The primary goal of this study is to further develop using analytical and computational procedures, the understanding of the mechanisms responsible for shear strain localization during the plastic deformation of both metals and polymers, as well as to improve the accuracy and efficiency of the computational algorithms used to simulate shear band formation. The so-called "thermo-mechanical mechanism" is primarily considered the mechanism responsible for flow localization at high rates of deformation. Efficient numerical algorithms are developed for the integration of the full tensorial form of strain-rate dependent constitutive relations. These numerical algorithms specifically account for strain softening phenomena by either thermal softening or by "fractures in progress" due to void growth or microcrack formation. Two main stages of the deformation are considered; namely, the pre-initiation regime (I) and the post- initiation regime (II). The study of regime I is concerned with the necessary and sufficient conditions for the onset of shear bands and the influence of several factors on the critical strain level at which bands may initiate. Such factors include heat conduction, thermal softening, strain rate sensitivity, elasticity, imperfections, and boundary conditions. The study of regime II is concerned with the phenomenon of band narrowing and the loss of local adiabaticity that leads to a quasi-steady-state condition within the bands. A model is constructed to derive the characteristic band thickness and the characteristic band spacing. Further, the change in material properties is accounted for within the bands, and the influence of any local phase transformation on the macroscopic behavior of the body is analyzed.
