These results are about a subject of Applied Mathematics; in a current sphere given the growing use of composites in technique.

This work is aimed at studying the macroscopic properties of bi-phase, three-phase, elastic, piezoelectric, lineal and non-lineal composites, reinforced with unidirectional cylindrical fiber. It is researched the propagation of waves in compound piezoelectric means and the effects that some fields of force cause in cracked piezoelectric ceramics. The results and the methodology used represent a significant advance in the research of materials' macroscopic properties, with high scientific and theoretical rigor with contributions to different concrete systems' behavior, in a very complex subject in which Mathematical (Functional Analysis, Theory of Operations and Approximate Methods) and Physical elements (Electricity, Piezoelectricity, etc.) are combined.

The work is conformed by 33 scientific articles, 19 of which have been published in 10 international magazines and the other 14 in memoirs of specialized events with arbitration, 3 doctorate theses (2 finished) and several master's degree theses and diplomate works.