The biomechanical stimulus is the most important factor for fracture healing and mainly determined by the structural stiffness of bone plate. Currently, the materials commonly used in bone plates are stainless steel and titanium, which often lead to stress shielding effects because of their higher elastic modulus compared with the bone. This article suggests an optimal design method of lattice bone plate based on fracture healing theory. First, the mechanical regulation model with deviatoric strain is established to simulate the tissue differentiation process during fracture healing process. The ratio of the average elastic modulus of callus at the 120th day to the elastic modulus of mature bone is used to characterize the fracture healing rate. Second, the optimal elastic modulus of the design domain is obtained by the optimization mathematical model with the maximum fracture healing rate. Then, the design domain is filled with microstructures, the porosity of which is adjusted to make it possible that the equivalent elastic modulus is equal to the optimized value. And the finite element analysis of the bone plate with microstructure is executed. Finally, the designed lattice bone plates are manufactured through 3D printing, and the mechanical test is carried out. The simulation results indicate that the fracture healing rate is maximum when the elastic modulus of material in design domain is 38 GPa under the constraints of fixation stability. And both the finite element analysis and experiment results show that the designed lattice bone plate meet the strength requirements of fracture internal fixation implants.
For effective bone healing, the stiffness of the bone plate should be adjusted to different bone‐healing processes. Thus, the design of stiffness‐changeable structures that take into account the time effect is of importance. To this end, this study introduces a novel topological optimization approach for the composite structural layout design considering material degradation to realize structures with changeable stiffness over time. In this approach, two sets of variables are used: a density field that defines the material layout, and a time field that determines the effect of material degradation on mechanical performance. The continuous degradation update formula is proposed by integrating the Heaviside projected function and Kreisselmeier–Steinhauser function to guarantee its derivability. The objective is to minimize the summed compliance in some specified time steps subject to the constraints of volume fraction. The sensitivity of the aforementioned objective with respect to the design variable is deduced by considering the material degradation over time. The proposed design formulation is general and is demonstrated with several design analyses, considering different fix and degradable interface boundary conditions. Moreover, the results are compared with the results of not considering material degradation and demonstrate the effectiveness of the proposed method.
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