Journal of Statistical Physics

, Volume 162, Issue 1, pp 232–241

Elasticity of Random Multiphase Materials: Percolation of the Stiffness Tensor


DOI: 10.1007/s10955-015-1387-6

Cite this article as:
Chen, Y. & Schuh, C.A. J Stat Phys (2016) 162: 232. doi:10.1007/s10955-015-1387-6


Topology and percolation effects play an important role in heterogeneous materials, but have rarely been studied for higher-order tensor properties. We explore the effective elastic properties of random multiphase materials using a combination of continuum computational simulations and analytical theories. The effective shear and bulk moduli of a class of symmetric-cell random composites with high phase contrasts are determined, and reveal shortcomings of classical homogenization theories in predicting elastic properties of percolating systems. The effective shear modulus exhibits typical percolation behavior, but with its percolation threshold shifting with the contrast in phase bulk moduli. On the contrary, the effective bulk modulus does not exhibit intrinsic percolation but does show an apparent or extrinsic percolation transition due to cross effects between shear and bulk moduli. We also propose an empirical approach for bridging percolation and homogenization theories and predicting the effective shear and bulk moduli in a manner consistent with the simulations.


Percolation Homogenization theory Elastic theory  Effective elastic moduli Random multiphase materials Composite materials 

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Materials Science and EngineeringRensselaer Polytechnic InstituteTroyUSA
  2. 2.Department of Materials Science and EngineeringMassachusetts Institute of TechnologyCambridgeUSA

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