Thermo-mechanical analysis of periodic multiphase materials by a multiscale asymptotic homogenization approach

H. W. Zhang, S. Zhang, Jin Ying Bi, B. A. Schrefler

Research output: Contribution to journalArticlepeer-review

72 Scopus citations


A spatial and temporal multiscale asymptotic homogenization method used to simulate thermo-dynamic wave propagation in periodic multiphase materials is systematically studied. A general field governing equation of thermo-dynamic wave propagation is expressed in a unified form with both inertia and velocity terms. Amplified spatial and reduced temporal scales are, respectively, introduced to account for spatial and temporal fluctuations and non-local effects in the homogenized solution due to material heterogeneity and diverse time scales. The model is derived from the higher-order homogenization theory with multiple spatial and temporal scales. It is also shown that the modified higher-order terms bring in a non-local dispersion effect of the microstructure of multiphase materials. One-dimensional non-Fourier heat conduction and dynamic problems under a thermal shock are computed to demonstrate the efficiency and validity of the developed procedure. The results indicate the disadvantages of classical spatial homogenization.

Original languageEnglish (US)
Pages (from-to)87-113
Number of pages27
JournalInternational Journal for Numerical Methods in Engineering
Issue number1
StatePublished - Jan 1 2007


  • Homogenization
  • Multiple scale method
  • Non-Fourier heat conduction
  • Non-local model
  • Structural dynamics

ASJC Scopus subject areas

  • Engineering (miscellaneous)
  • Applied Mathematics
  • Computational Mechanics


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