Material metric, connectivity and dislocations in continua

Summary.

In this paper, we present a framework within which the role of the initial material structure of a body, or its developing structure in the course of deformation, is accounted for in the constitutive equation of the material. The problem is dealt with at the local level, i.e., at the material neighborhood. If a neighborhood has structure then its geometry cannot be represented by a Euclidean metric. The entire body may thus be non–Euclidean. We formulate the constitutive equation for large deformation in the case where either a neighborhood is non–Euclidean because of its initial structure, or it becomes so by virtue of irreversible internal motion and/or induced dislocation fields, which we discuss at some length. In the formulation of the theory, questions of connectivity arise and are dealt with in the text.