Microsoft Word - ETASR_V13_N4_pp11210-11215 Engineering, Technology & Applied Science Research Vol. 13, No. 4, 2023, 11210-11215 11210 www.etasr.com Pervan et al.: Mechanical Stability Analysis of the External Unilateral Fixation Device due to the … Mechanical Stability Analysis of the External Unilateral Fixation Device due to the Impact of Axial Pressure Nedim Pervan University of Sarajevo, Faculty of Mechanical Engineering, Bosnia and Herzegovina pervan@mef.unsa.ba (corresponding author) Elmedin Mesic University of Sarajevo, Faculty of Mechanical Engineering, Bosnia and Herzegovina mesic@mef.unsa.ba Adis Muminovic University of Sarajevo, Faculty of Mechanical Engineering, Bosnia and Herzegovina adis.muminovic@mef.unsa.ba Enis Muratovic University of Sarajevo, Faculty of Mechanical Engineering, Bosnia and Herzegovina muratovic@mef.unsa.ba Muamer Delic University of Sarajevo, Faculty of Mechanical Engineering, Bosnia and Herzegovina delic@mef.unsa.ba Vahidin Hadziabdic University of Sarajevo, Faculty of Mechanical Engineering, Bosnia and Herzegovina hadziabdic@mef.unsa.ba Lejla Redzepagic-Vrazalica University of Sarajevo, Faculty of Dentistry with Clinics, Bosnia and Herzegovina lejlaredzepagic@yahoo.com Received: 27 March 2023 | Accepted: 7 March 2023 Licensed under a CC-BY 4.0 license | Copyright (c) by the authors | DOI: https://doi.org/10.48084/etasr.5888 ABSTRACT This study performed a mechanical stability analysis for the impact of axial pressure on an Ultra X external unilateral fixation device applied to a tibia with an open fracture. The real construction of the fixation device was used to create a 3D geometric model using a Finite Element Method (FEM) model, which was made to perform structural analysis in the CATIA V5 (Computer Aided Three-dimensional Interactive Application) CAD/CAE system. Specific stresses and displacements were observed at points of interest using structural analysis. The focus was on the relative displacements of the proximal and distal bone segments in the fracture zone. These displacements were used to calculate the stiffnesses of the bone in the fracture zone and the fixation device itself. The results obtained provide the necessary information regarding the stability of the Ultra X fixation device. Keywords-external unilateral fixation device; specific stresses; relative displacements, stiffness; stability Engineering, Technology & Applied Science Research Vol. 13, No. 4, 2023, 11210-11215 11211 www.etasr.com Pervan et al.: Mechanical Stability Analysis of the External Unilateral Fixation Device due to the … I. INTRODUCTION During the recent years, there has been a considerable improvement in external fixation devices in terms of their construction variants, which have been experimentally investigated to provide information on their characteristics and advantages in terms of stability, stiffness, mechanical properties, and patient comfort during treatment. Using software for 3D modeling and FEM analysis to perform mechanical stability analysis is not a substitution for an experimental examination but is exclusively a tool for data comparison and validation. The experimental investigation of fixation devices is mainly based on biomechanical properties, along with the influence of specific parameters on the stability of the device [1]. The results of these investigations are reflected in certain values, such as von Mises stresses, displacements, angular strains, and fixation device stiffnesses, and most of these studies provide results of the application of the fixation device [2-3]. In recent years, the most popular treatment for tibia fracture is by using intermediary fasteners [4]. In [5], the application of an external fixation device and intermediary fasteners was considered in an open tibia fracture taking into account the treatment time and other possible complications, such as the size, severity, etc. In [6], the stiffness of the fixation device was defined concerning the location of the fracture and the number of fasteners and pins. In [7], an analysis of the stiffness of the Hoofman unilateral and uniplanar fixation device was presented along with its relation to the number of fasteners, trusses, and couplings. The stiffness of the device is determined by the loads that simulate normal walking conditions. In [8], a comparative study was conducted on two external fixation devices: the original Hoffmann and the AO tabular device with four different construction solutions. In [9], the mechanical properties of the external pinless fixation device were experimentally investigated, comparing its results with the AO tabular and Ultra X devices. This study concluded that the AO tabular devices are far superior in comparison with the other two solutions. In [10], the Ilizarov fixation device was investigated experimentally. Furthermore, many studies have analyzed the mechanical stability of structures [11-13]. This study aimed to investigate the mechanical properties of the Ultra X external unilateral fixation device, applied to the open- fracture tibia bone under the impact of axial pressure. The construction parameters taken into account were the stiffness of the device, the values of the maximum von Mises stresses, and the displacements in specific points. II. DEVELOPMENT OF THE CAD/FEM MODEL The adjustable fixation device should be light, stiff, easy to implement, etc. Such devices should be part of the first response at accident sites so that basic stabilization could be performed before transporting patients. Figure 1 shows the Howmedic Ultra X external fixation device, which is one of the first modular fixation devices, and was used in the first Gulf War in 1991. The components of the device are mostly made of metals, alloys, and plastics such as polymers and carbon fibers. The Ultra X fixation device has a truss made of austenitic stainless steel X2CrNiMo17-12-2, while couplings and small and large spheres are made of polymeric materials, attributed with smaller strength, Young's modulus, density, specific weight, and great forming properties. The upper and lower parts of the coupling and the fastening head are made of special polyvinyl chloride (PVC), which has high hardness and good mechanical properties. Small and large spheres are made of polybutylene (PB), which has properties similar to PVC because it can be manufactured with any method of thermoforming, and therefore, it gives a lot of creativity during the shape-forming process. Table I shows the mechanical properties of the unilateral Ultra X fixation device [14]. Fig. 1. The Ultra X fixation device. TABLE I. MECHANICAL PROPERTIES OF THE UNILATERAL ULTRA X FIXATION DEVICE Component name Standard abbreviations (EN) Modulus of elasticity E (GPa) Poisson's coefficient υ Density ρ (kg/m3) Yield strength σv (MPa) Truss X2CrNiMo17- 12-2 230 0.29 8000 620 Sphere >PB< 2.9 0.4 1290 - Coupling >PVC< 3.3 0.38 1380 0.2 Fastener X5CrNi18-10 193 0.29 7900 205 Half-pin X2CrNiMo18- 14-3 196.4 0.3 8000 800 The CAD/FEM model of the Ultra X device was developed using CATIA V5 software. Device components were defined and modeled in the part design environment and subsequently assembled in the assembly design environment. The General Structural Analysis module was used in the next step of model creation to complete the FEM model and define the material for each component. The material of the bone fragments was assumed to be orthotropic with properties defined according to Table II [15-16]. After the materials were defined, the next step in FEM processing was the discretization of the model and the definition of the finite element type. Linear (TE4) and parabolic (TE10) elements were used for the model. The TE4 elements were used for the spheres, while the rest of the components were discretized with the TE10 elements. After the discretization was complete, it was necessary to define the constraints between the components of the device. The constraints used were the following: fastened connections between half-pins and bone segments, as shown in Figure 2(a), and contact connections between other components, as shown in Figure 2(b). In addition to defining the necessary constraints, it was also mandatory to define supports, as shown in Figure 3. Engineering, Technology & Applied Science Research Vol. 13, No. 4, 2023, 11210-11215 11212 www.etasr.com Pervan et al.: Mechanical Stability Analysis of the External Unilateral Fixation Device due to the … TABLE II. BONE MODEL MECHANICAL PROPERTIES Property Value Longitudinal modulus of elasticity 22900 MPa Tangential modulus of elasticity 10500MPa Normal modulus of elasticity 14200 MPa Poisson's coefficeint in the XY plane 0.29 Poisson's coefficeint in the XZ plane 0.19 Poisson's coefficeint in the YZ plane 0.31 Shear modulus in the XY plane 6480 MPa Shear modulus in the XZ plane 6000 MPa Shear modulus in the YZ plane 3700 MPa Density 1850 kg/m 3 The last step in creating the FEM model was to define the axial load, which is applied as the surface load on the top surface of the upper bone segment. The upper bone segment is constrained so it can only move in the z-axis direction, i.e. the direction of the applied force. The lower bone segment is supported by a spherical joint (Ball Joint) through a virtual part (Smooth Virtual Part). The spherical joint allows rotation around a predefined point (Handle Node), and all translations are restricted, as shown in Figure 4. The axial load was set to 200 N, according to orthopedic recommendations and [17-18]. (a) (b) Fig. 2. Defining connection constraints: (a) fastened, (b) contact. Fig. 3. Fixation device model with constraints and supports. Fig. 4. Fixation device FEM model with the applied load. III. DETERMINATION OF STRESS, DISPLACEMENT, AND STIFFNESS During structural analysis, specific points were monitored to obtain values of principal and von Mises stresses generated on the fixation device. The intensity of the equivalent one-axis stress, i.e. von Mises stress, is often used in mechanics defined as [19-20]: �� = ��� = �3� = �� ��� − � � + �� − ��� + ��� − ��� � (1) Apart from stresses, displacement values at the same points were monitored so the stiffness of the device can be defined as the ratio of the load and displacements. The device stiffness under the impact of axial load can be defined as [19, 21]: �� = ���� (2) where Fp is the axial force (N), and δp is the axial displacement of the bone segments at the fracture zone (mm). The fixation device stiffness is an important parameter, but it doesn't give direct information about displacements at the fracture zone, so the fracture stiffness needs to be defined. This was achieved by determining displacements in the x, y, and z directions of the pair of adjacents points on the planes of the proximal and distal bone segments at the fracture zone. For these points, the resultant vector of relative displacement Rmax has the highest value. Accordingly, the total fracture stiffness is defined as the ratio of the load and the resultant relative displacement of the observed pair of points [22-23]: ��� = ��� = �� �������� !����"�� !����#�� (3) Engineering, Technology & Applied Science Research Vol. 13, No. 4, 2023, 11210-11215 11213 www.etasr.com Pervan et al.: Mechanical Stability Analysis of the External Unilateral Fixation Device due to the … The relative displacements rD(x), rD(y), rD(z) of the observed points are defined as [24-25]: $%�&� = '��&� − '(�&� $%�)� = '��)� − '(�)� (4) $%�*� = '��*� − '(�*� where rD(x), rD(y), and rD(z) are the relative displacements for the points of bone segments (mm), Dp(x), Dp(y), and Dp(z) are the displacements of the proximal bone segment (mm), and Dd(x), Dd(y), and Dd(z) are the displacements of the distal bone segment in x, y, and z directions (mm). IV. RESULTS Figure 5 shows the displacement vectors due to the maximum axial load, where the course, direction, and intensity of the vectors for the analyzed points can easily be noticed. Table III shows the components of the displacement vectors and the displacement values for the maximum axial load of 200 N. The stiffness of the construction is determined using (2), based on the axial displacement in the z-axis direction (straight surface at the top of the proximal bone), while the fracture stiffness requires displacements at the proximal and distal bone segments at the fracture zone in the x, y, and z directions. This is done by observing which pair of points will result in the highest displacements, as shown in Figure 5 (detail A). Fig. 5. Displacement vectors for the specific points under the impact of maximum axial load. TABLE III. DISPLACEMENT AND STIFFNESS VALUES Displacement of the proximal segment (mm) Displacement of the distal segment (mm) F r a c tu r e st if fn e ss ( N /m m ) C o n st r u c ti o n st if fn e ss ( N /m m ) Load zone Fracture zone Fracture zone x y z Dp(x) Dp(y) Dp(z) Dd(x) Dd(y) Dd(z) Cpp Cp 0 0 -4.54 3.593 0.616 -4.76 3.744 0.701 0.246 39.89 44.05 Figure 6 shows the von Mises distribution. Truss is an important component of the fixation device that needs to be considered in the structural analysis, which is loaded with eccentric pressure (simultaneous bending and pressure) for the truss amount σvM=318.62 MPa, which is also the global maximum. Fig. 6. Von Mises stress distribution. Due to axial pressure, the bone is bent around the y-axis. This induces the location of the maximum stress at the bone circumference, i.e. the location of the peripheral points with the x-axis, as shown in Figure 7. Fig. 7. Von Mises stress distribution for the fixation device truss. Engineering, Technology & Applied Science Research Vol. 13, No. 4, 2023, 11210-11215 11214 www.etasr.com Pervan et al.: Mechanical Stability Analysis of the External Unilateral Fixation Device due to the … The intensities and the direction of principal stresses were monitored for the 10 most critical zones of the device construction, as shown in Figure 8. Table IV summarizes the values of principal and von Mises stress for these points. Fig. 8. Principal stresses at the critical zones of the construction. TABLE IV. STRESS VALUES DUE TO AXIAL PRESSURE LOAD Observed point Principal stresses at critical points (MPa) Von Mises stresses at critical points (MPa) PM+ PM- PM+ PM- σ1 σ2 σ3 σ1 σ2 σ3 σνΜ σνΜ 1 198.0 -5.13 -14.4 -8.04 -11.2 -202 208.1 196.1 2 193.7 4.859 4.38 -3.35 -3.79 -175 191.1 174.8 3 203.4 11.83 7.18 -9.99 -14.2 -218 196.5 208.4 4 126.5 -6.46 -11.5 -3.22 -4.32 -185 135.6 183.7 5 205.6 10.64 7.23 -8.24 -13.8 -225 199.3 230.9 6 170.4 3.84 3.39 11.7 6.66 -145 169.2 145.5 7 218.8 13.95 9.70 -10.8 -12.3 -202 209.2 206.3 8 142.0 13.9 0.89 -3.02 -4.10 -163 147.2 162.5 9 315.4 1.07 2.20 0.42 -1.82 -322 318.8 317.3 10 302.9 1.41 0.51 6.36 5.89 -296 302.3 298.7 V. DISCUSSION The maximum displacement in the device construction due to the impact of the axial load is located at the end of the second Schanz fastener and is 6.06 mm, as shown in Figure 5. Maximum displacements for the fracture zone are located at the edges of the proximal and distal bone segments, the values of which are given in Table III. When comparing these results with those of [26-27], it can be noticed that the Ultra X external fixation device has significantly higher displacements (80- 100% higher) than the other such devices for the same case of applied load. Displacements in the load zone are used as a basis for the stiffness of the fixation device, which was 44.05 N/mm. If this value is compared with other studies [23-24], it can be observed that the stiffness of the Ultra X device is much lower (3-5 times) than that of other devices under the same load conditions. Similarly, displacements in the fracture zone are used to calculate the fracture stiffness, which is 39.89 N/mm and is again 3-5 times lower compared than the values found in [26-27]. The results of the structural analysis show that the most critical zone of the fixation device construction is the middle of the truss where it establishes contact with large spheres. This zone is a load transfer zone, where the axial force is transmitted from the couplings to the truss through the Schanz fasteners. The highest principal stresses, regarding the whole construction, were σ1=315.41 MPa (global maximum) for the positive values and σ3=-322.65 MPa (global minimum) for the negative values. Both extreme values are located in the truss, have similar values, and are in correspondence with the results obtained in other studies [26-27]. It is also important to note that stresses in the fixation device construction satisfy the maximum permissible stress of the device material. VI. CONCLUSION This study conducted a stability analysis on the Ultra X external fixation device due to the impact of axial loads, developing a FEM model. This model was used to observe the movements and displacements of the fracture and establish a connection between these phenomena with the stiffnesses of the fracture zone and the device itself. The analysis of the results obtained showed relatively large displacements compared to other studies for the same load conditions. This can be justified by the fact that a truss diameter of an Ultra X device has a smaller cross-section, i.e. moment of inertia. Lower displacement values could be expected for the hollow circle cross-sections of greater diameter, i.e. with an increased moment of inertia by moving away the material from the own axis of the element. This led to the conclusion that the mechanical stability of the Ultra X fixation device is insufficient for application to fractures of the lower extremities. However, the Ultra X device is recommended for traumas of the upper extremities due to its good properties, such as ease of implementation and small dimensions. 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