光滑分布和奇异缺陷的几何和运动学
On the Geometry and Kinematics of Smoothly Distributed and Singular Defects
摘要：
提出了一个描述材料结构中缺陷的几何和运动学的连续力学框架。该设置适用于没有黎曼或平行结构的任何维的体流形。此外，连续分布的缺陷，以及奇异分布的理论涵盖。在一般情况下，材料结构由德拉姆电流$T$指定，相关缺陷由其边界给出。对于一个运动的缺陷与一个家庭的一个物质体的同构，它表明，缺陷的分布的变化率是由对偶的李导算子。
英文摘要：
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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