Plastic shearing of materials exhibiting strain hardening or strain softening (Q1079039)

The plastic shearing of a strain-rate dependent material (some kind of non Newtonian constitutive equation) exhibiting strain hardening or strain softening, subjected to steady shearing is considered. The existence of classical solutions is established and it is studied how the stability of the uniform shearing solutions is affected by the strain- hardening or by strain-softening. For materials exhibiting strain hardening or a moderate degree of strain softening it is shown that as time tends to infinity, every solution approaches, at specific rates of convergence, uniform shearing. Thus no shear bands formation occurs.