**6.5 Calculation of properties**

To find elastic constants of bone, fundamental elasticity equations were used assuming transverse isotropy of bone. Measurement of longitudinal and lateral

### **Figure 2.**

*Test sample, cubes of water Buffalo female (Bubalusbubalis), cut out of test specimen.*

*Mechanical Properties and Elasticity Model for Bovine Hard Tissue DOI: http://dx.doi.org/10.5772/intechopen.98410*

deformations facilitates the calculation of strains in respective directions. Stresses are evaluated from loads applied.

Sample calculation of Goat Male


Orthotropic material stiffness matrix constant of Goat Male (*Capra aegagrushircus*)

$$C\_{ijkl} = \begin{cases} 9.08 & \mathbf{1.81} & \mathbf{1.85} & \mathbf{0} & \mathbf{0} & \mathbf{0} \\\\ \mathbf{1.81} & 9.08 & \mathbf{1.85} & \mathbf{0} & \mathbf{0} & \mathbf{0} \\\\ \mathbf{1.85} & \mathbf{1.85} & \mathbf{13.4} & \mathbf{0} & \mathbf{0} & \mathbf{0} \\\\ \mathbf{0} & \mathbf{0} & \mathbf{0} & \mathbf{3.57} & \mathbf{0} & \mathbf{0} \\\\ \mathbf{0} & \mathbf{0} & \mathbf{0} & \mathbf{0} & \mathbf{3.57} & \mathbf{0} \\\\ \mathbf{0} & \mathbf{0} & \mathbf{0} & \mathbf{0} & \mathbf{0} & \mathbf{3.6} \end{cases} \tag{1}$$

Orthotropic material stiffness matrix constant of Water Buffalo Female (*Bubalusbubalis*) (**Table 1**)


### **Table 1.** *Mechanical properties derived from testing.*

$$C\_{ijkl} = \begin{cases} 5.19 & 1.12 & 1.2 & 0 & 0 & 0 \\ 1.12 & 5.19 & 1.2 & 0 & 0 & 0 \\ 1.2 & 1.2 & 8.28 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1.09 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1.09 & 0 \\ 0 & 0 & 0 & 0 & 0 & 2 \end{cases} \tag{2}$$

Orthotropic material stiffness matrix constant of Water buffalo Male (*Bubalusbubalis*)

$$\mathbf{C}\_{ijkl} = \begin{Bmatrix} 6.06 & 1.27 & 1.49 & 0 & 0 & 0 \\ 1.27 & 6.06 & 1.49 & 0 & 0 & 0 \\ 1.49 & 1.49 & 12.56 & 0 & 0 & 0 \\ 0 & 0 & 0 & 2.33 & 0 & 0 \\ 0 & 0 & 0 & 0 & 2.33 & 0 \\ 0 & 0 & 0 & 0 & 0 & 2.4 \end{Bmatrix} \tag{3}$$

## **7. Discussion**

This experimental study shows that Young's Modulus and Poisson's Ratio can be determined from load–displacement relation. When tested using UTM, All bone samples show much higher modulus in the axial direction (Ey) than the other two transverse directions, this is due to the transversely isotropic behavior of bone. This is attributed to the parallel orientation of grains along the longitudinal direction. In the other two transverse directions, Modulus was nearly the same. This is consistent with the values obtained by other researchers, Reilly and Burstein [15], Kulkarni and Sathe [16], R. Shahar [17]. Hence orthotropic nature of the material is exhibited by long bone. It is seen that the values of compression strain, Young's modulus, Poisson's ratio, and shear modulus are higher for Water Buffalo Male (Bubalusbubalis) than that of female showing gender difference. This may be attributed to lower bone density in females due to hormone secretion.

The results obtained here for Poisson's ratios of femur bone fall within a narrow range. The values found on our experiments for goat male 0.17 to 0.19, for Water Buffalo Female (Bubalusbubalis) 0.19 to 0.22, and for Water Buffalo Male (Bubalusbubalis) 0.22 to 0.23. These values are in good agreement with 0.20 to 0.22 reported by Kulkarni and Sathe [16], however, the range is different than 0.12 to0.63 reported by Pithioux et al. [18].

The values of compression strength of femur bones tested in this study show variation in three groups of samples. The compressive strength of the Goat male (Capra aegagrushircus) femur bone ranges from 92 MPa to 100 MPa in the longitudinal direction. The compression strength of the Goat Male (Capra aegagrushircus) femur bone reported in this work is 97 MPa. A previous study reported a similar value of compressive strength of femur bone in Ovis (sheep) 90 Mpa, Erickson et al. [19]. The compressive strength of Goat male (Capra aegagrushircus) femur bone ranges from 40 MPa - 52 MPa in the transverse direction.

Considering the above results following conclusions may be drawn:

1.Diameter of the diaphysis of Water Buffalo Female (Bubalusbubalis) femur bone was seen to be greater than Water Buffalo Male (Bubalusbubalis) femur bone but the stiffness constant shows the higher valves in Water Buffalo Male (Bubalusbubalis) than Water Buffalo Female (Bubalusbubalis) because in Water Buffalo Male (Bubalusbubalis) femur bone grains are closely spaced that is more compact cortical bone and less spongy but in Water Buffalo Female (Bubalusbubalis) femur bone grains are relatively sparsely spaced i.e. It also exhibits more cancellous bone and more spongy nature as compared to male bone sample, this difference is attributed may be due to hormonal effect.

