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Scaling Function in Mechanics of Random Materials

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Encyclopedia of Continuum Mechanics

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Synonyms

Composite materials; Dimensionless numbers; Homogenization; Mesoscale

Definitions

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.

Introduction

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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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, Northern Virginia Center, 22043, Room 434, 7054 Haycock Road, Falls Church, VA, USA

    Shivakumar I. Ranganathan

  2. Department of Mechanical Engineering, Rowan University, Glassboro, NJ, USA

    Muhammad Ridwan Murshed

Authors
  1. Shivakumar I. Ranganathan
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  2. Muhammad Ridwan Murshed
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Corresponding author

Correspondence to Shivakumar I. Ranganathan .

Editor information

Editors and Affiliations

  1. Institut für Mechanik, Otto-von-Guericke-Universität Institut für Mechanik, Magdeburg, Germany

    Holm Altenbach

  2. Griffith University (Gold Coast Campus), Griffith School of Engineering Griffith University (Gold Coast Campus), Southport, Queensland, Australia

    Andreas Öchsner

Section Editor information

  1. Department of Mechanical Science & Engineering, Institute for Condensed Matter Theory and Beckman Institute, University of Illinois at Urbana–Champaign, 1206 West Green Street, 61801, Urbana, IL, USA

    Martin Ostoja-Starzewski

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Ranganathan, S.I., Murshed, M.R. (2018). Scaling Function in Mechanics of Random Materials. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_72-1

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  • DOI: https://doi.org/10.1007/978-3-662-53605-6_72-1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53605-6

  • Online ISBN: 978-3-662-53605-6

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

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