On the Stress Analysis of Composite Materials

In this paper a variety of results for poly-reinforced matrix composites with inclusions are presented. There are no restrictions placed on the inclusions volume fraction or elastic properties. An analytical method of determining stress fields in composite materials is introduced. It is based upon a truncated multipole expansion about the centres of all inclusions within a representative volume of the Green's function tensor of the equilibrium equations. It is shown that if the inclusion is either cylindrical or spherical then exactly three terms are needed in this expansion. Predictions based upon the above method were compared with the results of experiments on composites consisting of an irregular array of unidirectional fibres embedded in a matrix. Simple approximate formulas were derived for the stress fields in poly-reinforced composites with arbitrarily distributed inclusions or unidirectional fibres of different sizes. For composites consisting of cubic arrays of incompressible inclusions under unidirectional loading it has been determined that the maximum stress concentration lies at the interfaces between the inclusions and the matrix for volume fraction of inclusions, less than 0.6 and within the matrix for greater than 0.6.