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.

中文翻译：

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具有时变刚度的可降解复合材料结构的拓扑优化

为了有效的骨愈合，应根据不同的骨愈合过程调整骨板的刚度。因此，考虑时间效应的刚度可变结构的设计很重要。为此，本研究引入了一种新的拓扑优化方法，用于考虑材料退化的复合结构布局设计，以实现刚度随时间变化的结构。在这种方法中，使用了两组变量：定义材料布局的密度场和确定材料退化对机械性能影响的时间场。通过整合Heaviside投影函数和Kreisselmeier-Steinhauser函数，提出了连续退化更新公式，以保证其可推导性。目标是在受体积分数约束的某些指定时间步长中最小化总合规性。通过考虑材料随时间的退化，推导出上述目标相对于设计变量的敏感性。建议的设计公式是通用的，并通过多个设计分析进行了演示，考虑了不同的固定和可降解界面边界条件。此外，将结果与不考虑材料降解的结果进行了比较，并证明了所提出方法的有效性。建议的设计公式是通用的，并通过多个设计分析进行了演示，考虑了不同的固定和可降解界面边界条件。此外，将结果与不考虑材料降解的结果进行了比较，并证明了所提出方法的有效性。建议的设计公式是通用的，并通过多个设计分析进行了演示，考虑了不同的固定和可降解界面边界条件。此外，将结果与不考虑材料降解的结果进行了比较，并证明了所提出方法的有效性。