Reflections on the structural and constitutive approaches to the theory of defects.

• Background on differential geometric concepts is provided in the short space available. • The theory of G-structures is shown to be relevant to both approaches mentioned in title. • A non-trivial example is presented to illustrate the theory. • Some epistemological questions are addressed, if very briefly. An attempt is made to bring into harmony two of the paradigms commonly used in the theory of continuous distributions of defects. It is shown that the common differential geometric apparatus is provided neatly by the theory of G-structures. In the case of a structural model, based on putative experimental observations at the microscopic level, a G-structure can be shown to emerge from the group of linear transformations that preserve a tensorial quantity. For the phenomenological (macroscopic) constitutive model, the G-structure arises from the notion of material isomorphism and the underlying local symmetry group of the constitutive law. A comparative example is presented in the framework of certain smectic liquid crystals. [ABSTRACT FROM AUTHOR]