A Study on Fundamental Properties of Elastic Parameters Related to Stress Field for Dissimilar Materials

Abstract

It is well-known that the stress field of 2-dimensional dissimilar materials relates to two independent elastic parameters and the effect of material combination on it is classified successfully by the so-called Dundurs' parameters (α, β). However, in case of 3-dimensional dissimilar materials, what parameter combination should be employed as the parameters like Dundurs' parameters for 2-dimensional problems has yet to be studied concretely, although it is known that three independent parameters are necessary. The authors discussed previously axisymmetric problems and showed that three independent parameters are necessary to deal with the problems and, as the parameters, the combination of (α, β, γ) (γ: product of two Poisson's ratios) is useful and effective. This paper purports to study the fundamental properties of (α, β, γ), which is expected as the parameter combination also for genera1 3-dimensional problems. The relations of (α, β, γ) to other possible parameter combinations are given first and it is shown that (α, β, γ) can exist only in the closed domain in the 3-dimensional space of (α, β, γ). Moreover, the stress concentration phenomenon at the interface edge peculiar to the axisymmetric problems is discussed. The distinction condition about it is given through theoretical consideration and its validity is confirmed by finite element analyses.