Improved estimates for the elastic properties of dilute composites with imperfect interfacial bondings of moderate anisotropy

Abstract

Estimates are proposed for the linearly elastic properties of dilute composites reinforced by either spherical particles or circular fibers that are imperfectly bonded to the surrounding matrix. Thisimperfection is represented via interfacial bonding conditions requiring continuity of tractions but permiting discontinuities of displacements that are proportional to the tractions. Elastic anisotropy of the matrix and the reinforcements can be arbitrary, but that of the interfacial bond is restricted to a particular form of common use. Like the variational estimates of Gallican et al. [J Elast 153: 373–398, 2023], the new estimates incorporate a dependence on bonding compliance through an equivalent stiffness tensor for the reinforcing phase. But instead of depending on either the arithmetic or harmonic mean of the bonding compliance, the equivalent stiffness tensor is made to depend on a function of the degree of bonding compliance anisotropy chosen in such a way that certain conditions for the elastic neutrality of rigid reinforcements are recovered exactly. The resulting estimates can be cast in variational form and interpreted as an interpolation between estimates of the arithmetic and harmonic type. Explicit expressions for effective shear moduli of isotropic composites are provided and confronted to exact results for assessment. Predictions are asymptotically exact when bonding compliance is weakly anisotropic, and are found to improve on earlier predictions of the arithmetic and harmonic type when bonding compliance is moderately anisotropic.