On the higher-order pseudo-continuum characterization of discrete kinematic results from experimental measurement or discrete simulation

TL;DR

This paper develops higher-order pseudo-continuum measures to characterize complex, non-affine discrete kinematic data from experiments or simulations, providing a new way to analyze microstructural deformation.

Contribution

It introduces a purely discrete method for higher-order continuum-like characterization of incompatible kinematic data, applicable to experimental and simulation results.

Findings

Higher-order measures capture complex lattice distortions.

Displacement data around dislocation cores are effectively characterized.

Nye tensor alone is insufficient for full distortion description.

Abstract

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.