The theory of continuous distributions of composite defects

Abstract

This work undertakes the analysis of continuous media that carry simultaneously two different material or geometric structures in the same material substrate. Even when these two structures are individually perfectly uniform and homogeneous, their combination may result in a non-uniform assembly. Thus, in contradistinction to the classical interpretation of material defectivity as a manifestation of material inhomogeneity, the lack of uniformity of a composite is physically interpreted as the presence of a different kind of continuously distributed material defects. Various quantitative measures of misalignment and lack of uniformity are proposed associated with solid constituents of different symmetry types. Finally, from a more formal point of view, the use of double groupoids and their associated double Lie algebroids is suggested as the natural setting for further developments of the theory.