Young’s moduli and shear moduli in cortical bone

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Abstract
Young's modulus and shear modulus are determined for cortical bone from mammals and birds and for antler bone, using three-point bending at a range of span-to-depth ratios between 25 and 10. Young's modulus is obtained by extrapolating the values for the flexural modulus E$_{\text{app}}$ to infinite span-to-depth ratios. The shear modulus is obtained from the dependance of E$_{\text{app}}$ on this ratio. The main determinant for the mechanical properties is the mineral content. For mammalian bone the frequency of Haversian systems correlates negatively with stiffness and resistance to shear. However, because Haversian systems have a lower mineral content than laminar bone (the main component), material and structural determinants can not be separated at present. The ratio of Young's modulus to shear modulus is of the order of 20:1. This high value is discussed in terms of the Cook-Gordon theory of controlled crack propagation as well as in its significance for protecting hollow bones from failing upon local impact.

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