Micromechanical modelling of an arbitrary ellipsoidal multi-coated inclusion

The present work aims to provide a general framework to deal with an elementary heterogeneous problem, where the inhomogeneity consists of an n-layered inclusion composed of n concentric ellipsoids made of anisotropic elastic materials. The methodology is based on a combination of Green's function techniques with interface operators, illustrating the stress and strain jump conditions at the interfaces between two adjacent coatings, which are considered perfectly bonded. The model is validated in the case of double-coated spherical inclusions made of isotropic materials, where the obtained analytical results cover the exact solution of Hervé and Zaoui. The model can be applied, after adequate choice of scale-transition methods, to describe the overall behaviour of real composite materials with complex microstructures that are significantly influenced by the presence of interphase layers between constituents (fillers and matrix). Such composites are widely employed in automotive and aerospace industries. As a typical example one can consider a composite with an epoxy matrix reinforced by glass beads coated using a thin soft polymeric phase or syntactic foams particulate composites obtained by filling a polymeric matrix with hollow solid inclusions.