Exact Results

  • Salvatore Torquato
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 16)


Due to the complexity of the microstructure, there are relatively few situations in which one can evaluate the effective properties of heterogeneous materials exactly. Such rare results are nonetheless quite valuable as benchmarks to test theories and computer simulations. Exact results also provide useful insights into the mechanisms responsible for the effective behavior, insights that extend beyond the specific microstructures for which they are derived. In Chapter 15 we discussed exact phase-interchange relations. In the ensuing sections we will derive and discuss some other known exact results that we will make use of in subsequent chapters.


Bulk Modulus Effective Conductivity Effective Elastic Modulus Composite Sphere Effective Shear Modulus 
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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Salvatore Torquato
    • 1
  1. 1.Department of Chemistry and Princeton Materials InstitutePrinceton UniversityPrincetonUSA

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