Computational modeling and uncertainty prediction of hyperelastic constitutive responses of damaged brain tissue under different temperature and strain rates.

The effect of strain rate and temperature on the hyperelastic material stress-strain characteristics of the damaged porcine brain tissue is evaluated in this present work. The desired constitutive responses are obtained using the commercially available finite element (FE) tool ABAQUS, utilizing 8-noded brick elements. The model's accuracy has been verified by comparing the results from the previously published literature. Further, the stress-strain behavior of the brain tissue is evaluated by varying the damages at various strain rates and temperatures (13, 20, 27, and 37°C) under compression test. Additionally, the sensitivity analysis of the model is computed to check the effect of input parameters, that is, the temperature, strain rate, and damages on the material properties (shear modulus). The modeling and discussion sections enumerate the inclusive features and model capabilities.

Evaluation of polymerization shrinkage stress and cuspal strain in natural and typodont teeth.

To evaluate the polymerization shrinkage stress and cuspal strain (CS) generated in an artificial (typodont) and in a natural tooth using different resin composites. Twenty artificial and 20 extracted natural molars were selected. Each tooth was prepared with a 4x4 mm MOD cavity. The natural and typodont teeth were divided into four experimental groups (n=10), according to the resin composite used: Filtek Z100 (3M Oral Care) and Beautifil II LS (Shofu Dental). The cavities were filled using two horizontal increments and the CS (µS) was measured by the strain gauge method. Samples were sectioned into stick-shaped specimens and the bond strength (BS) (MPa) was evaluated using a microtensile BS test. Shrinkage stress and CS were analyzed using 3D finite element analysis. No difference was found between the type of teeth for the CS as shown by the pooled averages: Natural tooth: 541.2 A; Typodont model: 591.4 A. Filtek Z100 CS values were higher than those obtained for Beautifil II LS, regardless of the type of teeth. No statistical difference was found for the BS data. Adhesive failures were more prevalent (79.9%). High shrinkage stress values were observed for Filtek Z100 resin, regardless of tooth type. The CS of typodont teeth showed a shrinkage stress effect, generated during restoration, equivalent to that of natural teeth.

Finite element modeling of stress distribution and safety factors in a Ti-27Nb alloy hip implant under real-world physiological loading scenarios.

Total hip arthroplasty (THA) is one of the most successful orthopaedic interventions globally, with over 450,000 procedures annually in the U.S. alone. However, issues like aseptic loosening, dislocation, infection and stress shielding persist, necessitating complex, costly revision surgeries. This highlights the need for continued biomaterials innovation to enhance primary implant integrity and longevity. Implant materials play a pivotal role in determining long-term outcomes, with titanium alloys being the prominent choice. However, emerging evidence indicates scope for optimized materials. The nickel-free ß titanium alloy Ti-27Nb shows promise with excellent biocompatibility and mechanical properties. Using finite element analysis (FEA), this study investigated the biomechanical performance and safety factors of a hip bone implant made of nickel-free titanium alloy (Ti-27Nb) under actual loading during routine day life activities for different body weights. The FEA modelled physiological loads during walking, jogging, stair ascent/descent, knee bend, standing up, sitting down and cycling for 75 kg and 100 kg body weights. Comparative analyses were conducted between untreated versus 816-hour simulated body fluid (SBF) treated implant conditions to determine in vivo degradation effects. The FEA predicted elevated von Mises stresses in the implant neck for all activities, especially stair climbing, due to its smaller cross-section. Stresses increased substantially with a higher 100 kg body weight compared to 75 kg, implying risks for heavier patients. Safety factors were reduced by up to 58% between body weights, although remaining above the desired minimum value of 1. Negligible variations were observed between untreated and SBF-treated responses, attributed to Ti-27Nb's excellent biocorrosion resistance. This comprehensive FEA provided clinically relevant insights into the biomechanical behaviour and integrity of the Ti-27Nb hip implant under complex loading scenarios. The results can guide shape and material optimization to improve robustness against repetitive stresses over long-term use. Identifying damage accumulation and failure risks is crucial for hip implants encountering real-world variable conditions. The negligible SBF effects validate Ti-27Nb's resistance to physiological degradation. Overall, the study significantly advances understanding of Ti-27Nb's suitability for reliable, durable hip arthroplasties with low revision rates.

Bone healing under different lay-up configuration of carbon fiber-reinforced PEEK composite plates.

Secondary healing of fractured bones requires an application of an appropriate fixator. In general, steel or titanium devices are used mostly. However, in recent years, composite structures arise as an attractive alternative due to high strength to weight ratio and other advantages like, for example, radiolucency. According to Food and Drug Administration (FDA), the only unidirectionally reinforced composite allowed to be implanted in human bodies is carbon fiber (CF)-reinforced poly-ether-ether-ketone (PEEK). In this work, the healing process of long bone assembled with CF/PEEK plates with cross- and angle-ply lay-up configurations is studied in the framework of finite element method. The healing is simulated by making use of the mechanoregulation model basing on the Prendergast theory. Cells transformation is determined by the octahedral shear strain and interstitial fluid velocity. The process runs iteratively assuming single load cycle each day. The fracture is subjected to axial and transverse forces. In the computations, the Abaqus program is used. It is shown that the angle-ply lamination scheme of CF/PEEK composite seems to provide better conditions for the transformation of the soft callus into the bone tissue.

Visco-hyperelastic material model fitting to experimental stress-strain curves using a genetic algorithm and its application to soft tissue simulants.

Ballistic impacts on human thorax without penetration can produce severe injuries or even death of the carrier. Soft tissue finite element models must capture the non-linear elasticity and strain-rate dependence to accurately estimate the dynamic human mechanical response. The objective of this work is the calibration of a visco-hyperelastic model for soft tissue simulants. Material model parameters have been calculated by fitting experimental stress-strain relations obtained from the literature using genetic algorithms. Several parametric analyses have been carried out during the definition of the optimization algorithm. In this way, we were able to study different optimization strategies to improve the convergence and accuracy of the final result. Finally, the genetic algorithm has been applied to calibrate two different soft tissue simulants: ballistic gelatin and styrene-ethylene-butylene-styrene. The algorithm is able to calculate the constants for visco-hyperelastic constitutive equations with high accuracy. Regarding synthetic stress-strain curves, a short computational time has been shown when using the semi-free strategy, leading to high precision results in stress-strain curves. The algorithm developed in this work, whose code is included as supplementary material for the reader use, can be applied to calibrate visco-hyperelastic parameters from stress-strain relations under different strain rates. The semi-free relaxation time strategy has shown to obtain more accurate results and shorter convergence times than the other strategies studied. It has been also shown that the understanding of the constitutive models and the complexity of the stress-strain objective curves is crucial for the accuracy of the method.

Influence of prosthetic index structures and implant materials on stress distribution in implant restorations: a three-dimensional finite element analysis.

BACKGROUND: Mechanical complications affect the stability of implant restorations and are a key concern for clinicians, especially with the frequent introduction of new implant designs featuring various structures and materials. This study evaluated the effect of different prosthetic index structure types and implant materials on the stress distribution of implant restorations using both in silico and in vitro methods. METHODS: Four finite element analysis (FEA) models of implant restorations were created, incorporating two prosthetic index structures (cross-fit (CF) and torc-fit (TF)) and two implant materials (titanium and titanium-zirconium). A static load was applied to each group. An in vitro study using digital image correlation (DIC) with a research scenario identical to that of the FEA was conducted for validation. The primary strain, sensitivity index, and equivalent von Mises stress were used to evaluate the outcomes. RESULTS: Changing the implant material from titanium to titanium-zirconium did not significantly affect the stress distribution or maximum stress value of other components, except for the implant itself. In the CF group, implants with a lower elastic modulus increased the stress on the screw. The TF group showed better stress distribution on the abutment and a lower stress value on the screw. The TF group demonstrated similar sensitivity for all components. DIC analysis revealed significant differences between TF-TiZr and CF-Ti in terms of the maximum (P < 0.001) and minimum principal strains (P < 0.05) on the implants and the minimum principal strains on the investment materials in both groups (P < 0.001). CONCLUSIONS: Changes in the implant material significantly affected the maximum stress of the implant. The TF group exhibited better structural integrity and reliability.

[Study on fatigue resistance of mechanical nickel-titanium files by phase-locked infrared flaw detection method].

PURPOSE: The movement trend of the posterior teeth and the distribution of the periodontal membrane stress were studied by using three-dimensional digital technology. METHODS: CBCT data of 88 patients admitted to our hospital from June 2017 to June 2022 were selected, and input into Mimics20.0 software for preliminary extraction of all parts and stored with STL files; then the data were repaired and optimized through Geomagic Studio 2014 software. With the help of normal phase extension, the invisible appliance and periodontal membrane were constructed. Finally, the six FEM models were simulated and observed by the current teeth in different groups. Statistical analysis was performed with SPSS 21.0 software package. RESULTS: The effect force of the largest periodontal membrane was distributed in the neck of the tooth, followed by the apical area, with the maximum effect force value in the NA group. In all accessory groups, the periodontal membrane maximum paradigm isoeffect force values of all patients in the accessory vertical rectangular group were significantly smaller than the values obtained in the horizontal rectangular group. CONCLUSIONS: The design of orthodontic tooth accessories has a strong inhibition effect on the position movement of anterior teeth during recovery, which improves the accuracy of tooth three-dimensional movement to a certain extent. Meanwhile, the normal equivalent stress of the periodontal membrane of patients in the initial application of the invisible appliance without brackets is large.

Study on rock fracture mechanism and hydraulic fracturing propagation law of heterogeneous tight sandstone reservoir.

Hydraulic fracturing technology is an effective way to develop tight sandstone reservoirs with low porosity and permeability. The tight sandstone reservoir is heterogeneous and the heterogeneity characteristics has an important influence on fracture propagation. To investigate hydraulic fracture performance in heterogeneous tight reservoir, the X-ray diffraction experiments are carried out, the Weibull distribution method and finite element method are applied to establish the uniaxial compression model and the hydraulic fracture propagation model of heterogeneous tight sandstone. Meanwhile, the sensitivity of different heterogeneity characterization factors and the multi-fracture propagation mechanism during hydraulic fracture propagation is analyzed. The results indicate that the pressure transfer in the heterogeneous reservoir is non-uniform, showing a multi-point initiation fracture mode. For different heterogeneity characterization factors, the heterogeneity characteristics based on elastic modulus are the most sensitive. The multi-fracture propagation of heterogeneous tight sandstone reservoir is different from that of homogeneous reservoir, the fracture propagation morphology is more complex. With the increase of stress difference, the fracture propagation length increases. With the increase of injection rate, the fracture propagation length increases. With the increase of cluster spacing, the propagation length of multiple fractures tends to propagate evenly. This study clarifies the influence of heterogeneity on fracture propagation and provides some guidance for fracturing optimization of tight sandstone reservoirs.

Influence of the biomechanical evaluation of rupture using two shapes of same intramedullary implant after proximal interphalangeal joint arthrodesis to correct the claw/hammer pathology: A finite element study.

We used finite element analysis to study the mechanical stress distribution of a new intramedullary implant used for proximal interphalangeal joint (PIPJ) arthrodesis (PIPJA) to surgically correct the claw-hammer toe deformity that affects 20% of the population. After geometric reconstruction of the foot skeleton from claw toe images of a 36-year-old male patient, two implants were positioned, in the virtual model, one neutral implant (NI) and another one 10° angled (10°AI) within the PIPJ of the second through fourth HT during the toe-off phase of gait and results were compared to those derived for the non-surgical foot (NSF). A PIPJA was performed on the second toe using a NI reduced tensile stress at the proximal phalanx (PP) (45.83 MPa) compared to the NSF (59.44 MPa; p < 0.001). When using the 10°AI, the tensile stress was much higher at PP and middle phalanges (MP) of the same toe, measuring 147.58 and 160.58 MPa, respectively, versus 59.44 and 74.95 MPa at corresponding joints in the NSF (all p < 0.001). Similar results were found for compressive stresses. The NI reduced compressive stress at the second PP (-65.12 MPa) compared to the NSF (-113.23 MPa) and the 10°AI (-142 MPa) (all p < 0.001). The von Mises stresses within the implant were also significantly lower when using NI versus 10°AI (p < 0.001). Therefore, we do not recommend performing a PIPJA using the 10°AI due to the increase in stress concentration primarily at the second PP and MP, which could promote implant breakage.

A forecasting model for suitable dental implantation in canine mandibular premolar region based on finite element analysis.

In recent years, dental implants have become a trend in the treatment of human patients with missing teeth, which may also be an acceptable method for companion animal dentistry. However, there is a gap challenge in determining appropriate implant sizes for different dog breeds and human. In this study, we utilized skull computed tomography data to create three-dimensional models of the mandibles of dogs in different sizes. Subsequently, implants of various sizes were designed and subjected to biomechanical finite element analysis to determine the optimal implant size. Regression models were developed, exploring the relationship between the average weight of dogs and the size of premolar implants. Our results illustrated that the regression equations for mean body weight (x, kg) and second premolar (PM2), third premolar (PM3), and fourth premolar (PM4) implant length (y, mm) in dogs were: y = 0.2785x + 7.8209, y = 0.2544x + 8.9285, and y = 0.2668x + 10.652, respectively; the premolar implant diameter (mm) y = 0.0454x + 3.3506, which may provide a reference for determine suitable clinical implant sizes for dogs.

Curving expectations: The minimal impact of structural curvature in biological puncture mechanics.

Living organisms have evolved various biological puncture tools, such as fangs, stingers, and claws, for prey capture, defense, and other critical biological functions. These tools exhibit diverse morphologies, including a wide range of structural curvatures, from straight cactus spines to crescent-shaped talons found in raptors. While the influence of such curvature on the strength of the tool has been explored, its biomechanical role in puncture performance remains untested. Here, we investigate the effect of curvature on puncture mechanics by integrating experiments with finite element simulations. Our findings reveal that within a wide biologically relevant range, structural curvature has a minimal impact on key metrics of damage initiation or the energies required for deep penetration in isotropic and homogeneous target materials. This unexpected result improves our understanding of the biomechanical pressures driving the morphological diversity of curved puncture tools and provides fundamental insights into the crucial roles of curvature in the biomechanical functions of living puncture systems.

Multi-physical field simulation calculation and analysis of simulated high-level waste liquid spray calcination.

Aiming at the independent research and development of a simulated high-level waste liquid spray calcination transformation treatment test device, a three-dimensional multi-physical field model of spray calcination was established by means of finite element analysis method. In this paper, the simulated high-level waste liquid is a mixed solution of nitrate solution and sucrose. The main chemical components of nitrate dissolution are HNO3 and NaNO3. The process of evaporation and calcination of high-level waste liquid to form oxides is also called the pretreatment of high-level waste liquid or the conversion of high-level waste liquid. In this experiment, the atomized droplets sprayed at high speed are evaporated, dried and calcined in turn in the calciner to obtain the calcined product. The distribution law of temperature flow field and chemical reaction state and results inside the test device were revealed by simulation calculation. The results show that under the condition of multi-physical field coupling, the chemical reaction temperature has an effect on the yield of the product. The temperature is positively correlated with the product concentration, and the effect of temperature on the yield of NO2 is greater than that of Na2O. At the same time, in this chemical reaction, the concentration of reactants (NaNO3 and HNO3) had a positive correlation with the concentration of main products (NO2 and Na2O). However, the rate of increase in the concentration of the main products (NO2 and Na2O) decreased with the increase of the concentration of the reactants (NaNO3 and HNO3).

Cryosurgery process applications - a mathematical review.

The present study reviews some of the prominent mathematical models that are used to simulate the cryosurgery treatment of tumor tissues, i.e., destruction of tumor tissues via controlled freezing with cryoprobes with minimizing the impact on surrounding healthy tissues. Numerical simulation of the appropriate mathematical models that reflect practical situations may help the physicians to design a planning framework for the treatment, which includes total number of cryoprobes to be used, their placement design and the duration of optimal freezing, etc. Finite element method, meshfree method, and finite volume method are some of the suitable numerical techniques for simulating bio-heat transfer process within complex tissues during treatment. Doi.org/10.54680/fr24510110112.

Assessment by finite element analysis modelling of tissue strains associated with the use of two different nasogastric tube securement devices.

OBJECTIVES: Nasogastric tube use can lead to pressure injury. Some nasogastric tube securement devices (NG-SD) include hard plastic components. In the current study, we assessed the differences in strain profiles for two NG-SD, one with hard segments and one without hard segments, using finite element analysis (FEA) to measure strain and deformation occurring at the nasogastric tube-tissue interface. METHODS: FEA in silico models of devices were based on device mechanical test data and clinically relevant placements. Peak strain values were determined by modelling different scenarios using Abaqus software whereby the tubing is moved during wear. RESULTS: The modelling showed peak strains ranging from 52% to 434% for the two NG-SD depending on the tubing placement and device type. Peak strain was always higher for the hard plastic device. Tissue strain energy was a minimum of 133.8 mJ for the NG-SD with no hard parts and a maximum of 311.6 mJ for the NG-SD with hard parts. CONCLUSIONS: This study provided evidence through in silico modelling that NG-SD without hard components may impart less strain and stress to tissues which may provide an option for tube securement that is less likely to cause medical device-related pressure injury.

Biomechanical comparison of an intramedullary nail combined with a reconstruction plate combination versus a single intramedullary nail in unstable intertrochanteric fractures with lateral femoral wall fracture: A finite element analysis.

This study aimed to compare the biomechanical performance of an intramedullary nail combined with a reconstruction plate and a single intramedullary nail in the treatment of unstable intertrochanteric femoral fractures with a fracture of the lateral femoral wall (LFW). A three-dimensional finite element (FE) femur model was established from computed tomography images of a healthy male volunteer. A major reverse obliquity fracture line, associated with a lesser trochanteric fragment defect and a free bone fragment of the LFW, was developed to create an AO/OTA type 31-A3.3 unstable intertrochanteric fracture mode. Two fixation styles were simulated: a long InterTAN nail (ITN) with or without a reconstruction plate (RP). A vertical load of 2100 N was applied to the femoral head to simulate normal walking. The construct stiffness, von Mises stress, and model displacement were assessed. The ITN with RP fixation (ITN/RP) provided higher axial stiffness (804 N/mm) than the ITN construct (621 N/mm). The construct stiffness of ITN/RP fixation was 29% higher than that of ITN fixation. The peak von Mises stress of the implants in the ITN/RP and ITN models was 994.46 MPa and 1235.24 MPa, respectively. The peak stress of the implants in the ITN/RP model decreased by 24% compared to that of the ITN model. The peak von Mises stress of the femur in the ITN/RP model was 269.06 MPa, which was lower than that of the ITN model (331.37 MPa). The peak stress of the femur in the ITN/RP model was 23% lower than that of the ITN model. The maximum displacements of the ITN/RP and ITN models were 12.12 mm and 13.53 mm, respectively. The maximum displacement of the ITN/RP model decreased by 12% compared with that of the ITN model. The study suggested that an additional plate fixation could increase the construct stiffness, reduce the stresses in the implant and femur, and decrease displacement after intramedullary nailing. Therefore, the intramedullary nail and reconstruction plate combination may provide biomechanical advantages over the single intramedullary nail in unstable intertrochanteric fractures with a fractured LFW.

A multiscale modeling to determine in vitro mechanical responses of different cells at the cell-substrate interface under fluid perfusion.

Investigating the influence of different cellular mechanical and physical properties on cells in vitro is important for assessing cellular activities like differentiation, proliferation, and migration. Evaluating the mechanical response of the cells lodged on a scaffold due to variations in substrate roughness, substrate elasticity, fluid flow, and the shapes of the cells is the main goal of the study. In this comprehensive analysis, a combination of the fluid structure interaction method and the submodeled finite element technique was employed to anticipate the mechanical responses across various cells at the interface between cells and the substrate. Fluid inlet velocity, substrate roughness, and substrate material were varied in this analysis. Different cell shapes were considered along with various components such as cell membrane, cytoplasm, nucleus, and cytoskeletons. This analysis shows the effect of these individual parameters on the elastic strain and strain energy density of cells at the cell-substrate interface. The results highlight that substrate roughness has a more significant impact on the mechanical response of cells at the interface than substrate elasticity. However, effect of the substrate elasticity becomes crucial for extremely soft substrate materials. The results of this research can be applied to identify the optimal parameters for fluid flow and create a suitable condition for cell culture.

Micro-osteoperforation for enhancement of orthodontic movement: A mechanical analysis using the finite element method.

BACKGROUND: Micro-osteoperforation is a minimally invasive technique aimed at accelerating tooth movement. The goal of this novel experimental study was to assess tooth movement and stress distribution produced by the force of orthodontic movement on the tooth structure, periodontal ligament, and maxillary bone structure, with and without micro-osteoperforation, using the finite element method. MATERIALS AND METHODS: Cone-beam computed tomography was used to obtain a virtual model of the maxilla and simulate the extraction of right and left first premolars. Three micro-osteoperforations (1.5 x 5 mm) were made in the hemiarch on the distal and mesial surfaces of upper canines, according to the power tip geometry of the Propel device (Propel Orthodontics, Ossining, New York, USA). An isotropic model of the maxilla was fabricated according to the finite element method by insertion of mechanical properties of the tooth structures, with orthodontic force (1.5 N) simulation in the distal movement on the upper canine of a hemiarch. RESULTS: Initial movement was larger when micro-osteoperforations were performed on the dental crown (24%) and on the periodontal ligament (29%). In addition, stress distribution was higher on the bone structure (31%) when micro-osteoperforations were used. CONCLUSIONS: Micro-osteoperforations considerably increased the movement of both the dental crown and periodontal ligament, which highlights their importance in the improvement of orthodontic movement, as well as in stress distribution across the bone structure. Important stress absorption regions were identified within micro-osteoperforations.

Motion reconstruction and finite element analysis of the temporomandibular joint during swallowing in healthy adults.

There is a close physiological connection between swallowing and the temporomandibular joint (TMJ). However, a shortage of quantitative research on the biomechanical behavior of the TMJ during swallowing exists. The purpose of this study was to reconstruct the movement of the temporomandibular joint (TMJ) based on in vivo experiment and analyze the biomechanical responses during swallowing in healthy adults to investigate the role of the TMJ in swallowing. Motion capture of swallowing, computed tomography (CT), and magnet resonance images (MRI) were performed on six healthy subjects. The movements of the TMJ during swallowing were reconstructed from the motion capture data. The three-dimensional finite element model was constructed. The dynamic finite element analysis of the swallowing process was performed based on the motion data. The range of condylar displacement was within 1 mm in all subjects. The left and right condyle movements were asymmetrical in two-thirds of the subjects. The peak stresses of the discs were relatively low, with a maximum of 0.11 MPa. During swallowing, the condylar displacement showed two trends: slow retraction and slow extension. The tendency to extend could lead to a gradual increase in stress on the disc.

Finite element analysis of fixation stability according to reduction position for internal fixation of intertrochanteric fractures.

In recent years, finite element analysis (FEA) has been instrumental in comparing the biomechanical stability of various implants for femur fracture treatment and in studying the advantages and disadvantages of different surgical techniques. This analysis has proven helpful for enhancing clinical treatment outcomes. Therefore, this study aimed to numerically analyze fixed stability according to location using FEA. In this study, a virtual finite element model was created based on a clinically anatomically reduced patient. It incorporated positive and negative support derived from intramedullary and extramedullary reduction from the anteroposterior (AP) view and neutral support from the lateral view. The generated model was analyzed to understand the biomechanical behavior occurring in each region under applied physiological loads. The simulation results of this study showed that the average von Mises stress (AVMS) of the nail when performing intramedullary reduction for femoral fixation was 187% of the anatomical reduction and 171% of the extramedullary reduction, and individually up to 2.5 times higher. In other words, intramedullary reduction had a very high possibility of fixation failure compared to other reduction methods. This risk is amplified significantly, especially in situations where bone strength is compromised due to factors such as old age or osteoporosis, which substantially affects the stability of fixation. Extramedullary reduction, when appropriately positioned, demonstrates greater stability than anatomical reduction. It exhibits stable fixation even in scenarios with diminished bone strength. In instances in which the bone density was low in the support position, as observed in the lateral view, the AVMS on the nail appeared to be relatively low, particularly in cases of positive support. Additionally, the femur experienced lower equivalent stress only in the extramedullary reduction-negative position. Moreover, by comparing different reduction methods and bone stiffness values using the same femoral shape, this study offers insights into the selection of appropriate reduction methods. These insights could significantly inform decision making regarding surgical strategies for intertrochanteric fractures.

Evaluation of the effect of different attachment configurations on molar teeth in maxillary expansion with clear aligners - a finite element analysis.

OBJECTIVE: To evaluate the effects of different attachment configurations with and without buccal root torque on expansion movements achieved with aligners through finite element analysis (FEA). METHODS: FEA modelling was done with 0.25 mm buccal expansion force application to the maxillary molars with different attachment configurations: Eight models were tested (1) no attachment (NA), (2) horizontal attachment (HA), (3) gingivally beveled horizontal attachment (GHA), and (4) occlusally beveled horizontal attachment (OHA), as well as models with 6obuccal root torque, (5) no attachment (TNA), (6) horizontal attachment (THA), (7) gingivally beveled horizontal attachment (TGHA), and (8) occlusally beveled horizontal attachment (TOHA). RESULTS: The first and second molars exhibited buccal tipping in all models. The highest amount of buccal tipping for the molars was observed in the NA (6CMB, 0.232 mm; 6CMP, 0.246 mm; 7CMB, 0.281 mm; 7CMP, 0.312 mm) and GHA (6CMB, 0.230; 6CMP, 0.245; 7CMB, 0.279 mm; 7CMP, 0.311 mm) models, respectively, while the least tipping was observed in the TOHA model (6CMB, 0.155 mm; 6CMP, 0.168 mm; 7CMB, 0.216 mm; 7CMP, 0.240 mm). In all groups, the buccal tipping of the second molars was higher than that of the first molars. CONCLUSION: This FEA study showed that expansion with aligners tip maxillary molars buccally and the use of occlusally beveled attachments and addition of buccal root torque reduces uncontrolled buccal tipping.