A general and explicit Eshelby-type estimator for evaluating the equivalent stiffness of multiply coated ellipsoidal heterogeneities

Abstract The paper presents an efficient estimator for the equivalent stiffness calculation of multiphase ellipsoidal heterogeneities. This estimator is derived from the exact effective stiffness of a generic monofiller composite associated with Eshelby's equivalence principle. It is originally developed for a two-phase ellipsoidal configuration and is subsequently generalized to multiphase heterogeneities via a layer-wise sweeping procedure. The developed estimator has an explicit form, which makes it amenable to computer programming. The performance of the proposed estimator is evaluated by analyzing several numerical examples of spherical compounds and two spheroidal ones spanning a wide range of elasticity contrasts, which are also examined by two other applicable Eshelby-type estimators. To assess the validity of our estimator in two-level homogenization problems, several examples of composite systems reinforced with core-shell inclusions are analyzed using a two-level homogenization scheme in which use is made of the estimator of this study. It is concluded that the presented estimator can be applied to a wide range of multiphase ellipsoidal heterogeneities or limit cases thereof, as well as heterogeneities with radially graded interphases.