ANALYSIS OF THE EFFECTIVE ELASTIC PROPERTIES OF A UNIDIRECTIONAL GLASS-REINFORCED PLASTIC BY THE GENERALIZED SELF-CONSISTENCY METHOD

The composites are widely used in various branches of science and engineering owing to high specific physical and mechanical properties of these materials. The behavior and properties of a composite are determined by complex interaction of a large number of elements forming the structure of the material. Since the structures of real composites are nonregular, the problems of prediction of the effective physical and mechanical properties of these materials requires a statistical formulation. A new method of the statistical mechanics of composites which is called the generalized self-consistency method [1] is presented to predict the effective elastic properties of composites. Unlike the familiar methods such as the method of singular approximation of the theory of stochastic functions or conventional selfconsistency methods [2-4], this method takes into account fine features of the real or model structures such as prescribed probabilistic laws of random mutual arrangement of inclusions and statistical scatter of the sizes of the inclusions in the composite. The generalized self-consistency method reduces the problem of prediction of the effective elastic properties of composites with random structures to solving more simple "averaged" problem for an inclusion with an intermediate layer in a medium with the desired effective elastic properties. The characteristic size of this intermediate layer is defined by the correlation radius of the random structure. The elastic properties of this layer take into account the short range order of mutual arrangement of the inclusions by means of the averaged characteristic function for the given model or real random structure of the composite.