Computational Mechanics

, Volume 44, Issue 3, pp 433–445 | Cite as

Multi-length scale micromorphic process zone model

  • Franck VernereyEmail author
  • Wing Kam LiuEmail author
  • Brian Moran
  • Gregory Olson
Original Paper


The prediction of fracture toughness for hierarchical materials remains a challenging research issue because it involves different physical phenomena at multiple length scales. In this work, we propose a multiscale process zone model based on linear elastic fracture mechanics and a multiscale micromorphic theory. By computing the stress intensity factor in a K-dominant region while maintaining the mechanism of failure in the process zone, this model allows the evaluation of the fracture toughness of hierarchical materials as a function of their microstructural properties. After introducing a multi-length scale finite element formulation, an application is presented for high strength alloys, whose microstructure typically contains two populations of particles at different length scales. For this material, the design parameters comprise of the strength of the matrix–particle interface, the particle volume fraction and the strain-hardening of the matrix. Using the proposed framework, trends in the fracture toughness are computed as a function of design parameters, showing potential applications in computational materials design.


Multiscale micromorphic theory Fracture mechanics Materials design Ductile failure Multi-length scale finite elements 


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Civil, Environmental and Architectural EngineeringUniversity of Colorado at BoulderBoulderUSA
  2. 2.Department of Mechanical EngineeringNorthwestern UniversityEvanstonUSA
  3. 3.Department of Civil EngineeringNorthwestern UniversityEvanstonUSA
  4. 4.Department of Material Science and EngineeringNorthwestern UniversityEvanstonUSA

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