Continuum Mechanics and Quantum Mechanics are two basic theories of matter and fields. Depending on the objective and the scale of research, either of these theories happens to be at work in one way or another. This classification can also be expressed as macroscopic and microscopic theories, respectively. Macroscopic theory is applied to a wide spectrum of materials with particular attention being paid to their nonlinear and irreversible behavior. In view of its wide scope, it has proved formidable to deal in depth with the approach of quantum mechanics to each type of material. As a matter of fact, in the development of material science and theory of matter, it would appear appropriate to integrate macroscopic and microscopic theories of matter. Micromorphic, Micropolar and nonlocal formulations of modern continuum mechanics and some functional models of the constitutive theories have already established such a bridge between the macroscopic and microscopic theories (Eringen,1972).