“…Aifantis (1981, 1982) and Aifantis (1984a, b) suggested a gradient approach to deformation to describe plastic instabilities including dislocation patterning and spatial characteristics of shear bands. This initial work and subsequent articles by Aifantis and coworkers (e.g., Aifantis and Hirth, 1985;Aifantis, 1987;Zbib and Aifantis, 1988;Walgraef and Aifantis, 1988;Vardoulakis and Aifantis, 1989;Mu¨hlhaus and Aifantis, 1991;Walgraef and Aifantis, 1995;Voyiadjis et al, 2001a) have contributed to appreciating the potential and applicability of the gradient approach to a variety of material instability problems ranging from metal fatigue and polycrystal/soil shear banding to the failure of concrete and liquefaction. Computational issues of the gradient theory for plasticity (e.g., Mu¨hlhaus and Aifantis, 1991;de Borst et al, 1995;Ramaswamy and Aravas, 1998;Bammann et al, 1999;Dorgan, 2004a, 2005), damage (e.g., Pijaudier-Cabot and Bazˇant, 1987;Bammann et al, 1999;Peerlings et al, 1996;Kuhl et al, 2000), and coupled damage-plasticity (e.g., Pamin and de Borst, 1999;Dorgan, 2001, 2005;Voyiadjis et al, 2001aVoyiadjis et al, , b, 2004 have been discussed extensively in the literature.…”