We describe multiscale geometrical changes via structured deformations [Formula: see text] and the non-local energetic response at a point x via a function [Formula: see text] of the weighted averages of the jumps [Formula: see text] of microlevel deformations [Formula: see text] at points y within a distance r of x. The deformations [Formula: see text] are chosen so that [Formula: see text] and [Formula: see text]. We provide conditions on [Formula: see text] under which the upscaling “[Formula: see text]” results in a macroscale energy that depends through [Formula: see text] on (1) the jumps [Formula: see text] of g and the “disarrangement field”[Formula: see text], (2) the “horizon” r, and (3) the weighting function [Formula: see text] for microlevel averaging of [Formula: see text]. We also study the upscaling “[Formula: see text]” followed by spatial localization “[Formula: see text]” and show that this succession of processes results in a purely local macroscale energy [Formula: see text] that depends through [Formula: see text] upon the jumps [Formula: see text] of g and the “disarrangement field”[Formula: see text] alone. In special settings, such macroscale energies [Formula: see text] have been shown to support the phenomena of yielding and hysteresis, and our results provide a broader setting for studying such yielding and hysteresis. As an illustration, we apply our results in the context of the plasticity of single crystals.
Crystal Plasticity Analysis of Development of Intragranular Misorientations due to Kinking in HCP Single Crystals Subjected to Uniaxial Compressive Loading