Numerical Version of Self-Consistent Scheme for Heterogeneous Materials

Abstract

The self-consistent scheme (Budiansky, 1965) is one of the analytical methods to predict the effective properties of heterogeneous material. However, it has been noticed that this scheme cannot take the micro-structural information into the estimation. The full scale numerical simulation considering elaborately the micro-morphological characteristics, under certain conditions, needs too much computational resources (memory and time). A numerical version of self-consistent scheme based on finite element analysis is proposed to overcome the above drawbacks by combining the characteristics of numerical simulation and self-consistent scheme. As a demonstration, such scheme is applied to estimate the effective mechanical properties of bi-continuous composite in which all the constituent phases are on the equal status. The prediction is in good agreement with the full scale numerical simulation while the requirement on computational resource is reduced dramatically.