5.2 Mesh Optimization
5.3.2 Simulation results using ABAQUS: Orthotropic
For the mechanical analysis, the bone model was imported to ABAQUS and properties were assigned. The orthotropic properties shown in the below table 5.2.1 were assigned to the cortical and the cancellous sections respectively. Same loading and boundary conditions were applied, as discussed in the previous case, and the stress distribution was obtained.
Parameter Cortical bone Cancellous bone
Density (kg/m3) 2000 1300
Modulus of Elasticity (Mpa)
= 6982.9 = 6982.9 = 18155
= 2029.4 = 2029.4 = 3195.3 Poisson’s Ratio /=0.4
/=0.25 /=0.25
/=0.4 /=0.25 /=0.25 Shear Modulus (Gpa) "= 4.69
"= 5.61
"= 7.68
"= 4.69
"= 5.61
"= 7.68
Table 5.2 The orthotropic constants of cortical and cancellous sections [10].
Before carrying out the simulations, in ABAQUS, for any type of anisotropic material, it is required to define a local coordinate system. This helps in defining the principal direction. For this, direction “3” is assumed as the direction of principal stress, which is the Y-direction (The longitudinal axis of the bone).
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Fig 5.6 a) Stress distribution in cortical section. b) The maximum principal stress values
The maximum principal stress distribution for the cortical section is shown in above fig 5.6. The regions of highest stress are located in the neck and top portion of the shaft region. In the neck region the applied load is transverse to the loading direction which acts as a bending load and creates high compressive stress in the lower neck and high tensile stress in the upper neck region.
The maximum stress value is 0.384 GPa.
Fig 5.7 a) Stress distribution in cancellous section. b) The maximum principal stress values
The maximum principal stress distribution in the cancellous portion of the bone model is shown in above fig 5.7. The regions of highest stress are located in the neck region of the cancellous bone. In the neck region the applied load is transverse to the loading direction, acts as a bending load, which creates high compressive stress in the lower neck and high tensile stress in the upper neck region. The highest stress value is 0.087 GPa.
a) b)
a) b)
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Chapter 6
Results and Discussion
Earlier chapters described the details of geometrical modelling, loading, boundary conditions, mesh optimization and the maximum principal stress distribution with different material models. This chapter discusses about the obtained results and conclusions that can be drawn from the results.
With the help of CT images, the 3D realistic human femur bone model has been created to imitate the geometrical features of the femur bone. The model was created as an assembly of two main sections of the bone, cortical and cancellous part. The model then meshed in AMIRA and quality assessment was performed before analysis. The meshed model, taken as an orphan mesh in ABAQUS, cannot be refined in ABAQUS in terms of mesh density. The element type can be changed from 4-node to 10-node tetrahedral without altering the number of mesh elements.
In first case, the Isotropic linear elastic behavior is assumed for both the sections of the bone with different material constants. A compressive load of 1700N is applied along the longitudinal direction of the bone, with bottom of the shaft as a fixed boundary, for a duration of 1 sec. 1700N load is the maximum applied load on femur by the hip joint in the gait cycle of a 75kg male human while walking. The average duration of gait cycle is around 1.1sec [10].
In the cortical section, the maximum stress of 0.465GPa, was appeared in the neck region.
In the shaft portion also high stress values are obtained. This is because, in the neck region, even in shaft portion, the applied load would create a bending couple and that creates high compressive stresses in the lower neck and high tensile stresses in the upper neck region. The same phenomena happens in the cancellous section of the bone. The maximum stress value in cancellous part is 0.057 GPa which is lower compared to the values obtained in cortical section, because the cortical section is stiffer compared to cancellous section so it produces high amount of stresses compered that of cancellous stress.
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In the second case, the orthotropic behavior for both the cortical and the cancellous sections and assumed. The properties were assigned accordingly. The behavior of the bone model was studied under the same physiological conditions as stated in the first case. The maximum principal stress distribution was obtained. The orthotropic assumption brings the analysis a step closure, if not completely, to the actual anisotropic behavior of the bone.
The maximum principal stress value of cortical section was 0.384 GPa in the neck region.
There is a significant decrease in the maximum stress value for the cortical section, because the orthotropic properties show huge variation in directions 1 and 2 (perpendicular to the longitudinal axis). But, still the cortical is stiffer than the cancellous.
The maximum principal stress value of the cancellous section was 0.087GPa situated in the neck region only. Here, there is an increment in the maximum stress value compared to the first case. This is because, the properties are not much varying from isotropic to orthotropic assumption in other two directions (perpendicular to principal direction). And the orthotropic behavior of the cortical bone transfer more load to the cancellous section there by generating more stress in the cancellous neck region.
If we observe the femur bone of a human, the cancellous section is widely distributed and cortical section is thinner in the neck region, and being the weak section of the bone it is vulnerable to fractures. In case of osteoporotic conditions the situation becomes worse and even a small amount of sudden load can break the femur neck.
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