The use of frictional and bonded contact models in finite element analysis for internal fixation of tibia fracture

A BSTRACT . Tibia is one of the bones that often fracture, generally occurring due to a car accident, falling from high places, work accidents, and sports injuries. Internal fixation is one of the solutions to repair broken bones. In some cases, internal fixation also failed to carry out its function, so the healing process was disturbed and did not run according to the plan. Factors that might interfere with the process can be analyzed using FEM. The objective of this study is to study the effect of the contact model used to model the connection between broken bones of the tibia, to stress distribution that occurs on fixation plate for walking conditions. Analysis was carried out by using ANSYS software with fine-sized tetrahedrons mesh. Two contact models were used. Namely, friction and bonded. The load amount used is based on the average weight of Indonesian Adults, i.e. 63 kg. The results of the analysis show that, for the friction contact model, higher stress is found in the middle area plate, adjacent to the broken location on the bone. Different results are found in the bonded contact model, larger stress occurs in the upper-end area fixation plate.

INTRODUCTION he tibia is the medial bone of the lower leg that connects the knee to the ankle and has the function of forming the leg skeleton and supporting body weight [1]. In some cases, the tibia is often fractured, generally occurring due to a car accident, falling from high places, work accident, and sports injuries [2]. The main factors that cause fracture are the torsion and the bending moment [3]. Fractured is a medical condition in which the continuity of bone tissue is damaged, resulting in fracture and loss of bone integrity. Recovery of fractures in the tibia can be accomplished with internal fixation. Internal fixation is an orthopedic surgical procedure by placing implants in the form of plates and screws on the inside of the skin in the fracture area to stabilize the damaged bone tissue [4]. In some cases, internal fixation also failed to carry out its function, so the healing process was T disturbed and did not run according to the plan. Factors that might interface with the process can be analyzed using the Finite Element Method (FEM) [5]. Several studies have been performed related to Finite Element Analysis (FEA) on tibia fracture. Hiranda, Afif [6] has examined the effect of element size on the result of the von Mises stress distribution in tibial fracture simulations where the results show that fine mesh is better to be used. Besides the mesh, there are other factors that affect the simulation results. The type of contact used in the fracture may also affect the distribution of the von Mises stress that occurs in the simulated internal fixation of tibial fracture. The objective of this study is to study the effect of the contact model used on the connection between broken bones of the tibia, to stress distribution that occurs on the fixation plate. Although there are several types of materials that are often used for fracture implants, such as cobalt-chromium alloy [7,8] and titanium-based alloy [9,10,11], stainless steel 316 was employed in this research for plate and screw to avoid the issue of the formation of chromium carbide which causes intergranular corrosion of the implant [12]. The load used refers to the average weight of an Indonesian male adult, which is 63 kg with loading conditions during walking.

MATERIALS AND METHODS
nternal fixation for a tibial fracture is shown in Fig. 1. The figure shows the geometry and dimensions of the tibia, along with the position of the plate in the middle of the tibia. The Plate has a length of 103 mm with a thickness of 3.8 mm. The screw used has a head diameter of 8 mm and a length of 28 mm [13,14,15]. The detailed dimensions of the plate and screw can be seen in Fig. 2.  The type of material used for the plate and the screw is AISI 316 Stainless Steel. Stainless steel 316 is a material that is used because it can reduce the formation of chromium carbide which causes intergranular corrosion in implants [10][11][12]. The mechanical properties of stainless steel 316 are shown in Tab. 1. As for the tibia, the mechanical properties of the bone material used can be seen in Tab Table 2: Mechanical properties of the tibia [17].

BOUNDARY CONDITIONS
n this boundary condition setup (Fig. 3), the actual condition of the tibial fracture internal fixation model will be determined based on assumptions from various supporting literature. In this condition, the fixed support is still determined in section A and the load is given to sections M and L with the proportion of the load distribution being 60% in the medial (M) and 40% in the lateral (L) [18]. The load used in the simulation refers to the average weight of male Indonesian adults, which is 63 kg [19]. The mesh used is fine-sized tetrahedrons (Fig. 4), because this mesh is suitable for complex geometries [20]. The contact model condition between the plate and the tibia is frictional, and the contact model condition between the screw and the tibia is bonded. The coefficient of friction used in the frictional contact model is 0.2 [13,21]. Meanwhile, the contact model that occurs between bones in the fracture area is varied with two types, namely bonded and friction. Variations in the contact model were performed to see the effect of the contact model on the stress distribution on the internal fixation model for the tibia.

RESULTS AND DISCUSSION
he results of the analysis to see the stress distribution on the tibia internal fixation model during walking 1.4 seconds from two different contact models were carried out using ANSYS based on the element method. Fig. 6 presents the contours of the von Mises stress distribution on internal fixation for the frictional contact model. It was observed that the stress distribution was focused on the center of the plate, adjacent to the broken location on the bone. This is clarified by Fig. 7, wherein from 6 points of stress magnitude taken at each time for 1.4 seconds during walking, it is seen that point 3 and point 4 have a higher stress magnitude than the other points. Different results are found in the bonded contact model, Fig. 8. It can be seen that the stress distribution is focused on the upper end of the plate. This is then clarified in Fig. 9, it can be seen that point 1 has a higher stress magnitude than the other 5 points. In addition to P1, 0.8 seconds and 1.0 seconds also have a higher von Mises stress distribution at P3 and P4 than other times. When the walking condition was at a time of 0.8 seconds, the position of the leg with the internal fixation on the tibia becomes a support for the body-weight so that it receives a high force. The high force causes a high-stress distribution in the center of the plate (P3 and P4).   From the results of the analysis on the internal fixation of the tibia for two contact models, it was found that the use of the frictional contact model in the simulation of the Finite Element Analysis (FEA) is suitable for the geometry model of the tibia with fractured. The bonded contact model is suitable for the geometric model in which the tibia has completely healed, but the internal fixation has not been removed.

CONCLUSIONS
n this study, the contact model has an influence on the results of the finite element analysis as the hypothesis developed at the beginning of the study. Two different contact models, namely the frictional contact model and the bonded contact model, produce a different magnitude and distribution of von Mises stress on the plate used. The frictional contact model seems to be more suitable for initial plate placement conditions where the two fractured bones have not yet fused, while the bonded contact model is more suitable for fracture conditions where the bones have started to fuse. Furthermore, the influence of the screw mounting angle on the analysis results are not yet known so further studies still need to be carried out.