Continuous distributions of dislocations VI. Non-metric connexions
Continuous distributions of dislocations VI. Non-metric connexions
复制标题
位错的连续分布 VI．
DOI：
--
复制
发表时间：
1966
期刊：
影响因子：
--
通讯作者：
M. Zorawski
中科院分区：
文献类型：
--
作者：
B. Bilby;L. Gardner;A. Grinberg;M. Zorawski
包含位错和额外物质连续分布的晶体固体的准静态塑性-弹性变形被重新检查，保留晶格结构无处不在的唯一定义的假设。各种变形被认为是在一个形式序列中发生的，并且假定当变形连续发生时，固体作为一个连续的整体通过一系列广义空间。指出了将适当的可微流形与固体的每种状态相关联所使用的原理，并强调，如果总是通过流形的扭转来测量位错密度，则需要非度量连接理论。这种联系的重要性被强调了，因为真正的晶体物质实际上是由于位错的运动而发生塑性变形的。本文还证明了非度量线性连接理论特别适合于描述晶格几何，特别是纯应变和旋转的空间增量。将控制方程表述为任意一个流形都可以被视为初等流形，并讨论了该分析与使用不同坐标系的其他工人的处理之间的关系。
The quasi-static plastic-elastic deformation of a crystalline solid containing a continuous distribution of both dislocations and extra-matter is reexamined, retaining the assumption that the lattice structure is everywhere uniquely defined. The various distortions are considered to occur in a formal sequence and the solid is assumed to pass as a continuous whole through a series of generalized spaces as the distortions occur in succession. The principles used in associating the appropriate differentiable manifold with each state of the solid are indicated, and it is emphasized that the theory of non-metric connexions is required if the dislocation density is always to be measured by the torsion of the manifold. The importance of this association is emphasized, since real crystalline matter does in fact deform plastically by the motion of dislocations. It is also shown that the theory of non-metric linear connexions is especially suitable for describing the lattice geometry, and particularly the spatial increments of pure strain and rotation. The governing equations are formulated in such a way that any of the manifolds may be regarded as primary, and the relation of the analysis to treatments of other workers using different coordinate systems is discussed.