Elastic ellipsoidal inhomogeneity with imperfect interface: Complete displacement solution in terms of ellipsoidal harmonics

The complete, infinite series solution has been obtained for the elastic ellipsoidal inhomogeneity imperfectly bonded to the matrix. By combining Papkovich-Neuber representation of general displacement solution in terms of scalar harmonic potentials, their expansion in terms of solid ellipsoidal harmonics and accurate fulfilling the interface conditions, the boundary value problem is reduced to an infinite system of the linear algebraic equations. Maxwell homogenization scheme has been extended to the elastic ellipsoidal particle composites with imperfect interface. The scheme takes into account the volume content and elastic moduli of constituents, shape, size and orientation statistics of inhomogeneities and contact stiffness of interface. The numerical algorithm of the method provides fast and accurate analysis of the problem for a whole range of the structure parameters. The reported numerical data illustrate the convergence rate of solution and the interface stiffness effect on the stress field and macroscopic elastic moduli of the ellipsoidal particle composite. (C) 2019 Elsevier Ltd. All rights reserved.