Structural and Multidisciplinary Optimization

, Volume 57, Issue 5, pp 1937–1954 | Cite as

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

  • Junji Kato
  • Shun Ogawa
  • Toshiki Ichibangase
  • Tomohiro Takaki


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.


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



This work was supported by MEXT KAKENHI Grant Numbers 16H04394 and Honda R&D. These supports are gratefully acknowledged.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Junji Kato
    • 1
  • Shun Ogawa
    • 1
  • Toshiki Ichibangase
    • 1
  • Tomohiro Takaki
    • 2
  1. 1.Department of Civil and Environmental EngineeringTohoku UniversityAoba-kuJapan
  2. 2.Faculty of Mechanical EngineeringKyoto Institute of TechnologySakyoJapan

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