A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials

K. Matous, M.G.D. Geers, V. Kouznetsova, A. Gillman

Research output: Contribution to journalArticleAcademicpeer-review

340 Citations (Scopus)
19 Downloads (Pure)


Since the beginning of the industrial age, material performance and design have been in the midst of innovation of many disruptive technologies. Today’s electronics, space, medical, transportation, and other industries are enriched by development, design and deployment of composite, heterogeneous and multifunctional materials. As a result, materials innovation is now considerably outpaced by other aspects from component design to product cycle. In this article, we review predictive nonlinear theories for multiscale modeling of heterogeneous materials. Deeper attention is given to multiscale modeling in space and to computational homogenization in addressing challenging materials science questions. Moreover, we discuss a state-of-the-art platform in predictive image-based, multiscale modeling with co-designed simulations and experiments that executes on the world’s largest supercomputers. Such a modeling framework consists of experimental tools, computational methods, and digital data strategies. Once fully completed, this collaborative and interdisciplinary framework can be the basis of Virtual Materials Testing standards and aids in the development of new material formulations. Moreover, it will decrease the time to market of innovative products.
Original languageEnglish
Pages (from-to)192-220
Number of pages29
JournalJournal of Computational Physics
Publication statusPublished - 1 Feb 2017


  • Big Data
  • Co-designed simulations and experiments
  • Computational homogenization
  • High performance computing
  • Image-based multiscale modeling
  • Model reduction
  • Predictive science
  • Verification and validation


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