Mechanical properties of hydroxyapatite-reinforced gelatin as a model system of bone

The elastic Young's modulus of hydroxyapatite-reinforced gelatin as a mechanical model system of bone was measured as a function of the volume fraction of hydroxyapatite, phi h. Initially, the Young's modulus gradually increased with an increase in phi h and then increased rapidly in the vicinity of phi h approximately 0.2. The phi h dependence of the Young's modulus was analysed by means of the theory of composite materials. It was found that with the increase in phi h the initial uniform stress deformation mode of the sample changed to the uniform strain deformation mode. The non-linear character in phi h dependence of the Young's modulus of this system was considered to reproduce well the novel behaviour of the mechanical properties of bone as a function of the mineral fraction. The situation was considered to be similar to a percolation problem. A preliminary analysis revealed that the critical exponent about the viscosity of the system accorded with the theoretically expected value. The result may present the evidence that the discontinuous point in mechanical properties of bone would be originated from an interaction such as a percolation of mineral particles on a matrix protein.