Elastic stiffness of three-phase composites by the generalized Mechanics-of-Materials (GMM) approach

Abstract

A Generalized Mechanics-of-Materials (GMM) model is developed herein for practical approximation to the stiffness of three-phase composites. The three classes of composites considered are unidirectional two-fiber composite system, two-particulate composite system and combined fiber and particulate system. The geometrical model for the representative volume element (RVE) adopted is that of alternating cubic array of two arbitrary cuboid reinforcements. Non-dimensionalized stiffness of the three classes of three-phase composites are addressed by altering the dimensions of the reinforcing cuboids. The reinforcements in the RVE are in parallel to the applied load while the displaced surface of the RVE is assumed uniform. Verification of the model was carried out by reducing the three-phase model to that of two-phase ones, as well as by comparison with previous experimental results. Generalization for the three classes of composite stiffness was attained through a judicious choice of expression, which resulted in the identification of a parameter that conveniently describes the effect of reinforcement geometry.