Complexity science of multiscale materials via stochastic computations

Wing Kam Liu, Larbi Siad, Rong Tian, Sanghoon Lee, Dockjin Lee, Xiaolei Yin, Wei Chen, Stephanie Chan, Gregory B. Olson, Lars Erik Lindgen, Mark F. Horstemeyer, Yoon Suk Chang, Jae Boong Choi, Young Jin Kim

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


New technological advances today allow for a range of advanced composite materials, including multilayer materials and nanofiber-matrix composites. In this context, the key to developing advanced materials is the understanding of the interplay between the various physical scales present, from the atomic level interactions to the microstructural composition and the macroscale behavior. Using the developing 'multiresolution data sets mechanics', the 'predictive science-based governing laws of the materials microstructure evolutions' are derived and melted into a 'stochastic multiresolution design framework.' Under such a framework, the governing laws of the materials microstructure evolution will be essential to assess, across multiple scales, the impact of multiscale material design, geometry design of a structure, and the manufacturing process conditions, by following the cause-effect relationships from structure to property and then to performance. The future integrated multiscale analysis system will be constructed based on a probabilistic complexity science-based mathematical framework. Its verification, validation and uncertainty quantification are done through carefully designed experiments, and the life-cycled materials design for products design and manufacturing is performed through the use of petascale computing. The various techniques of microstructure reconstruction result in the generation of model microstructures that, at some level, has the same statistical properties as the real heterogeneous media. Having reconstructed the heterogeneous medium, one can then evaluate its effective properties via direct numerical simulation and compare these values with experimentally measured properties of the actual medium. The proposed analysis will be dynamic in nature to capture the multi-stage historical evolvement of material/structure performance over the life span of a product. In addition to providing more accurate assessment of structure performance with stochastic multiscale analysis, our development will provide the capability of predicting structure failures and system reliability to enable more reliable design and manufacturing decisions in product development.

Original languageEnglish (US)
Pages (from-to)932-978
Number of pages47
JournalInternational Journal for Numerical Methods in Engineering
Issue number6-7
StatePublished - 2009


  • Bayesian
  • Calibration
  • DNS
  • Damage
  • Ductile
  • Failure
  • Heterogeneous
  • MRCT
  • Material
  • Modeling
  • Morphology
  • Probabilistic
  • RVE
  • Realization
  • Reconstruction
  • Scale
  • Stochastic
  • Uncertainty
  • Validation
  • Variability

ASJC Scopus subject areas

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


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