  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.
