In the companion article a case study problem was presented that illustrated a
dynamic instability related to nonassociated plastic flow. This instability allows stress
waves to grow in both amplitude and width as they propagate. In addition to this
physically implausible behavior, multiple solutions to the equations of motion
were shown to exist, which causes numerical solutions not to converge with
mesh refinement. Reformulation of some aspects of traditional plasticity
theory is necessary since associated models over-predict the amount of plastic
dilatation, and nonassociated models may result in this physically unrealistic
behavior. The case study solutions in the companion paper were limited
to a few relatively simple plastic models. The purpose of this paper is to
investigate the effects of various traditional and nontraditional plasticity
features on the existence of the instability and resulting nonuniqueness. The
instability and nonuniqueness are shown to persist with both hardening and
softening. An incrementally nonlinear model is shown to eliminate the instability
and result in mesh-independent solutions. A viscoplastic model is shown to
lead to unstable solutions for all loading rates. However, mesh-independent
numerical solutions are found when the loading timescale is much less than the
plastic relaxation time. A nonlocal plasticity model is shown to produce
solutions that are both unstable and mesh-dependent. Therefore, of the
models considered, only the incrementally nonlinear model was capable of
eliminating this nonphysical instability. This work provides much needed direction
for laboratory investigations of the validity of incrementally nonlinear flow
rules.
