Vladislav Demenko

The subject of this article is the stress and strain fields in an isotropic elastic layer in contact with rigid supports and weakened by a system of longitudinal cylindrical cavities. The goal of this study is to mathematically model the stress-strain state of an elastic layer with a specified number of cylindrical cavities; to develop a mathematical model and improve an analytical-numerical approach based on the generalized Fourier method for the exact determination of stress fields in an elastic layer with a specified number of cylindrical cavities under the action of infinitely distributed spatial loads. Tasks: to formulate a boundary value problem of elasticity theory for a multiconnected layer considering loads that do not decay at infinity; to construct a general solution of the Lamé equation by the superposition method using the auxiliary problem introduction algorithm; to reduce the boundary value problem to solving a quasi-regular infinite system of linear algebraic equations; to perform a numerical analysis for a layer with three cavities and to evaluate the effect of concentrators on stress distribution. The generalized Fourier method is applied to a layer in the Cartesian coordinate system and cavities in local cylindrical coordinate systems. The scientific novelty lies in the creation of an improved approach that combines the generalized Fourier method with the auxiliary problem algorithm. For the first time, the stress distribution and stress concentration patterns in the vicinity of holes for spatially distributed loads acting on an infinite length have been established. This made it possible to obtain the following results: correctly take into account loads that do not have a periodic structure and do not attenuate at infinity; for an aluminum layer with three cavities, accurate pictures of the distribution of stress tensor components were obtained and zones of their maximum concentration were determined; analysis of the stress state showed that ignoring the mutual influence of cutouts leads to an underestimation of the calculated stresses by more than 20%. Conclusions: The study's results explain the complex interactions among general layer bending, local deformations, and stress-field interference from neighboring concentrators. The significant asymmetry of the stress state confirms the presence of bending moments, and the rapid attenuation of disturbances is consistent with Saint-Venant’s principle. The practical value of the work lies in the potential to use the obtained data to design critical components of aviation technology (integral wing panels, floor power profiles) to increase reliability and optimize weight

Background/Objectives: Finite element analysis (FEA) can predict biomechanical performance of dental implants in compromised bone. In the posterior maxilla, low bone density, thin cortex, and variable regenerated bone stiffness may lead to pathological peri-implant strains. This study examined the effects of implant diameter, cortical thickness, cancellous bone type, and regenerated bone elasticity on strain distribution in short plateau (Bicon SHORT^®) implants. Methods: Three-dimensional FEA models of type III and IV maxillae with cortical layers of 1.0, 0.75, and 0.5 mm were developed. Implants of 4.5, 5.0, and 6.0 mm diameter were tested, with regenerated bone elasticity set to 25–100% of cortical values. An oblique load of 120.9 N at 75° was applied under full osseointegration, and first principal strains were compared with Frost’s 3000 με threshold. Results: Cortical strains remained at physiological levels, but cancellous bone in type IV often exceeded 3000 με, especially with smaller diameters and low regenerated stiffness. Enlarging implant diameter to 6.0 mm lowered cancellous maximal first principal strain by up to 56% in type III and 36% in type IV bone. Reduced regenerated bone elasticity markedly increased risk, particularly with cortical thickness < 0.75 mm. Conclusions: Biomechanical risk depends on implant diameter and regenerated bone quality. Wide short implants (6.0 mm) most effectively limited pathological strain under low cortical support and poor regenerated stiffness. Patient-specific FEA may guide implant choice and improve outcomes in atrophic maxilla rehabilitation.

Implant-supported cantilever crowns can serve as a viable alternative in certain clinical scenarios to circumvent additional surgical procedures either prior to or concurrently with implant placement. Despite the favorable clinical results seen with cantilever crowns, concerns have been raised regarding the long-term biomechanical implications and associated technical challenges. Multiple research investigations have demonstrated that implant-supported cantilever crowns have the potential to generate heightened stress concentrations within the underlying alveolar bone. The aim of the study is in the biomechanical analysis of stress fields in atrophic posterior maxilla with implant-supported cantilever crown. Functionally important two molars loss was analyzed to provide the implant placement in atrophic maxilla with types III and IV bone, when implantation is complicated due to insufficient bone height (less than 10 mm), low bone density and rigidity, thin cortical core (thickness less or equal to 0.5 mm). In such challenging conditions, placement of cantilever crowns was proposed as an advanced approach. The recommendations for practitioners were formulated after thorough modeling of bone-implant interface with preliminary evaluation of stress fields in adjacent bone. Two (narrow and wide) implants of two lengths were studied (4.5×5.0 mm, 4.5×8.0 mm, 6.0×5.0 mm, 6.0×8.0 mm) as the supports for two teeth loss restoration. Also, a wide spectrum of human bone elasticity parameters was studied in order to generalize the results of the study to wide range of patients (patient-specific approach). Validation of FEA algorithms was provided to receive necessary accuracy of numerical analysis and support developed clinical recommendations. Based on the conducted research results, we draw the attention of implantologists to the fact that the load-bearing capacity of proposed cantilever crown which are supported by short plateau implants is predetermined by the adjacent bone strains because bone stresses in all studied restorative structures were less than the bone ultimate strength.

At present, the topic of traumatism of the maxillofacial region is topical and requires the search for contemporary biomechanical solutions. It is known that the problem of mandibular traumatism ranks first among all injuries of the maxillofacial region. Treatment of mechanically failured human mandible was considered as the example of its body fracture in accordance with European classification of maxillofacial trauma. This type of injury was chosen because of its widespread, statistically supported incidence. The treatment method was based on the use of osteosynthesis systems, widely used in the healthcare systems of Western European countries. The purpose of the study was in biomechanical support of existing clinical protocols for the osteosynthesis system elements application to ensure positive treatment prospects. Finite element analysis of acting deformations and displacements in the adjacent bone tissues was carried out for the case of reconstruction of the lower jaw damaged by an oblique fracture in its middle part (body) using two mini-plates in accordance with current clinical protocol. In our case, fracture was fixated with two 1.25 mm in thickness titanium mini-plates. Two types of mini-plates with lengths of 27 mm (long) and 20.5 mm (short) between the axes of the outer holes were analyzed. The results was revealed that osteosynthesis systems technology provides the conditions for the fixed mandible ridges healing under gentle functional loading due to safe micromotions which do not exceed 150 micrometer threshold of safe displacements (0.15 mm for long mini-plate 27×2.5×1.25 mm and 0.13 mm for short mini-plate 20.5×3.5×1.25mm). Also, the largest sliding distance in the fracture section are 0.11 mm for long mini-plate 27×2.5×1.25 mm and 0.06 mm for short mini-plate 27×2.5×1.25 mm. From this viewpoint, short mini-plate is recommended as preferable. However, care should be taken in transferring the results to the clinical situation. First of all, the wider range of possible bone fractures and their actual shapes with possible deviations from a flat contour should be taken into account. Also, more adequate simulation of the crack ridges interface should be provided to answer the question on micromotion data accuracy influencing the crack fixation and the success of the bone healing.

Background/Objectives: Dental implants have emerged as a modern solution for edentulous jaws, showing high success rates. However, the implant’s success often hinges on the patient’s bone quality and quantity, leading to higher failure rates in poor bone sites. To address this issue, short implants have become a viable alternative to traditional approaches like bone sinus lifting. Among these, Bicon^® short implants with a plateau design are popular for their increased surface area, offering potential advantages over threaded implants. Despite their promise, the variability in patient-specific bone quality remains a critical factor influencing implant success and bone turnover regulated by bone strains. Excessive strains can lead to bone loss and implant failure according to Frost’s “Mechanostat” theory. To better understand the implant biomechanical environment, numerical simulation (FEA) is invaluable for correlating implant and bone parameters with strain fields in adjacent bone. The goal was to establish key relationships between short implant geometry, bone quality and quantity, and strain levels in the adjacent bone of patient-dependent elasticity to mitigate the risk of implant failure by avoiding pathological strains. Methods: Nine Bicon Integra-CP™ implants were chosen. Using CT scans, three-dimensional models of the posterior maxilla were created in Solidworks 2022 software to represent the most challenging scenario with minimal available bone, and the implant models were positioned in the jaw with the implant apex supported by the sinus cortical bone. Outer dimensions of the maxilla segment models were determined based on a prior convergence test. Implants and abutments were considered as a single unit made of titanium alloy. The bone segments simulated types III/IV bone by different cancellous bone elasticities and by variable cortical bone elasticity moduli selected based on an experimental data range. Both implants and bone were treated as linearly elastic and isotropic materials. Boundary conditions were restraining the disto-mesial and cranial surfaces of the bone segments. The bone–implant assemblies were subjected to oblique loads, and the bone’s first principal strain fields were analyzed. Maximum strain values were compared with the “minimum effective strain pathological” threshold of 3000 microstrain to assess the implant prognosis. Results: Physiological strains ranging from 490 to 3000 microstrain were observed in the crestal cortical bone, with no excessive strains detected at the implant neck area across different implant dimensions and cortical bone elasticity. In cancellous bone, maximum strains were observed at the first fin tip and were influenced by the implant diameter and length, as well as bone quality and cortical bone elasticity. In the spectrum of modeled bone elasticity and implant dimensions, increasing implant diameter from 4.5 to 6.0 mm resulted in a reduction in maximum strains by 34% to 52%, depending on bone type and cortical bone elasticity. Similarly, increasing implant length from 5.0 to 8.0 mm led to a reduction in maximum strains by 15% to 37%. Additionally, a two-fold reduction in cancellous bone elasticity modulus (type IV vs. III) corresponded to an increase in maximum strains by 16% to 59%. Also, maximum strains increased by 86% to 129% due to a decrease in patient-dependent cortical bone elasticity from the softest to the most rigid bone. Conclusions: The findings have practical implications for dental practitioners planning short finned implants in the posterior maxilla. In cases where the quality of cortical bone is uncertain and bone height is insufficient, wider 6.0 mm diameter implants should be preferred to mitigate the risk of pathological strains. Further investigations of cortical bone architecture and elasticity in the posterior maxilla are recommended to develop comprehensive clinical recommendations considering bone volume and quality limitations. Such research can potentially enable the placement of narrower implants in cases of insufficient bone.

The stress state of a homogeneous isotropic layer under the action of a spatial static external load is studied. Two circular cylindrical supports are cut into the body of the layer parallel to its borders. The supports and body of the layer are rigidly coupled. The spatial problem theory of elasticity is solved using the analytical-numerical generalized Fourier method. The layer is considered in the Cartesian coordinate system, the supports are considered in the local cylindrical coordinates. Stresses are set on the upper and lower surfaces of the layer. The supports are considered as cylindrical cavities in a layer with zero displacements set on their surfaces. Satisfying the boundary conditions on the upper and lower surfaces of the layer, as well as on the cylindrical surfaces of the cavities, a system of infinite integro-algebraic equations, which are further reduced to linear algebraic ones, is obtained. An infinite system is solved by the reduction method. In the numerical studies, the parameters of integration oscillatory functions are analyzed, problems at different distances between supports are solved. A unit load in the form of a rapidly decreasing function is applied to the upper boundary between the supports. For these cases, an analysis of the stress state was performed on the surfaces of the layer between the supports and on the cylindrical surfaces in contact with the supports. The numerical analysis showed that when the distance between the supports increases, the stresses σx on the lower and upper surfaces of the layer and the stresses τρφ on the surfaces of the cavities increase. The use of the analytical-numerical method made it possible to obtain a result with an accuracy of 10-4 for stress values from 0 to 1 at the order of the system of equations m=6. As the order of the system increases, the accuracy of fulfilling the boundary conditions will increase. The presented analytical-numerical solution can be used for high-precision determination of the stress-strain state of the presented problems type, as well a reference for problems based on numerical methods