4. Conclusion

Heterogeneous materials play an important role in many industrial sectors, such as functional materials engineering. Among the wide variety of heterogeneous materials and their associated properties, the linear elastic behavior of composites consisting of an isotropic homogeneous matrix and inclusions (solids and voids), spherical, flattened and cylindrical, has been the focus of attention. The article brings together a number of formulas for engineers wishing to estimate the elastic characteristics of these materials, chosen from among the most popular in the composites field. These relationships can be used as a guide for the design of functional materials. However, they cannot take into account all the effects produced by complex microstructures. Similarly, they cannot correctly predict equivalent material properties if the characteristic size of the heterogeneities is close to that of...