**3. Composition of bone**

Bone matrix is material having both fluid and solid phases. Two main solid phases; the organic and the inorganic (mineral) substance, give bones their hard calcified structure.

## **3.1 Organic material**

Organic matrix consist of type I collagen fibrils and non-collagenous components.


### **3.2 Inorganic material (minerals)**

The term mineralized and calcified arises from the fact that the major component of bone is calcium phosphate in the form of crystalline carbonate apatite.

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

The mineral substance of bone is calcium phosphate hydroxyapatite. On the other hand, they may vary according to the type of bone and may change during the calcification process. In reality, the organic–inorganic relationships in bone are still completely known. Unlike collagen, apatite crystals (Ap) are very stiff and strong. However, bone strength is higher than that of either collagen or apatite, it is because of similar to concrete, the softer component prevents the brittle cracking of stiff one from, while the soft one prevents the stiff component from yielding. The organic material provides bone its flexibility, while the inorganic material provides bone its resilience.

The bone composition depends on many factors, such as the species, type of bone, sample location from which it is taken, and the sex, age, and bone tissue, for example, woven, cortical, cancellous. However, the overall composition roughly estimated by volume is 1\3 rd Ap, 1\3 rd collagen, other organic contents, and 1\3 rd H2O. A roughly amount of Calcium and phosphate is about 65–70% dry weight of a bone. Collagen fibers compile approximately 95% of the extracellular matrix and it is about 25–30% of the bone's dry weight. The amount of water is up to 25% of the total wt. of bone, while 85% of the water to be found in the organic matrix surrounding the ground substance and collagen fibers. The 15% is located in cavities and canals that residence the bone cells.

### **4. Structure of bone**

As described by K. Endo et al. [6], bone is recognized as cancellous, also known as spongy or trabecular and cortical also known as compact. In any long bone, Cortical bone is about four times the accumulation of cancellous bone. The basic material of cancellous and compact bone is identical; thus, the difference between the two is the amount of porosity and the organization. The porosity of cancellous bone ranges from 30 to 90%, while the porosity of cortical bone ranges from 5 to 30%. Bone porosity is not permanent and can alter in response to disease, transformed loading, and the aging process. The periosteum is the fibrous outer covering present in all bones except the joint regions, which are enclosed with articular cartilage. There are various terms used to explain the complex design of bone at a higher resolution. Both cancellous and cortical bone may contain two types of vital architecture, lamellar and woven. Bone can also be termed as primary or secondary bone. The term either haversian or laminar is used for regions within cortical bone. The relative proportion between the compacta and the diverse medulla with the skeletal segments and their role, but the higher strength-to-weight ratio maintains its validity. The calcified volume of thick compacta of cortical bone at the diaphysis of long bones is about 90% and an eccentric cylinder medulla, which containing hemopoietic, red bone marrow in youth, and fatdepleted, yellow, non-hemopoietic marrow in adults. At the flared metaphyseal region the thickness of the compacta is negligible. The short and flat bones, as well as the metaphysis and epiphysis of the long bones, are lined with thin compacta. The medulla consists of interlacing laminar termed, osseous trabeculae.

### **5. Literature review**

Experimental verification of size effects in loaded bovine cortical bone has been carried out by Kieser et al. [7] They represented 2 and 3-dimensional finite element– based numerical models of loaded bovine cortical bone which incorporate the dominant microstructural feature: the vascular channel or Haversian canal system.

The numerical results for the virtual material samples when loaded in bending showed that they revealed size effects not forecast by either classical (Cauchy) or more generalized elasticity theories. The comparison between the values of flexural modulus and characteristic length in bending, for the specimens with axial and transversely orientated voids derived from experimentally measured size effects and those computed with a void fraction of 0.145, SX of 0.5 mm, SY of 0.433 mm, and matrix modulus of 20 GPa was given. They noted the value of axial Young's modulus as17.9GPa and transverse Young's modulus 8.6 GPa. The finite element method showed the value of axial Young's modulus 16.4 GPa and transverse Young's modulus 8.4 GPa.

Wei Sheng et al. [8] and T Attia [9] assessed femur biomechanics of different material assignments. Based on the validity of the assignment using the Finite element method they suggested how to choose the most simple and economic material assignment method. Kaori Endo et al. [6] In this paper they studied the influence of volume of cancellous bone and baseline structure on the variation in cancellous bone strength when subjected to cyclic loading. Two 2-year-old bovines were used to prepare fifteen cubic cancellous bone specimens. They were divided into three groups: femoral head, neck, and proximal metaphysis. Micro-computed tomography was used to determine structural indices of each 5-mm cubic specimen. First samples were subjected to uniaxial compressive loading at 0.05 mm/min with initial 20 N loading, 0.3 mm displacement for five cycles, and then unloading to 0.2 mm with 0.1 mm displacement for five successive cycles. During five loading cycles, elastic modulus and yield stress of cancellous bone decreased exponentially. They correlated the decrease ratio of yield stress clearly with bone volume fraction (BV/TV, r = 0.96, p < 0.01) and structural model index (SMI, r = 0.81, p < 0.01). The linking of bone strength after yield stress with structural deterioration of cancellous bone was indicated from data. Finally, they proposed that estimated baseline cancellous bone structure from non-fractured bone contributes to the cancellous bone strength during the collapse. During five loading cycles, elastic modulus and yield stress of cancellous bone decreased exponentially. Yield stress in the bovine femur was Metaphysis, neck and head are 16.8 MPa, 16Mpa, and 30Mpa respectively. Elastic properties were ranging from 428 to 625 MPa.

David C. Kieser et al. [7], Havaldar [10] and Kottha [11] considered cortical and medullary diaphyseal diameters, cortical cross-sectional area, bone length, cortical thickness, and bone density for morphological comparison. The four-point flexure tests for bending stiffness, Young's modulus of bending, and ultimate strength in bending tests was conducted as Biomechanical tests. Mid-diaphyseal cortical compressive elastic modulus and strength for torsional stiffness (Nm/degree) were also studied. Three samples of every bone type


Young's modulus and ultimate strength in bending for whole bone samples were determined by a four-point bend test of the whole femora. The load was applied through the top rollers, with the lower supporting rollers being self-aligning. The previously reported ultimate strength for deer femora was 174 MPa but they observed a lower value of 98 MPa. For sheep femur, it was 44 MPa.

Mohamed S. Gaith and Imad Al-Hayek [12] compared elastic stiffness and the degree of anisotropy for the femur human and bovine bones is presented.

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

Orthotropic symmetry is used to model Bovine and human femurs. The mechanical elastic stiffness can be described by nine independent elastic stiffness coefficients which are a function of elastic material parameters, namely, Young's modulus, shear modulus, and Poisson's ratio. The largest value (72 GPa) was noted for bovine plexiform while the human tibia bone has the smallest. The bulk modulus and the overall elastic stiffness have the same behavior for all bones except phalanx. Elastic moduli are an important parameter to expose internal anisotropy and its effect on bonding strength. In conclusion, they stated that the largest overall elastic stiffness observed for bovine femur plexiform and has the most isotropic (least anisotropic) symmetry also seen in bovine [13, 14].
