Localization in rate-dependent shearing deformation, with application to torsion testing

The localization of plastic deformation in rock is of particular interest in geology in connection with the formation of “ductile” shear zones. It is commonly conjectured that strain softening, as evidenced by a falling stress–strain curve at constant strain rate, is likely to lead to strain localization. Yet observations in torsion tests at constant twist rate fail to show such an effect. However, a more sophisticated analysis using the theory of Fressengeas and Molinari (J. Mech. Phys. Solids 1987, 35, 185–211) for material showing strain-rate dependence of the flow stress does show that, when the boundary conditions are specified in terms of displacements, no localization is predicted in case of strain softening. In contrast, if the boundary conditions are set in terms of forces, localization can be expected for a strain softening material. This prediction needs experimental testing.