“…A full 3D model with realistic imperfections, either macro or micro-meso scale (grains or second phase particles, for example), however, is nontractable currently even with the simplest constitutive laws adopted for constituent materials, since it needs an unrealistically large number of elements to cover all micro-meso scale and macro scale features. Therefore, most finite element studies that incorporate microstructural information to assess strain localization (Delannay et al 2008;Hu et al 2007Hu et al , 2008bKuroda and Tvergaard 2007;Wu et al 2004bWu et al , 2007 or other problems (Utsunomiya et al 2004a,b;Wu et al 2003;Wu and Lloyd 2004a;Zhang et al 2007), such as roping, surface roughening or just average response of stress, strain, etc., are still limited to two-dimensional simulations. There are some 3D unit-cell models with statistically generated grain structures (Delannay et al 2006(Delannay et al , 2008Miller et al 2008), a small portion of measured 3D grain structures (Nakamachi et al 2007) or large particles (Chawla et al 2004) by serial sectioning methods, but these studies usually account for the local or average response of stress, strains or texture evolution in globally uniform elasto-plastic deformation region.…”