First-Order Microstructure Sensitive Design Based on Volume Fractions and Elementary Bounds

  • Surya R. Kalidindi
  • David T. Fullwood
  • Brent L. Adams

Prior chapters of this book have focused largely on the experimental aspects of EBSD technique. We shift our attention here to a mathematical framework for establishing invertible linkages between the mesoscale internal structure of the material and the macroscale properties exhibited by the material. It is noted that the current practice in engineering design does not pay adequate attention to the internal structure of the material as a continuous design variable. The design effort is often focused on the optimization of the geometric parameters of the component being designed using robust macroscale numerical simulation tools, while the material selection is typically relegated to a relatively small database. Furthermore, material properties are usually assumed to be isotropic, and this significantly reduces the design space.


Orientation Distribution Function Property Closure Lattice Orientation Continuous Design Variable Local State Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Financial support for this work was provided by the Army Research Office, Proposal No. 46886 MS, Dr. David Stepp, Program Director.


  1. Adams BL, Henrie A, Henrie B, Lyon M, Kalidindi SR, Garmestani H (2001) Microstructure-sensitive design of a compliant beam. J Mech Phys Solids 49(8):1639–1663MATHCrossRefADSGoogle Scholar
  2. Adams BL, Lyon M, Henrie B (2004) Microstructures by design: linear problems in elastic-plastic design. Int J Plasticity 20(8–9):1577–1602MATHCrossRefGoogle Scholar
  3. Bunge H-J (1993) Texture analysis in materials science. Mathematical methods. Morris PR (trans) Cuvillier Verlag, GöttingenGoogle Scholar
  4. Hill R (1952) The elastic behavior of a crystalline aggregate. Proc R Soc Lond A 65:349–354Google Scholar
  5. Hill R (1963) Elastic properties of reinforced solids: some theoretical principles. J Mech Phys Solids 11:357–372MATHCrossRefADSGoogle Scholar
  6. Houskamp JR, Proust G, Kalidindi SR (2007) Integration of microstructure sensitive design with finite element methods: elastic-plastic case studies in FCC polycrystals. Int J Multiscale Comput Eng 5:261–272CrossRefGoogle Scholar
  7. Kalidindi SR, Houskamp JR (2007) Application of the spectral methods of microstructure design to continuous fiber reinforced composites. J Compos Mater 41:909–930CrossRefGoogle Scholar
  8. Kalidindi SR, Houskamp JR, Lyons M, Adams BL (2004) Microstructure sensitive design of an orthotropic plate subjected to tensile load. Int J Plasticity 20(8–9):1561–1575MATHCrossRefGoogle Scholar
  9. Knezevic M, Kalidindi SR (2007a) Fast computation of first-order elastic-plastic closures for polycrystalline cubic-orthorhombic microstructures. Comput Mater Sci 39(3): 643–648CrossRefGoogle Scholar
  10. Knezevic M, Kalidindi SR (2007b) Fast computation of first-order elastic-plastic closures for polycrystalline cubic-orthorhombic microstructures. Comput Mater Sci 39: 643–648CrossRefGoogle Scholar
  11. Knezevic M, Kalidindi SR, Mishra RK (2008) Delineation of first-order closures for plastic properties requiring explicit consideration of strain hardening and crystallographic texture evolution. Int J Plasticity 24:327–342CrossRefGoogle Scholar
  12. Lyon M, Adams BL (2004) Gradient-based non-linear microstructure design. J Mech Phys Solids 52(11): 2569–2586MATHCrossRefMathSciNetADSGoogle Scholar
  13. Paul B (1960) Prediction of elastic constants of multiphase materials. T Metall Soc AIME 218:36–41Google Scholar
  14. Proust G, Kalidindi SR (2006) Procedures for construction of anisotropic elastic-plastic property closures for face-centered cubic polycrystals using first-order bounding relations. J Mech Phys Solids 54(8):1744–1762MATHCrossRefMathSciNetADSGoogle Scholar
  15. Sintay DS, Adams BL (2005) Microstructure design for a rotating disk: with application to turbine engines. 31st Design automation conference (IDETC/CIE), Long Beach, CaliforniaGoogle Scholar
  16. Wu X, Proust G, Knezevic M, Kalidindi SR (2007) Elastic-plastic property closures for hexagonal close-packed polycrystalline metals using first-order bounding theories. Acta Mater 55(8):2729–2737CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Surya R. Kalidindi
    • 1
  • David T. Fullwood
    • 2
  • Brent L. Adams
    • 1
  1. 1.Department of Materials Science and EngineeringDrexel UniversityPhiladelphiaUSA
  2. 2.Department of Mechanical EngineeringBrigham Young UniversityProvoUSA

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