**5. Finite element analysis**

As an artificial hip joints need to be designed to withstand the loads that they are expected to bear without fracture or fatigue, stress analysis is therefore required to ensure that all components of the device operate below the fatigue limit. For simple calculations, simple analytical calculations usually suffice. Unfortunately, analytical solutions are limited to linear problems and simple geometries governed by simple boundary conditions.

Implants as a hip joint involve some combinations of material or geometry non-linearity, complex geometry and mixed boundary conditions. Applying analytical methods to such a problem would require so many assumptions and simplifications. An alternative is the use of approximate or numerical methods. The most popular numerical method for solving problems in continuum mechanics is the finite element method (FEM), also referred to as finite element analysis (FEA).

FEA uses a complex system of points called nodes which make a grid called a mesh. The complex structure is divided into a large number of smaller parts, or elements, with interconnecting nodes, each with geometry much simpler than that of the whole structure. This mesh is programmed to contain the material and structural properties which define how the structure will react to certain loading conditions. Nodes are assigned at a certain density throughout the material depending on the anticipated stress levels of a particular area. Regions expected to receive large amounts of stress usually will have a higher node density than those which experience little or no stress.

Titanium as a Biomaterial for Implants 157

*Determination of fatigue properties of the femoral stem components without the application of torsion*. The second condition corresponds to the implant attached to bone under the action of an arbitrary load. This last condition analysed the distribution of stresses and strains that

Three materials were considered in the simulation: a low carbon stainless steel 316L in semi hard condition, a typical Ti-6Al-4V titanium alloy and a low modulus beta-Ti alloy, Ti-

For the stem support for fatigue testing, the material of the support was assumed to have an

To characterize the mechanical behaviour of the bone, all materials were considered as isotropic. The cortical and cancellous bones were assumed to have an elastic modulus of

For fatigue testing, we performed three finite element models in which, in each case, it was changed the material properties of the implant. The models accounted for stem, the test stand and also a piece to apply the load. Full 3D model were considered, with solid

> Tensile strength (MPa)

316L 196 861 620 0.3 Ti6Al4V 115 860 795 0.33 Ti35Nb7Zr5Ta 55 596 547 0.33

Because the stem consists of two parts and a fastener, frictional contact was modelled at the interface. The remaining interactions were assumed as tied. A total of 106,195 elements and 26,192 nodes were used in the analyses. The meshed finite element model is

For implant attached to bone finite elements models were realized, in which the hip implant and the femur were represented. Four nodes solid elements were used in the models, to realize 4 finite elements models. Three of them were developed with the implant and an additional model was analyzed without the implant. This was considered as a control

For those models with implant, the implant was completely fastened to the bone through an interaction in which "slave" nodes are tied to the master surface of the bone. So the degrees of freedom in the exterior side of the implant associates to the degrees of freedom of the

Yield strength (Mpa)

Poisson ratio

35Nb-7Zr-5Ta. The mechanical properties of these materials are given in Table 6.

16,200 MPa and 380 MPa, respectively and to have a Poisson ratio of 0.3

modulus (GPa)

Table 6. Mechanical properties of implant materials considered in the simulation

The proposed stem design was thought to minimise stress shielding.

elastic modulus E of 2.7 GPa and a Poisson ratio of 0.3.

produces the implant on the femur.

**5.2.2 Finite element models** 

shown in Figure 1.

tetrahedral and hexahedral elements.

Material Young's

solution for evaluation of stress shielding.

bone surface in contact to it.

One of the meshed finite element model is shown in Figure 2.

**5.2.1 Methods** 

The behaviour of the unknown variable within the element and the shape of the element are represented by simple functions that are linked by parameters that are shared between the elements at the nodes. Using boundary conditions, a large system of equations results and they are solved simultaneously using interactive means.

The essential steps in the FEM follow:


Following are presented some examples of the application of FEM in the estimation of fatigue life in a hip implant made in different materials. The materials implant analysed were: 316L stainless steel, Ti6Al4V, Ti-35Nb-7Zr-5Ta (low modulus -Ti alloy) and sintered porous Ti.

### **5.1 Mechanical behaviour of hip implant**

Currently, total hip arthroplasty (THA) is a common technique used in cases of reconstruction when the functionality of the natural hip joint and the leg is impaired. Despite great progress in biomaterials, fixation of the prosthesis to the bone remains a problem because the commercial metallic THA implants are five to six times stiffer than bone. The difference in elastic modulus between the bone and the implant material has been identified as the major cause of implant loosening from stress shielding.

The regenerative and remodelling processes in bone are directly triggered by loading, i.e. bone subjected to loading or stress regenerates and bone not subjected to loading results in atrophy. Thus, the effect of a much stiffer bone implant is to reduce the loading on bone resulting in the phenomenon called as stress shielding (Katti, 2004).

A stem of a lower stiffness material (e.g. a titanium alloy) will transfer more of the load to the femur proximally, reducing stress shielding, however, this is achieved at the expense of higher load transfer stresses at the cement interfaces with the bone and implant and the risk of cement failure (Gross & Abel, 2001). A goal to reach would be a low stress shielding and low interface shear stresses in this type of implant, but nowadays there are no means to reach that goal, so, the existing designs are based in a compromise between them.

There are many issues related to implants and prostheses, but in general the magnitude and direction of the load change and are not accurately known, and are patient dependant in any case. The average load on a hip joint is estimated to be up to three times body weight and the peak load during other activities such as jumping can be as high as 10 times body weight. Besides, hip joints may undertake cyclic loading as high as 106 cycles annually. This led the setting of different standards for testing mechanical strength.

### **5.2 Simulation of the mechanical behaviour of uncemented femoral stem of a hip prosthesis**

For the present study we considered two conditions. The first of them corresponds to the layout and loads used in the fatigue test established in the Standard IRAM 9422-3 *Determination of fatigue properties of the femoral stem components without the application of torsion*. The second condition corresponds to the implant attached to bone under the action of an arbitrary load. This last condition analysed the distribution of stresses and strains that produces the implant on the femur.

The proposed stem design was thought to minimise stress shielding.
