Simplified Micro-Mechanical Approach for Coated Viscoelastic Inclusion

The present work deals with the analytical resolution of the problem of viscoelastic coated inclusion embedded in a viscoelastic matrix.In a first step, we will study the problem of a linear viscoelastic inclusion, without coating, embedded in a linear viscoelastic matrix.Then, the problem of coated viscoelastic inclusion considering the coating as a thin layer whose viscoelastic properties are different from those of the inclusion and the matrix is performed.The resolution of this problem will be based simultaneously on the Green function technique as well as the interface operator. The analytical expression of the solution is obtained by assuming the isotropy of the matrix as well as the spherical shape of the coatedinclusion.These results are used to determine the effective properties of a heterogeneous medium from a self-consistent approach taking into accountthe interactions between coated inclusions and the equivalent homogeneous medium.

EFFECTIVE MEDIUM APPROXIMATION FOR CONDUCTIVITY OF COATED-INCLUSION COMPOSITES WITH ANISOTROPIC COATING

Effective medium approximations are developed to estimate the macroscopic conductivity of coated-inclusion composites with thin anisotropic coating. The two-phase coated-inclusion are substituted by equivalent one-phase inclusion, using the multi-coated spheres assemblage and the differential substitution approaches. Then, the usual effective medium approximation schemes are applied to the equivalent medium to estimate the conductivity of original three-phase composites. The results obtained were compared with the numerical simulation by finite element method in 2D show the effectiveness of the methods.

XFEM/Level-set for modelling of coated inclusion composites

In this paper, Extended Finite Element method (XFEM) is used to model the embedded coated inclusion composite. The coated inclusion with finite thickness is associated with two level-set functions, which describe its inside and outside interfaces. A simple integration rule is employed for numerical quadrature in elements cut by two interfaces. Accuracy and efficiency of the proposed approach are demonstrated through 3D numerical examples and applied to homogenization of such materials.