The purpose of this work is the development and determination of higher-order continuum-like kinematic measures which characterize discrete kinematic data obtained from experimental measurement (e.g., digital image correlation) or kinematic results from discrete modeling and simulation (e.g., molecular statics, molecular dynamics, or quantum DFT). From a continuum point of view, such data or results are in general non-affine and incompatible, due for example to shear banding, material defects, or microstructure. To characterize such information in a (pseudo-) continuum fashion, the concept of discrete local deformation is introduced and exploited. The corresponding measures are determined in a purely discrete fashion independent of any relation to continuum fields. Demonstration and verification of the approach is carried out with the help of example applications based on non-affine and incompatible displacement information. In particular, for the latter case, molecular statics results for the displacement of atoms in and around a dislocation core in fcc Au are employed. The corresponding characterization of lattice distortion in and around the core in terms of higher-order discrete local deformation measures clearly shows that, even in the simplest case of planar cores, such distortion is only partly characterized by the Nye tensor.

这项工作的目的是开发和确定高阶类似连续体的运动学测量，这些测量表征从实验测量（例如，数字图像相关性）获得的离散运动学数据或从离散建模和模拟（例如，分子静力学、分子动力学或量子 DFT）。从连续统一体的角度来看，这些数据或结果通常是非仿射的和不相容的，例如由于剪切带、材料缺陷或微观结构。为了以（伪）连续方式表征此类信息，引入并利用了离散局部变形的概念。相应的度量以纯粹离散的方式确定，独立于与连续域的任何关系。该方法的演示和验证是在基于非仿射和不兼容位移信息的示例应用程序的帮助下进行的。特别是，对于后一种情况，采用了 fcc Au 中位错核中和周围的原子位移的分子静力学结果。在高阶离散局部变形测量方面，核心内部和周围的晶格畸变的相应表征清楚地表明，即使在平面核心的最简单情况下，这种畸变也仅部分地由 Nye 张量表征。