The purpose of the present article is provide a perspective for computational predictions related to such plastic instabilities as buckling, necking and flow localization including shear–banding under a wide range of deformation rates for a variety of materials, including single– and polycrystals. Computational bifurcation analyses for general cases, axisymmetric to nonaxisymmetric deformation, very thin–walled bodies, and specific materials with nonstandard constitutive equations are given. The postbifurcation analyses and regularization schemes to remedy the problems associated with spurious mesh sensitivity and incorrect convergence in finite element prediction of flow localization behavior are discussed. The instability behavior of thick circular tubes deformed under pressure and combined loading of internal/external pressure and axial force, neck and bulge propagations in polymeric materials, wrinkling of thin plates and shells under sheet metal forming processes, flow localization of thermo–elasto–viscoplastic materials under a wide range of deformation rates including adiabatic shear banding, and flow localization behavior of mono– and polycrystalline solids are reviewed with illustrative examples.

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