Model reduction in computational homogenization for transient heat conduction

Abdullah Waseem, Thomas Heuze, Laurent Stainier , Marc Geers, Varvara Kouznetsova (Corresponding author)

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18 Citations (Scopus)
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This paper presents a computationally efficient homogenization method for transient heat conduction problems. The notion of relaxed separation of scales is introduced and the homogenization framework is derived. Under the assumptions of linearity and relaxed separation of scales, the microscopic solution is decomposed into a steady-state and a transient part. Static condensation is performed to obtain the global basis for the steady-state response and an eigenvalue problem is solved to obtain a global basis for the transient response. The macroscopic quantities are then extracted by averaging and expressed in terms of the coefficients of the reduced basis. Proof-of-principle simulations are conducted with materials exhibiting high contrast material properties. The proposed homogenization method is compared with the conventional steady-state homogenization and transient computational homogenization methods. Within its applicability limits, the proposed
homogenization method is able to accurately capture the microscopic thermal inertial effects with significant computational efficiency.
Original languageEnglish
Pages (from-to)249-266
Number of pages18
JournalComputational Mechanics
Issue number1
Early online date18 Sept 2019
Publication statusPublished - 1 Jan 2020


  • Homogenization
  • Inclusions
  • Model reduction
  • Non-homogeneous media
  • Transient


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