Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Scaling Function in Mechanics of Random Materials

  • Shivakumar I. Ranganathan
  • Muhammad Ridwan Murshed
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_72-1



The concept of a dimensionless scaling function is introduced and its role is discussed in the context of multiscale mechanics of random composites. The proposed scaling function stems from the scalar contraction of the ensemble averaged tensors obtained using Dirichlet and Neumann type boundary conditions. In its most generic form, the scaling function depends upon the phase contrast, volume fraction, material anisotropy, and mesoscale. The scaling function essentially quantifies the departure of a random medium from a homogeneous continuum.


Recent advances in computational mechanics have dramatically changed the landscape of engineering and science. The primary driving force is due to a rapid decrease in the computational cost which is estimated as a billion-fold reduction during the last 40 years (Belytschko et al., 2007). In particular, computational mechanics has led to...

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Copyright information

© Springer-Verlag GmbH Germany 2018

Authors and Affiliations

  • Shivakumar I. Ranganathan
    • 1
  • Muhammad Ridwan Murshed
    • 2
  1. 1.Department of Mechanical Engineering, Virginia Polytechnic Institute and State UniversityNorthern Virginia CenterFalls ChurchUSA
  2. 2.Department of Mechanical EngineeringRowan UniversityGlassboroUSA

Section editors and affiliations

  • Martin Ostoja-Starzewski
    • 1
  1. 1.Department of Mechanical Science & Engineering, Institute for Condensed Matter Theory and Beckman InstituteUniversity of Illinois at Urbana–ChampaignUrbanaUSA