Neutral coated circular inclusions in finite plane elasticity of harmonic materials

We study the neutrality of circular inclusions with single or multiple coatings in the context of finite plane elasticity. All the phases in the composite belong to a particular class of compressible hyperelastic solids of harmonic-type. For an N-phase structure, at most 2N different remote uniform hydrostatic loading states can be found for which the stress field in the surrounding matrix is the same as for a matrix containing no inclusions. For a three-phase structure, in which the asymptotic behavior of the harmonic materials obeys a constitutive restriction proposed by Knowles and Sternberg (1975) and the material parameter β is constant, we identify a critical value of the coating thickness parameter, above which the coated inclusion is neutral with respect to four different hydrostatic loading states, and at or below which the coated inclusion is neutral to only two different hydrostatic loading states.