Qualitative analysis of strain localization. Part II: Transversely isotropic elasticity and plasticity

We consider first materials whose elastic and plastic properties display rotational symmetry about a common axis. Loading is restricted to uniaxial tractions. We obtain the anisotropic materials through a perturbation, by a finite number of parameters, of an isotropic reference. For the anisotropic materials, there is, to within some particular cases, a finite number of critical planes along which the onset of strain localization may occur simultaneously. In contrast, for the isotropic reference, there exists a cone of critical planes. We analyze the localization characteristics as the isotropic reference is approached. The direction of approach in the space of anisotropic parameters plays a crucial role on the orientation of the critical planes of localization. In a second step, the analysis is repeated assuming the elastic and plastic symmetry axes to be distinct. The influence of each of the three directions involved, namely loading, elastic and plastic symmetry axes, on the shear band orientation is shown to be weighted by the absolute and relative amounts of elastic and plastic anisotropies.