Prediction of damage in human tibia using finite similitude theory

Performing experiments is essential for studying biomechanical issues; however, direct testing is frequently limited by factors such as restricted availability or ethical considerations. These challenges have led to the representation of a new procedure according to the finite similitude theory. In other words, this theory serves as an alternative to actual biomechanical tests. In this study, a new definition of damage in brittle materials, such as bone, is developed to enable its application to the tibia using finite similitude theory. The complex geometry of the human tibia is 3D-printed using PLA polymer and subjected to axial compression and three-point bending tests. The results are then reversed using finite similitude theory to derive the corresponding outcomes for the human tibia bone. Results with and without considering damage is compared with the experimental results on the human tibia bone. Those consistently demonstrate that incorporating the damage parameter significantly reduces prediction errors. In the compression test, considering damage improves the prediction error by 34.2% compared to the undamaged case, while for bending loading, the error is reduced by 15.3%. The results of this study clearly demonstrate that the finite similitude theory enables the use of different materials for the physical and trial spaces. These findings highlight the use of the finite similitude theory with considering the damage has a strong potential for the analysis of the bone.