Elasticity of Random Multiphase Materials: Percolation of the Stiffness Tensor

Abstract

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.Keywords Percolation · Homogenization theory · Elastic theory · Effective elastic moduli · Random multiphase materials · Composite materials Predicting the effective elastic properties of heterogeneous materials is a fundamental interdisciplinary problem in physics, materials, and mechanics due to the pervasive presence of random multiphase materials in nature and engineering [1,2]. Many composite homogenization theories for effective elastic properties have quantitatively incorporated the effects of phase geometry and anisotropy, but largely overlook the role of disorder, topology, and per-B Ying Chen

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