  The inelastic incompressibility is a typical feature of metal
plasticity/viscoplasticity. Over the last decade, there has been a great amount
of research related to construction of numerical integration algorithms which
exactly preserve this geometric property. In this paper we examine, both
numerically and mathematically, the excellent accuracy and convergence
characteristics of such geometric integrators.
  In terms of a classical model of finite viscoplasticity, we illustrate the
notion of exponential stability of the exact solution. We show that this
property enables the construction of effective and stable numerical algorithms,
if incompressibility is exactly satisfied. On the other hand, if the
incompressibility constraint is violated, spurious degrees of freedom are
introduced. This results in the loss of the exponential stability and a
dramatic deterioration of convergence behavior.
