Effective elastic properties of two-phase composites

Expressions for the effective elastic constants of two-phase composites in the form of series obtained with Fourier transforms have been analyzed. In certain cases, such series are shown to be fully summed up; as a result, one can directly obtain exact expressions for the effective bulk modulus of a composite. It is found that the symmetry of the coefficients in series for the shear modulus and Young’s modulus and the corresponding reciprocal quantities can be used to relate these series to each other. Thus, all well-known exact relations for the effective elastic constants can be derived. A set of equations is proposed to compute the effective constants of a two-dimensional isotropic symmetrical composite with arbitrary properties of its phases.