Preface -- 1. Introduction ; 1.1. The objective of the work ; 1.2. For whom is this work intended ; 1.3. State of the art ; 1.4. Summary of the content ; 1.5. Acknowledgements ; 1.6. Reference list -- 2. Physical basis ; 2.1. Deformation mechanisms of single crystals ; 2.1.1. Plastic glide and twinning ; 2.1.2. Hierarchy of plastic slip processes ; 2.1.3. Localised forms of plastic deformation ; 2.1.4. Physical nature of shear bands ; 2.2. Plastic deformation in polycrystals ; 2.2.1. Mechanisms of plastic deformation and the evolution of internal micro stresses ; 2.2.2. Micro-shear bands hierarchy and their macroscopic effects ; 2.2.3. Physical nature of micro-shear bands in polycrystals ; 2.2.4. Comments on "adiabatic" micro-shear bands ; 2.3. Reference list -- 3. Incorporation of shear banding activity into the model of inelastic deformations ; 3.1. Plastic deformation of metallic solids vis-à-vis the continuum ; 3.2. Hypothesis on the extension of the RVE concept ; 3.3. Model of shear strain rate generated by micro-shear bands ; 3.4. Reference list</p> <p><b>4. Basics of rational mechanics of materials ; 4.1. A recollection of rational continuum mechanics ; 4.2. The rational theory of materials -- epilogue ; 4.2.1. The concept of the deformable body ; 4.2.2. The motion of a body ; 4.2.3. The deformation of a body ; 4.2.4. The deformation gradient ; 4.3. Reference list -- 5. Continuum mechanics description of shear banding ; 5.1. System of active micro-shear bands idealised as the surface of strong discontinuity ; 5.1.1. On finite inelastic deformations with high lattice misorientation ; 5.2. Macroscopic averaging ; 5.3. Reference list -- 6. Deformation of a body due to shear banding -- theoretical foundations ; 6.1. Basic concepts and relations of finite deformation of crystalline solids ; 6.2. Continuum model of finite inelastic deformations with permanent lattice misorientation ; 6.3. Basic concepts and relations of constitutive description -- elastic range ; 6.4. The yield limit versus shear banding -- the "extremal surface" ; 6.5. Reference list -- 7. The failure criteria concerning the onset of shear banding ; 7.1. The yield condition for modern materials -- the state of the art ; 7.2. The yield condition for the isotropic materials revealing the strength differential effect ; 7.3. Examples and visualisations of the particular Burzyński failure criteria ; 7.4. Remarks on the extension of limit criteria including anisotropic materials ; 7.5. Reference list -- 8. Constitutive description of viscoplasticity accounting for shear banding ; 8.1. The model of plastic flow with nonlinear development of kinematic ; 8.2. The Perzyna viscoplasticity model accounting for shear banding ; 8.3. Identification of viscoplasticity model ; 8.4. The crystal plasticity modelling of deformation processes in metals accounting for shear banding ; 8.5. Viscoplastic deformation of nanocrystalline metals ; 8.6. Reference list -- 9. Conclusions ; 9.1. Concluding remarks ; 9.1.1. Shear banding mediated flow vis-à-vis ductile failure analysis ; 9.1.2. Application of peridynamic numerical simulations of shear banding processes ; 9.2. Reference list -- Index