On the elastic far-field response of a two-dimensional coated circular inhomogeneity: Analysis and applications

The paper studies the conditions under which the far-field response of a two-dimensional coated circular inhomogeneity embedded into an infinite matrix and subjected to uniform stresses at infinity is identical to that of a perfectly bonded inhomogeneity. The problem is considered in plane strain and antiplane settings. All constituents of the composite systems are assumed to be isotropic or transversely isotropic (with the axis Oz in longitudinal direction) and linearly elastic. For the plane strain problem and hydrostatic load or antiplane problem, it is shown that there always exists an equivalent inhomogeneity of the radius equal to the external radius of the coating that produces the elastic fields inside the matrix that are identical to those of the original coated inhomogeneity. For the plane strain and deviatoric load, the elastic fields in the matrix due to these two composite systems are always different, except for the equal shear moduli case. However, it is rigorously proved here that, for the deviatoric load and any combination of the material parameters, there exists the equivalent inhomogeneity of the radius equal to the external radius of the coating that induces the same dipole moments as those induced by the coated inhomogeneity. The existence of the equivalent inhomogeneities whose radius is different from the external radius of the coating is also investigated. The application of the proposed procedure to the homogenization problems leads to the new closed-form expression for the effective transverse shear modulus of transversely isotropic unidirectional composites. The findings presented here provide an insight on the influence of the interphases that could be useful in the analysis of some types of inverse problems.