LAUSR

Abstract The representative unit cell (RUC) model of elastic heterogeneous solid with imperfectly bonded ellipsoidal inhomogeneities is developed. The periodic displacement solution has been obtained by combining the superposition principle, Papkovich-Neuber representation of displacement in terms of scalar harmonic potentials and expansion of these potentials in terms of periodic ellipsoidal harmonics. By accurate fulfilling the interface conditions, the RUC model boundary value problem is reduced to an infinite system of linear algebraic equations for the series expansion coefficients. The modified Rayleigh homogenization scheme has been extended to the elastic composite with ellipsoidal inhomogeneities and imperfect interface. The scheme takes into account volume content and elastic moduli of constituents, shape, size and arrangement of inhomogeneities, interaction between them and elastic stiffness of interface. Numerical algorithm of the method provides an accurate analysis of the RUC model for a whole range of the structure parameters. The reported numerical data illustrate convergence rate of the series solution and discover an effect of the volume content, elastic properties and arrangement of particles and interface stiffness on the stress field and macroscopic elastic moduli of the ellipsoidal particle composite.