The Elastic Properties of Dilute Solid Suspensions with Imperfectly Bonded Inclusions of Ellipsoidal Shape: Bounds, Asymptotics, Approximations

The elastic properties of dilute solid suspensions with imperfectly bonded inclusions of ellipsoidal shape are estimated. The imperfect bonding is regarded as a sharp interface across which the displacement jumps in proportion to the surface traction. Elastic compliances of the matrix and inclusion phases can exhibit arbitrary anisotropy while that of the bonding exhibits an anisotropy that depends on the interface normal only. A variational framework is employed to generate pairs of elementary bounds, asymptotically exact results, and approximations for the effective elasticity tensor. Each member of the pair differs in the way the bonding compliance is averaged over the interfacial surface: an ‘arithmetic’ mean in one case and a ‘harmonic’ mean in the other case. The results are used to infer the most convenient approximation for a given range of material parameters.