Simulation of the multi-scale convergence in computational homogenization approaches

Kenjiro Terada, Muneo Hori, Takashi Kyoya, Noboru Kikuchi

Research output: Contribution to journalArticlepeer-review

358 Citations (Scopus)

Abstract

Although the asymptotic homogenization is known to explicitly predict the thermo-mechanical behaviors of an overall structure as well as the microstructures, the current developments in engineering fields introduce some kinds of approximation about the microstructural geometry. In order for the homogenization method for periodic media to apply for general heterogeneous ones, the problems arising from mathematical modeling are examined in the framework of representative volume element (RVE) analyses. Here, the notion of homogenization convergence allows us to eliminate the geometrical periodicity requirement when the size of RVE is sufficiently large. Then the numerical studies in this paper realize the multi-scale nature of the convergence of overall material properties as the unit cell size is increased. In addition to such dependency of the macroscopic field variables on the selected size of unit cells, the convergence nature of microscopic stress values is also studied quantitatively via the computational homogenization method. Similar discussions are made for the elastoplastic mechanical responses in both macro- and microscopic levels. In these multi-scale numerical analyses, the specific effects of the microstructural morphology are reflected by using the digital image-based (DIB) finite element (FE) modeling technique which enables the construction of accurate microstructural models.

Original languageEnglish
Pages (from-to)2285-2311
Number of pages27
JournalInternational Journal of Solids and Structures
Volume37
Issue number16
DOIs
Publication statusPublished - 2000 Apr

Keywords

  • Digital image-based modeling
  • Homogenization methods
  • Periodic boundary conditions
  • RVE

ASJC Scopus subject areas

  • Modelling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Simulation of the multi-scale convergence in computational homogenization approaches'. Together they form a unique fingerprint.

Cite this