TY - JOUR
T1 - Multi-phase field topology optimization of polycrystalline microstructure for maximizing heat conductivity
AU - Kato, Junji
AU - Ogawa, Shun
AU - Ichibangase, Toshiki
AU - Takaki, Tomohiro
N1 - Funding Information:
Acknowledgements This work was supported by MEXT KAKENHI Grant Numbers 16H04394 and Honda R&D. These supports are gratefully acknowledged.
Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2018/5/1
Y1 - 2018/5/1
N2 - 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.
AB - 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.
KW - Heat conductivity
KW - Multi-scale analysis
KW - Phase field method
KW - Polycrystalline structure
KW - Topology optimization
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U2 - 10.1007/s00158-018-1965-8
DO - 10.1007/s00158-018-1965-8
M3 - Article
AN - SCOPUS:85044353301
VL - 57
SP - 1937
EP - 1954
JO - Structural and Multidisciplinary Optimization
JF - Structural and Multidisciplinary Optimization
SN - 1615-147X
IS - 5
ER -