A hybrid finite element-analytical method for determining the intrinsic elastic moduli of particles having moderately extended shapes and a wide range of elastic properties

Abstract

The presence of a low (dilute) concentration of particulate inclusions having any shape and any property mismatch with the matrix in which they are placed, influences the elasticity of the resulting composite material. This influence is via the intrinsic moduli, which characterize the first-order term in an expansion of the effective properties in terms of the volume fraction of inclusions. The intrinsic moduli have only been solved exactly for general property mismatch in the case of ellipsoidal particles, and are analytically intractable for more general geometries. The problem of computing intrinsic elastic moduli for general geometries is approached by combining exact information that is known from analytical theory with numerical finite element computations to obtain an approximate analytical description of the intrinsic bulk ( K) and shear ( G) moduli of the particles as a function of shape and matrix and inclusion elastic properties. The approximant analytical equations are developed for a wide range of isotropic elastic property ( K, G, and Poisson’s ratio) mismatch with the matrix and a modest range in shape, so that these approximants should be useful in characterizing property changes in real composite materials (e.g., concrete and polymer nanocomposites) to which a dilute concentration of particles have been added. Particular emphasis is given in this initial study to particles having a rectangular parallelepiped shape.