Gradient Deformation Models at Nano, Micro, and Macro Scales

Various deformation models incorporating higher-order gradients are discussed and their implications are considered in a variety of problems ranging from the determination of the size of dislocation cores or elastic dislocation interaction to the determination of wavelengths of dislocation patterns or heterogeneous dislocation distributions and the determination of the structure of solid interfaces and of localized strain zones during adiabatic shear deformation. Different scales are involved in each one of these problems: the nanoscale for single dislocations, the microscale for dislocation patterning, and the macroscale for adiabatic shear banding. Accordingly, different gradient models apply for each case, different types of gradient terms are involved and different expressions of the gradient coefficients are assumed.