“…Various theoretical analyses for localized and di use bifurcation modes of deformation have been attempted (Cheng et al, 1971;Miles, 1971;Hutchinson and Miles, 1974;Rudnicki and Rice, 1975;Hill and Hutchinson, 1975;Young, 1976;Arthur et al, 1977;Needleman, 1979;Vardoulakis, 1979Vardoulakis, , 1980Vardoulakis, , 1981aVardoulakis, , b, 1983Miles and Nuwayhid, 1985;Yatomi et al, 1989;Chau and Rudnicki, 1990;Tatsuoka et al, 1990;Bardet, 1991;Han and Vardoulakis, 1991;Chau, 1992;Iizuka et al, 1992;Chau, 1993;Papamichos and Vardoulakis, 1995;Desrues et al, 1996;Gudehus et al, 1997;Yatomi and Shibi, 1997). Results of these studies suggest the deÿciency of traditional elastoplastic constitutive equations (e.g.…”