Idealization of functionally graded porous tubes for buckling modelling of bone structures

The objective of this study is to develop mathematical modelling for predicting buckling behaviour of bone structures. The modelling is established within the framework of refined theory including several important stress and strain components which are generally neglected in some modellings due to the simplicity. The proposed modelling is effective and can be applicable for various bone-geometry ratios and bone compositions (compact bone, sponge bone and bone's marrow). Several important parameters such as bone strength, bone-geometry ratios and the porous coefficient in the sponge bone are taken into account for illustrating buckling behaviour of the bones. According to the results, it is worth to reveal that the porous coefficient and the area of sponge bone are the key factors on buckling of bones. Increasing the porous coefficient and the area of sponge bone leads to the considerable reduction of the critical buckling force. Thus, the bones can be easier to be broken due to the reduction of their buckling force.