Cross-property relations for two-phase planar composites

The overall property of a composite material is dictated by parameters that characterize its microstructure. Theoretically, cross-links between different physical properties of the same material have been established by eliminating all or partially these microstructural parameters. Practically, such a correlation may be used to determine one property from another once the latter is measured or calculated: the success of this approach depends on whether the correlation is insensitive to the detailed material microstructure. In the present paper, cross-property relations for planar two-phase composites are examined using both analytical approaches and the digital-based finite element method. Both isotropic and transversely isotropic two-phase planar composites are studied. Focus is placed on studying how the microstructure (e.g., shape, size, distribution and volume fraction of inclusions) affects the correlation between two different overall properties of the composite. At a fixed volume fraction, questions on whether the correlation is one-to-one and whether it is sensitive to large material contrast (e.g., voids or rigid inclusions) or how the inclusions are distributed in the matrix will be answered.