Analytical relations for the undetermined constitutive coefficients of a binary mixture of elastic solids with no relative component motion and an application for semi-infinite mixture continuum

Abstract

In this paper, a formulation is proposed to predict the three undetermined constitutive elastic coefficients λ3, λ4 and μ3 of a mixture of two elastic solids. Due to the formal similarity to a single linear elastic solid, constitutive equations developed by Green and Steel defining the elastic mixture continua are used. After summarizing the mathematical background where the deformation of each constituent belonging to the mixture of two linear elastic solids differs from each other, we assume that there is no relative displacement (mutual motion) between the mixture components (perfectly bonded interface) and by using this assumption, we make use of some elementary elasticity problems to determine the unknown constitutive coefficients. In order to test the obtained relations, the semi-infinite binary mixture of linear elastic solids subjected to a sinusoidal distributed load problem is examined. Under the appropriate boundary conditions, the problem is solved using the Galerkin vector and Love's strain functions, and with the help of the data for the composite of Al2O3−NiAl, some plots representing the behavior of the mixture continuum are given.