Steady state analyses often provide the best
approach for the study of forming processes.
Because constitutive equations for most
materials of interest are nonlinear,
must be used to obtain solutions.
Usually, the iterations consist
of solving the equilibrium equation for
velocity (with stress assumed known),
and then solving the constitutive equation for stress
(with velocity assumed known).
Under some circumstances the iterations
converge to acceptable solutions;
however, when the
elastic response becomes significantly
more pronounced than the non-elastic
response, these algorithms tend to diverge.
To overcome this difficulty, the rate-equilibrium
equations have been used to calculate the velocity
velocity field which has proven
successful for constitutive models that incorporate
a hypoelastic material. In this research,
this same approach is extended to hyperelastic materials
that exhibit yield surfaces and consequent plastic