2014/01/14 by Epstein, Marcelo, Segev, Reuven
#58A25 #74A05 #74E20 #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1401.3152
A continuum mechanical framework for the description of the geometry and kinematics of defects in material structure is proposed. The setting applies to a body manifold of any dimension which is devoid of a Riemannian or a parallelism structure. In addition, both continuous distributions of defects as well as singular distributions are encompassed by the theory. In the general case, the material structure is specified by a de Rham current T and the associated defects are given by its boundary. For a motion of defects associated with a family of diffeomorphisms of a material body, it is shown that the rate of change of the distribution of defects is given by the dual of the Lie derivative operator.