A multi-scale continuum theory for heterogeneous materials

Franck Vernerey, Cahal McVeigh, Wing Kam Liu, Brian Moran

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


For the design of materials, it is important to faithfully model the physics due to interactions at the microstructural scales [18, 17, 19]. While bruteforce modeling of all the details of the microstructure is too costly, current homogenized continuum models suffer from their inability to sufficiently capture the correct physics - especially where localization and failure are concerned. To overcome this limitation, a multi-scale continuum theory is proposed so that kinematic variables representing the deformation at various scales are incorporated. The method of virtual power is then used to derive a system of coupled governing equations, each equation representing a particular scale and its interactions with the macro-scale. A constitutive relation is then introduced to preserve the underlying physics associated with each scale. The inelastic behavior is represented by multiple yield functions, each representing a particular scale of microstructure, but collectively coupled through the same set of internal variables. The proposed theory is applied to model porous metals and high strength steel. For the high strength steel the microstructure of interest consists of two populations of inclusions at distinct scales, in an alloy matrix.

Original languageEnglish (US)
Title of host publicationComputational Plasticity
EditorsEugenio Onate, Roger Owen
Number of pages11
ISBN (Print)9781402065767
StatePublished - 2007
Externally publishedYes
Event8th International Conference on Computational Plasticity, 2005 - Barcelona, Spain
Duration: Sep 5 2005Sep 8 2005

Publication series

NameComputational Methods in Applied Sciences
ISSN (Print)1871-3033


Other8th International Conference on Computational Plasticity, 2005

Bibliographical note

Publisher Copyright:
© 2007 Springer. Printed in the Netherlands.

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Modeling and Simulation
  • Biomedical Engineering
  • Computer Science Applications
  • Fluid Flow and Transfer Processes
  • Computational Mathematics
  • Electrical and Electronic Engineering


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