Summer Workshop of Applied Mechanics. Theoretical Analysis of Total Hip Joint Replacement of Sandwich design by FEM

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1 Summer Workshop of Applied Mechanics June 2002 Department of Mechanics Faculty of Mechanical Engineering Czech Technical University in Prague Theoretical Analysis of Total Hip Joint Replacement of Sandwich design by FEM Tomáš Goldmann, Svatava Konvičková 1 Laboratory of Biomechanics of Man Department of Mechanics Czech Technical University in Prague Prague, CZECH REPUBLIC goldmann@biomed.fsid.cvut.cz Keywords: total hip replacement, elliptical sandwich design of total hip replacement, FEM, stress distribution, non linear contact problem, contact pressures 1 Introduction The aim of this study was to solve the problem of total hip replacement of sandwich elliptical construction in view of biomechanics, strength and tightness. The similar problem was solved in the past. In the past there were enlarged two versions of CAD model; three dimensional one and axially symmetric one. There were also assigned boundary conditions and material characteristic of particular components of the total replacement. Created CAD models were meshed by finite elements mesh and there were realised finite elements solution of contact pressures, stress analysis, tribological analysis and fatigue strength analysis. This present paper deals with total hip joint replacement of sandwich construction with elliptical acetabular part. The advantage of this elliptical shape is a better allocation of the hip joint into the acetabular bone during medical surgery. The mathematical model of described hip joint replacement should be assembled in this project, there should be also assessed its boundary conditions and there should be computed static strength and tightness analysis by the Finite Element Method. There is also very important to know stress distribution in bones, which circumfuse round the joint replacement, stress distribution in separate components of hip joint and contact pressures among them. 32

2 Theoretical Analysis of Total Hip Joint Replacement of Sandwich design by FEM 2 Materials and Methods The femoral part of total hip replacement consists of the femoral steel shaft and the femoral capitulum, which is made of Al 2 O 3. The acetabular fossa consists of own fossa which is made of UHMWPE and titanium capsule (Ti6Al4V). This sandwich construction of acetabular fossa improves fortunate material properties of particular layers. The sliding couple Al 2 O 3 capitulum - UHMWPE fossa brings into construction advantageous tribological properties. The Al 2 O 3 capitulum delivers also hardness and high abrasion resistance into arthral surface. The disadvantage of Al 2 O 3 is a poor absorption of shock action and it is eliminated by the UHMWPE fossa. The titanium capsule provides plasticity into the construction. There is limited UHMWPE abrasion by this way. The next function of titanium capsule is better stress distribution on the boundary surface hip replacement - acetabular bone. The cutout of acetabular bone is also a part of the FEM model. The material properties and technical documentation of all components of total hip joint was provided by WALTER a.s. and material properties are shown in the le below. Component Materiál ISO Young s Modulus E MPa] Poisson s Ratio Femoral FeNiCr ISO 2,1E5 0,3 Shaft Steel 5832/1 Femoral Capitulum Al 2 O 3 ISO ,8E5 0,26 Acetabular Fossa UHMWPE ISO 5832/4 3,4E4 0,35 Titanium Ti6Al4V ISO 1,13E5 0,342 Capsule 5832/3 Acetabuar bone Spongy Bone 1,4E4 0,36 Table 2: Material Properties of Components of Total Hip Joint The friction ratio between particular contact components of total hip joint is here also defined, which is shown in the le below. This research problem was solved by the Finite Element Method. The structured inputs into the computational modelling are geometry, material properties, loads and boundary conditions. These specifications were assigned by Walter a.s. The computerized inputs are represented by finite element mesh, used types of finite elements and boundary conditions. The outputs of solution are strength, stress and contact pressure distribution. 33

3 Theoretical Analysis of Total Hip Joint Replacement of Sandwich design by FEM First Part of Contact Second Part of Contact Friction Couple Contact Couple Type Ratio Femoral Shaft Femoral Capituluding Small Sli- 0,11 Femoral Capitulum Acetabular Fossa Small Sliding 0,08 Acetabular Fossa Titanium Capsulding Small Sli- 0,2 Titanium Capsule Acetabuar bone Tied - Table 4: Friction s Ratio between Particular Contact Component For the geometrical modelling and the finite element mesh were used FEM system ANSYS 5.5. This model was converted by converting program into FEM system ABAQUS 5.8. where the problem was also solved and results were carried out. The FEM model has three dimensional character. The problem was solved at four cpu s computer ORIGIN The following figures display CAD model and finite element mesh of researched total hip joint. This research problem has non-linear character. Non-linearity is caused by contact interactions among the separated components. In respect of geometrical demanding and relatively high count of contact pairs there should be expected extensive difficulty during computing (large cpu s time). The model of total hip replacement was partly simplified. There are not considered fixating screws between titanium capsule and acetabular bone and there is modelled contact type TIED with high friction ratio. In respect of difficulty of problem there are not also considered soft tissues, which circumfuse round total replacement, but there are considered bones, which circumfused round this replacement. 3 Results This research problem was successfully solved by system ABAQUS. There was achieved stress analysis. The results of stress analysis were carried out as distribution of von Mises stresses and contact pressures along each component. These values were evaluated and none of these values have exceeded safe figures. Following figure shows examples of the von Mises stress distribution. The tribological analysis was also accomplished in this project. This analysis was computed on rotary symmetric model. There was detected dependency of contact pressures between femoral capitulum and acetabular fossa on different values of friction ratio. 34

4 Theoretical Analysis of Total Hip Joint Replacement of Sandwich design by FEM Figure 1: CAD Model of Total Hip Joint Figure 2: Finite Element Mesh and Boundary conditions of Elliptical Total Hip Joint 35

5 Theoretical Analysis of Total Hip Joint Replacement of Sandwich design by FEM Figure 3: Example of Distribution of von Mises Stress of Femoral Shaft Figure 4: Example of Distribution of von Mises Stress of Femoral Capitulum 36

6 Theoretical Analysis of Total Hip Joint Replacement of Sandwich design by FEM Figure 5: Examples of Distribution of von Mises Stress of Acetabular Fossa Figure 6: Examples of Distribution of von Mises Stress of Titanium Capsule 37

7 Theoretical Analysis of Total Hip Joint Replacement of Sandwich design by FEM Figure 7: Examples of Distribution of von Mises Stress of Acetabular Bone Cut-out 4 Conclusion The assignment of this research work was the theoretical analysis of the total hip replacement with elliptical design of acetabullar fossa in view of biomechanics, tribology and fatigue strength and tightness. The drawing documentation, properties of materials and other input data were offered by Walter a.s. The problem has been solved by finite element method. The geometrical and mathematical model have been created in system ANSYS and solved by system ABAQUS. There were propounded two models in respect of rotary symmetric character of total replacement. The symetric one and three dimensional one. Solution of symetric model is designed to compute a tribological analysis and as a gross conception of distribution of stresses and contact presures. Both models have been successfully solved and tribological analysis has been also carried out. The problem of fatigue strength analysis has not been successfully solved since now and it is now in progress. There is also next problem, which should be researched in the future and it is biomechanics of soft tissues in the surrounding of the hip joint replacement. 38

8 Theoretical Analysis of Total Hip Joint Replacement of Sandwich design by FEM Acknowledgement This research project has been supported by grant No.VS 96045CZ and J04/98: