Effective properties of polyphase materials

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Abstract
A method is developed for the calculation of some coefficients of an effective tensor of a two-phase material. The method is based upon two essential steps. First the representative volume element, which is the smallest rectangular parallelepiped representative of the behaviour of the material, is transformed into an equivalent element. The latter element, which is also a rectangular parallelepiped, contains a rectangular parallelepiped of one of the two phases. Second parts of the equivalent element are considered to be in parallel or series connection, so that two expressions for the coefficients can be obtained, which in the case of the effective elastic moduli roughly correspond with the avoidance of the weakening and of the stiffening effect due to shear, respectively. From these two results one expression for the effective coefficients is obtained. By repeating the procedure the effective properties of materials with more than two phases can also be approximated. Numerical results obtained for some examples of such materials are in fair agreement with experimental results.