PSI - Issue 28

Hassan Mansour Raheem et al. / Procedia Structural Integrity 28 (2020) 1727–1732 Hassan Mansour Raheem et al. / Structural Integrity Procedia 00 (2019) 000–000

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divided into elements. The type of elements was a hexahedral element with 20 node and other types of elements, such as (quadratic element, etc.) were used. After the types of elements and the meshing process had assigned, the boundary conditions were applied. The upper surface of the upper vertebra was subjected to various displacements in compression in the z-direction (U z =0 -2.5 mm) for 10 steps with the displacement in x and y direction were fixed (U x =0 and U y =0). The lower surface of the lower vertebra was fixed in three directions (U x =0, U y =0, and U z =0).

Table1. Material properties

Component

Young modulus (MPa) Poisson ratio

Bulk Modulus (MPa)

Shear Modulus (MPa)

Annulus fibrosus Nucleus pulpous

4.2

0.45

14

1.448 0.334

1

0.499

166.7

2.3. Validation of the model To validate the response of the model, a similar procedure of Meakin et al. study (Meakin and Hukins 2001) have conducted. Briefly, the response of the model, i.e. the axial and bulging displacements, under the axial compression load (1.5 kN) was compared with those of the literature results for the human spinal disc and simulated results for the intervertebral disc (Meakin and Hukins 2001). To find Young's modulus of the annulus fibrosus for the model, its valve change from 1 to 10 MPa as shown in Fig. 2. The real behavior of the disc occurs when both axial displacement and the bulging in the disc are 1 mm under a compressive load of 1.5 kN. Therefore, it is considered that the input value of Young’s modulus of the annulus fibrosus for the model is obtained at 1 mm for both axial and bulging. Figure 2 shows the comparison between the behaviors of the model with the literature data (Meakin and Hukins 2001). It seems that the annulus fibrosus Young modulus of this study equals to 4.2 MPa and it is close to (Meakin and Hukins 2001), where they reported the modulus 5 MPa, However, the result of the model is in line with the literature (Chen et al. 2001). Thus, Young's modulus of the annulus fibrosus is assumed to be 4.2 MPa.

Fig. 2. Comparison between the response of the FEA model and the literature data (Meakin and Hukins 2001).