Micro-macro concurrent topology optimization for nonlinear solids with a decoupling multiscale analysis

Junji Kato, Daishun Yachi, Takashi Kyoya, Kenjiro Terada

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)


The present study proposes a method of micro-macro concurrent topology optimization for a two-phase nonlinear solid to minimize the end compliance of its macrostructure undergoing large deformation. To reduce the computational costs to solve a 2-scale boundary value problem under geometrically nonlinear setting, we use the so-called method of decoupling multiscale structural analysis, in which the microscopic and macroscopic boundary value problems are decoupled in the homogenization process. An isotropic hyperelasticity model is used for the constitutive model for microstructures, while an orthotropic one is assumed to represent the macroscopic material behavior. Owing to this decoupling framework, the micro-macro concurrent optimization problem can be split into 2 individual problems at the microscale and macroscale for the sake of algorithmic simplicity. Also, a 2-scale adjoint sensitivity analysis can be performed within the framework of computational homogenization. It is verified from a series numerical examples that the proposed method is capable of computing the optimal structures at both microscale and macroscale, according to the level of applied load.

Original languageEnglish
Pages (from-to)1189-1213
Number of pages25
JournalInternational Journal for Numerical Methods in Engineering
Issue number8
Publication statusPublished - 2018 Feb 24


  • decoupling multi-scale analysis
  • homogenization
  • large deformation
  • multi-scale topology optimization
  • nonlinear mechanics


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