Finite Element models used in this study to carry out the finite element analysis with the software COMSOL Multiphysics (COMSOL Multiphysics, COMSOL AB, Sweden), were created by digital acquisition of 3D model of femoral stem with 3D- Fig. 1 Orientation of the
stem for fatigue test (ISO 7206-4:2002)
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laser scanner (SCANNY3D- base, SCANNY3D s.r.l., Italy). A post-elaboration was then performed with the software CAD Rhinoceros (Rhinoceros 4.0, McNeel, USA) to improve scanned surfaces and to refine the model (Fig.2).
The femoral stem adopted is a straight stem (size: 115 mm) for an uncemented implant, made of titanium alloy, with a neck-shaft angle of 125and cone 12/14.
The aim of the numerical model was to reproduce the real configuration used during mechanical tests performed in the laboratory. Thus, the complete model consisted of: head and stem of hip prosthesis; cement mantle; an external metallic fixture dimensionally equal to the real specimen holder.
In order to respect the boundary conditions required in the Standard, the pros- thesis was enveloped with a cement mantle inside the metallic fixture and then rigidly fixed at 0.4CT. A load of 3 kN was applied at the centre of the head on a surface of 311 mm2, that has the same dimension of mechanical element used in the laboratory tests for heads of 28 mm of diameter, so as to distribute the stress over the prosthesis head. Finally, the base of the metallic fixture was bound.
As for the interfaces of the model: prosthesis/cement and cement/ metallic fixture interfaces were assumed to be fully bonded. The first assumption, which is the most appropriate interface boundary condition to be used especially when the cement mantle is quite thick, was done in agreement with Raimondi and Pietrabissa (1999) and Griza et al. (2008a).
As for the stem orientation, and in order to investigate how different testing conditions are associated with the variation of stem maximum stress, not only the standard configuration was implemented, with stem adduction anglea ¼10and stem flexion angleb ¼9, but also other angular positions were implemented and examined, with anglearanging from 2to 15and anglebranging from 2to 13. Finally, the mechanical properties of the materials used in the simulation are reported in Table1.
Fig. 2 Complete model created to implement finite element analysis: Model1
Regarding the procedure for the mesh generation of the model, special attention was paid to the surface of the stem at the level of its connection with the cement mantle. A mesh refinement was employed by setting some boundary mesh parameters: element growth rate at 1.4, mesh curvature factor at 0.4 and mesh curvature cutoff at 0.02. The mesh characteristics of the complete model consist of 23,834 tetrahedral elements and 102,666 degrees of freedom as shown in detail in Table2.
2.2.1 Model1: Validation of the Model
In order to validate the numerical methodology used in the present investigation, the numerical model of Griza et al. (2008a) was replicated as a first step, and the results compared. Griza’s model, in fact, represents a valuable contribution in stem numerical simulation, and the cited paper contains all the relevant information about the model they created and the main parameters they included in their simulations. The aim of their work was to show how a specific cemented hip prosthesis design, created to provide axial stability, might be vulnerable to fatigue fracture. To this aim, they performed FE analysis to examine the effect of the incorporated geometrical feature on the prosthesis mechanical behavior under physiological loading; the computational algorithm was based on the ISO Standard ISO 7206-4:2002, and simulations were implemented with the software Abaqus 6.5. As for material properties, the stem was modeled in stainless steel ASTM F-745. In the validation step of the present study, a CAD model was constructed Table 1 Material properties
Material properties
Femoral head Femoral stem Cement Fixture Femur
Co – Cr – Mo (ISO 5832-IV)
Ti – 6Al – 4V (ISO 5832-III)
PMMA (Technovit 4071)
Stainless steel
Cortical bone Elastic modulus
[GPa]
220 114 3 200 17
Poisson’s ratio 0.33 0.24 0.30 0.33 0.29
Density [kg/m3] 8,830 4,400 1,190 7,850 2,000
Table 2 Characteristics of mesh for Model1 and Model2
Mesh parameters Model1 Model2
Number of degrees of freedom 102,666 123,531
Number of elements 23,834 28,150
Number of mesh points 4,633 5,649
Tetrahedral 23,834 28,150
Number of boundary elements 7,307 7,174
Number of triangular elements 4,485 7,174
Number of edge elements 543 813
Number of vertex elements 50 84
Minimum element quality (value between 0 and 1) 0.245 0.258
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with the same Griza’s dimensions and used under the same Griza’s simulation conditions. The results obtained during the validation phase were in agreement with Griza’s main results: for principal stress distribution, Griza et al. reported a maximum value of 329 MPa located in correspondence with the upper surface of the cement, whilst the present validation study delivered a maximum value of 332 MPa in the same region with a difference of only 0.91%.
Another relevant issue was deeply investigated in the validation phase, i.e. the suitability of conducting numerical analysis under a static regimen condition, without taking into account frequency. Even though this represents a common approach in the relevant literature, the validity of such an assumption was here investigated by implementing some numerical simulations and analyzing the vibra- tion modes of the complete model. From the analysis four vibration modes were identified, and the first frequency oscillation was found equal to 431.2 Hz, which is well above the 10 Hz frequency used in laboratory fatigue test. Furthermore, stress values in static than dynamic regimen resulted to be very similar. Based on the above findings, frequency was not taken into account in the numerical analysis conducted in the present study.
2.2.2 Model1: Method to Determine Critical Conditions
As a first operative step, efforts were made on the implementation of a model to reproduce the same conditions of the mechanical experimental tests performed in the Authors’ Laboratory according with ISO Standard 7206, and also to identify the most critical conditions for femoral stem during such a test. To this second aim, a set of numerical simulations was conducted by varying the stem orientation in both the sagittal and frontal anatomical planes within angular ranges which might be reasonable both from a clinical and experimental point of view (the latter, in fact, has to cope with geometrical constraints and dimensional limitations). In particular, the adduction angleawas varied from 2to 15– step 1– while the flexion angleb was kept fixed at 9 as indicated by the above ISO Standard; successively, the flexion anglebwas increased from 2to 13– step 1– while the adduction anglea was kept fixed at 10 as indicated in the Standard. Among the outcomes of the simulations, attention was focused on the maximum value of Von Mises stress in order to identify the stem most critical condition. The assumption was here to consider as a critical configuration the combination of the alpha and beta angles in correspondence of which the maximum value of Von Mises stress had been localized on the stem, without considering all possible angular combinations and/or smaller angular steps. Implementation of such investigations were behind the purpose of the current study; however, they are discussed in the final part of the present chapter. Besides Von Mises maximum stress, other parameters were also monitored in the simulations, i.e. first principal stress, normal stress-z direction and displacement in z direction, but they were not taken into account for the identifica- tion of the critical configuration.