**5.2.1 Methods**

156 Recent Advances in Arthroplasty

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

i. Discretization of the region of interest by the subdivision of the region (continuum) in

ii. Definition of the unknown variables (stress, strain and displacement) in each element

iii. Formulation in each element of the equations that define the behaviour of the unknown variables (stress-strain or strain-displacement relationships) in the form of matrices. These element matrices are assembled into a global system of equations for the entire

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

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

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

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

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

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

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

reach that goal, so, the existing designs are based in a compromise between them.

they are solved simultaneously using interactive means.

iv. Solving of the global system of equations by interactive means.

identified as the major cause of implant loosening from stress shielding.

resulting in the phenomenon called as stress shielding (Katti, 2004).

led the setting of different standards for testing mechanical strength.

The essential steps in the FEM follow:

small elements,

within the continuum,

discretized domain,

**5.1 Mechanical behaviour of hip implant** 

porous Ti.

**prosthesis** 

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

For the stem support for fatigue testing, the material of the support was assumed to have an elastic modulus E of 2.7 GPa and a Poisson ratio of 0.3.

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