth when biting:         3 cos , 3 cos z i y i F F F F     (7) where F i =50, 100, 150 N and i =4 and 5 were the load amplitude and the number of the loaded segments according to Fig. 2, с ; α was the inclination angle. In the contact area between the implants and the zygomatic bone, the contact boundary conditions provided for equality of displacements at the “implant–zygomatic bone” interface. In other words, the rigid fixation (ideal contact) conditions were implemented, implying successful osseointegration. The use of the Ti-6Al-4V alloy, widely implemented for biomedical applications, was a topic discussion in recent years since its elastic modulus exceeded 100 GPa, i.e. it was mechanically incompatible (significantly superior) to that of bone tissue (5– 30 GPa) [24]. This fact could provide the “stress shielding” phenomenon, which was observed when the implant absorbed applied loads and did not stimulate bone growth, enabling peri-implant bone resorption [25-30]. In addition, this led to fracture of natural bone tissue (aseptic loosening). However, this alloy (mainly with a protective coating deposited to prevent release of aluminum into a human body) is still a leader in the manufacturing medical implants, in particular those used in this study. Polymethyl methacrylate (PMMA) was selected as a material for prosthetic structures (denture base), products from which could be manufactured by 3D printing [31]. The skull bones possessed averaged parameters for a moderately mineralized aged state, with additional continuum averaging that did not take into account the distinction between cortical and trabecular parts. Values of the material properties of the model elements used in the calculations are presented in Tab. 1. 0, 0, 0 x y z A A A u u u    (4)

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