The dual approach to smooth defects

Abstract

Within the theory of continuous distributions of defects in materials, this paper advocates a point of view based on the geometry of differential forms. Applications to smectic liquid crystals and to multi-walled nanotube composites serve to show how this dual mathematical approach fits perfectly with the intended physical reality. Moreover, the weak formulation of the theory in terms of de Rham currents delivers the description of discrete isolated dislocations as a generalization of the smooth theory.