Elastic Moduli of Composites Containing a Low Concentration of Complex-Shaped Particles Having a General Property Contrast with the Matrix

Published

March 29, 2012

Author(s)

Edward Garboczi, Jack F. Douglas

Abstract

There are diverse material science problems concerned with how the presence of a low concentration of particulate inclusions having mechanical properties distinct from the matrix in which they are placed influences the elasticity of the resulting composite material. Although there is a classical treatment of the calculation of the leading order virial coefficient for the bulk modulus K and shear modulus G, or intrinsic moduli [K] and [G], for ellipsoidal inclusions having a general contrast between the elastic properties of the particle inclusions and the matrix, the treatment of other, more physically interesting, shapes such as gravel in concrete is analytically intractable. With literal concrete applications in mind, we treat construction gravel as being composed of block-like particles having an equivalent length, width, and thickness, and we develop numerical approximants for [K] and [G] for these block structures based on finite element calculations and limiting analytic information, an approach that generalizes our previous treatment of the electrical conductivity of composites containing complex-shaped objects having a general property contrast with the suspending matrix. We verify that our approximants provide an accurate description of [K] and [G] for general property contrast conditions and extensive tabulations of data based on finite element calculation for a wide range of object shapes.

Citation

Mechanics of Materials

Volume

51

Pub Type

Journals

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DOI Link

Keywords

intrinsic moduli, bulk modulus, shear modulus, Poisson ratio, finite element method, approximant, composite, block, gravel, concrete

Citation

Garboczi, E. and Douglas, J. (2012), Elastic Moduli of Composites Containing a Low Concentration of Complex-Shaped Particles Having a General Property Contrast with the Matrix, Mechanics of Materials, [online], https://doi.org/10.1016/j.mechmat.2012.03.009 (Accessed December 10, 2024)