Extended general interfaces: Mori–Tanaka homogenization and average fields

Abstract

A well-established methodology to capture interphases in heterogeneous materials is to replace them by a zero-thickness interface model. Commonly accepted interface models intuitively assume that to satisfy the angular momentum balance, interfaces must coincide with the mid-layer of their corresponding interphases. Recently, via adopting weighted averages, an extended general interface model has been developed that allows for arbitrary interface positions while fulfilling the angular momentum balance. This manuscript incorporates this novel interface model into the Mori–Tanaka method within the framework of homogenization. Analytical solutions are developed to determine effective properties as well as average local fields for fiber-reinforced and particle-reinforced composites. Computational simulations using the finite element method (FEM) are carried out to compare with the analytical solutions. Through a set of numerical examples, the significance of the interface position on the overall response of heterogeneous materials is highlighted. Our extended framework clarifies various ambiguous observations originating from the trivial assumption of restricting the interface position to the mid-plane. One advantage of the current interface model is that it covers both the elastic and cohesive interface models at its limits and therefore the analytical solutions are widely applicable regardless of the interface type.