Stress field and effective elastic moduli of periodic spheroidal particle composite with Gurtin-Murdoch interface

The periodic spheroidal particle nanocomposite with Gurtin-Murdoch type interface stress is considered. A complete semi-analytical solution to the unit cell model problem has been obtained by the multipole expansion method. To this end, the displacement perturbation field of the periodic array of inhomogeneities is expanded over a set of the periodic vector solutions of Lamé equation in spheroidal basis. An accurate fulfilling the interface conditions reduces the model boundary value problem to an infinite set of linear algebraic equations for the multipole strengths. The obtained solution provides evaluation of the displacement, strain and stress in every point of the unit cell being, at the same time, the representative volume element of composite. Surface averaging the local strain and stress fields yields an exact expression of the effective stiffness tensor of composite in terms of the induced dipole moment of spheroidal inhomogeneity. Numerical examples demonstrate an accuracy and computational efficiency of the developed approach and shows significant combined effect of the geometry and elastic properties of interface on the elastic fields and macroscopic stiffness of periodic nanocomposite.