Craig-Bampton Modal Reduction Applied to Human Tibia Tradeoff Between Accuracy and Speed

Abstract

Human bones adapt to external loading through bone growth and resorption processes (1). Strains within specific range induced by physical loading can lead to strengthening of affected bones. On the other hand, when external forces are too high, it can lead to bone fracture (2) or cause significant loads in the joints, which in turn can be damaging for the cartilage surfaces (3) and ligaments. Optimization of the gym equipment as well as the techniques of exercising is necessary to achieve bone growth stimulation without overloading the bones or the joints. This issue has been recently addressed with the use of flexible multibody simulations supported by modal reduction techniques. Although the strain output of the simulations is sound (4), it is necessary to understand the tradeoffs between accuracy and speed of the modal reduction methods. This paper presents a comparison of the tibial strains, stresses and global displacements obtained from modal representation of the bone and results obtained from the initial finite element model. Strains are obtained at the same nodes in both models during various static case loadings. Efficiency of both methods is compared by correlating computation times. Accuracy of modal representation is verified by using bending, torsion, tension and compression tests, which represent the possible physical loading conditions of tibia. Influence of the material models as well as discretization level has also been taken into account. Finally conclusions are drawn from the results providing guidelines for future work.