New micromechanical modeling of the elastic behavior of composite materials with ellipsoidal reinforcements and imperfect interfaces

In this work, a new micromechanical model to determine the effective elastic behavior of composite materials with ellipsoidal reinforcements and imperfect interfaces is developed. By using the Green's functions technique, the integral equation of the linear elastic medium is reformulated in the presence of imperfect interfaces. The integral equation is then solved in the case of an ellipsoidal inclusion embedded in an infinite matrix with imperfect interface. By introducing the concept of interior and exterior-point Eshelby tensors, the solution of the inclusion problem is obtained in the case of displacement discontinuities and continuous traction across the interface between inclusion and matrix. The concentration equations are then exactly expressed in the general case of anisotropic elastic behavior and ellipsoidal inclusions with imperfect interface. In the case of spring interface model, the explicit concentration equations are obtained. In the case of isotropic elasticity, we retrieved the analytical strain concentration tensors from the literature for spherical inclusion morphology. The Mori-Tanaka homogenization scheme is used to determine the local strain and stress fields in each phase and effective elastic moduli of composite materials. In the case of fibrous composites under plane strain loading, the effective elastic moduli are successfully compared to those obtained by complex variable methods. The combined influence of shape of inclusions and interface parameters is analyzed on the effective elastic behavior.