A stress analysis with the finite element method of a tibia model with a bone callus

Human tibial fractures are complex injuries that usually result in long periods of hospitalization and rehabilitation. During the slow healing process, the bone callus gradually increases its mechanical properties. The aim of this work is to evaluate the structural influence of the gradual mechanical properties of a callus bone due to a transverse tibial fracture. Thus, a 2D tibia model was constructed and analysed using the finite element method (FEM). At the transverse fracture site, a bone callus was considered. In order to simulate the healing process, four distinct Young’s moduli were assumed for the bone callus, ranging between the soft callus (250 MPa) and hard callus (6000 MPa) stages. All materials were assumed homogeneous, isotropic, and linear elastic. Distinct geometries and load cases were considered, simulating a normal alignment and malalignment conditions, such as a valgus and a varus knee. Each model was analysed with FEM assuming an elasto-static analysis and using constant strain triangular elements. Von Mises effective stress and principal stress fields were obtained for each model. The obtained results show that, compared to the aligned condition, both malalignment conditions induce the highest stress levels in the model. The maximum stresses were observed in the tibia model with the 250 MPa callus and gradually decreased with the increase of the mechanical properties of the callus.