A class of general algorithms for multi-scale analyses of heterogeneous media

K. Terada, N. Kikuchi

Research output: Contribution to journalArticlepeer-review

401 Citations (Scopus)


A class of computational algorithms for multi-scale analyses is developed in this paper. The two-scale modeling scheme for the analysis of heterogeneous media with fine periodic microstructures is generalized by using relevant variational statements. Instead of the method of two-scale asymptotic expansion, the mathematical results on the generalized convergence are utilized in the two-scale variational descriptions. Accordingly, the global-local type computational schemes can be unified in association with the homogenization procedure for general nonlinear problems. After formulating the problem in linear elastostatics, that with local contact condition and the elastoplastic problem, we present representative numerical examples along with the computational algorithm consistent with our two-scale modeling strategy as well as some direct approaches.

Original languageEnglish
Pages (from-to)5427-5464
Number of pages38
JournalComputer Methods in Applied Mechanics and Engineering
Issue number40-41
Publication statusPublished - 2001 Jul 20


  • Heterogeneous media
  • Homogenization theory
  • Multi-scale analysis
  • Nonlinear behavior
  • Variational methods

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications


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