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arXiv · 1401.3152

On the Geometry and Kinematics of Smoothly Distributed and Singular Defects

Marcelo Epstein·Reuven Segev
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Abstract

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.

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Marcelo Epstein, Reuven Segev. 2014-01-14. On the Geometry and Kinematics of Smoothly Distributed and Singular Defects. https://arxiv.org/abs/1401.3152

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