Topology optimization of degradable composite structures with time-changeable stiffness

Heng Zhang, Akihiro Takezawa*, Xiaohong Ding, Shipeng Xu, Hao Li, Honghu Guo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)4751-4773
Number of pages23
JournalInternational Journal for Numerical Methods in Engineering
Issue number17
Publication statusPublished - 2021 Sep 15


  • biodegradable materials
  • composite structures
  • time-changeable stiffness
  • topology optimization

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics


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