Multi-phase field topology optimization of polycrystalline microstructure for maximizing heat conductivity

Junji Kato, Shun Ogawa, Toshiki Ichibangase, Tomohiro Takaki

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


The present study proposes multi-scale topology optimization for polycrystalline microstructures applying a multi-phase field method. The objective function is to maximize the heat compliance of macrostructure and the equality constraint is the material volume of constituents in an alloy consisting of two components with different heat conductivity. Two-scale steady-state heat conduction problem based on a homogenization method is conducted. The Allen-Cahn non-conserved time evolution equation with the additional volume constraint scheme is employed as the optimization strategy for updating the crystal configuration. In the time evolution equation, sensitivities of objective function with respect to phase-field variables are considered to relate topology optimization to the multi-phase field method. It is verified from a series of numerical examples that the proposed method has great potential for the development of material design underlying polycrystalline structure.

Original languageEnglish
Pages (from-to)1937-1954
Number of pages18
JournalStructural and Multidisciplinary Optimization
Issue number5
Publication statusPublished - 2018 May 1


  • Heat conductivity
  • Multi-scale analysis
  • Phase field method
  • Polycrystalline structure
  • Topology optimization

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Control and Optimization


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