## 3 Materials and Methods
### Finite Element Models Proposed
#### 3.2.1 Mechanical Properties and Material Behavior  
As described in the introduction, several authors have considered both linear and non-linear behavior for the study of Cam-type hip joints by means of the FEM. For example, in [9] an isotropic and linear elastic FE model of the bone and cartilage was considered. In this case, the [PERSON]'s modulus (E) and [PERSON]'s ratio (\(\
u\)) considered for the cartilage were 12 MPa and 0.45 MPa respectively. However, for the cortical and cancellous bone, the values were 20 MPa and 100 MPa respectively. In [10], the cartilage was also modeled as a linear elastic material with E = 12 MPa and \(\
u\) = 0.45. In this study, both the cortical and cancellous bone of the hip and femur were considered to be rigid elements. In a very similar way, other authors [12] considered the behavior of cartilage as linear elastic and isotropic behavior with E = 12 MPa and \(\
u\) = 0.4, whereas the bony components were assumed to be rigid. Other authors [49] have concentrated on the Cam-type hip joint. In doing so, they have taken into account the age of the patient and assumed an isotropic behavior and linear elastic material properties for the cortical and trabecular bones. For example, for an age range of 30 to 35 years, the authors considered E = 1 GPa for the cancellous bone and 17 GPa for the cortical bone. The Poisson's ratio was 0.4 for both. For older patients (of 70 to 79 years of age) the authors considered E = 1 GPa for the cancellous bone and 15.4 GPa for the cortical bone, with a Poisson's ratio of 0.4 for both. In a similar way to [9], other authors [50] have considered cartilage to be isotropic and linear elastic with a Young's modulus of 12 MPa and Poisson's ratio of 0.42 and 0.495 (for linear elastic and neo-Hookeian behavior). The cortical and trabecular bones for the femur and hip were modeled as rigid. On the other hand, some authors have considered non-isotropic and non-linear FE models for the bone and cartilage. For example [31; 51] considered an orthotropic behavior for the bones and isotropic for the cartilage. They assumed that E\({}_{1}\) = 11.6 GPa, E\({}_{2}\) = 12.2 GPa, E\({}_{3}\) = 19.9 GPa, shear moduli G\({}_{12}\) = 4.0 GPa, G\({}_{13}\) = 5.0 GPa, G\({}_{23}\) = 5.4 GPa and Poisson's ratio \(\
u_{12}\) = 0.42 and \(\
u_{13}\) = \(\
u_{23}\) = 0.23 for the femur and hip. However, for cartilage E = 12 MPa and \(\
u\) = 0.4. Other authors [14] considered the material properties of bones to be based on empirical formula and subject to subject specific bone material properties using the Hounsfield units. The elastic modulus considered for the cortical bone was calculated according to E = 12,900.\(\varrho\) (MPa), where \(\varrho\) was the bone density, the Poisson's ratio was assumed to be 0.3 and the cartilage was modeled with a constant Young's modulus of 6 MPa and with a Poisson's ratio of 0.49. More recently [52], the authors assumed an elastoplastic and isotropic behavior for the bones (E = 17,000 MPa and \(\
u\) = 0.3 for the cortical bone; E = 150 MPa and \(\
u\) = 0.3 for the cancellous bone) and linear elasticity for the cartilage (E = 12 MPa and \(\
u\) = 0.4).  
Figure 5: Mesh imported into the Mentat-Mar® software: (**a**) FE model with hip joint damaged (with CAM), (**b**) details of the femur and (**c**) details of the pelvis and cartilage.  
In the current paper, and according to the considerations made by the aforementioned authors, an isotropic and linear elastic behavior of the bone and cartilage was considered. For the cortical and trabecular bone, 17,000 MPa and 150 MPa were assumed for the [PERSON]'s modulus, whereas the Poisson ratio was 0.3 for both. Finally, it was assumed that E = 12 MPa and \(\
u\) = 0.4 for the cartilage.