Bifurcation behaviour of non-uniformly stressed solids with the non-associated flow law.

In order to establish a numerical procedure for predicting the bifurcation behaviour of a non-uniformly stressed body, the generalized version of Hill's theory of uniqueness and bifurcation to materials obeying the non-associated flow rule, proposed recently by Raniecki et al., is employed. To obtain an improved lower bound to the bifurcation point, the steepest descent method is introduced to optimize a parameter r^-, which is introduced into the constitutive equation to establish a variational principle governing the bifurcation behaviour. The obtained results for pressure-sensitive and dilatant annular plates, subjected to uniform tension at the outer edge, show that the bifurcation is notably accelerated compared with that for plates obeying the associated flow rule. The effect of the pressure-sensititve yielding on the bifurcation behaviour is more remarkable than that of the dilatant plasticity. It is clarified that optimization of the parameter r^- is quite important in achieving considerable improvement of the lower bound of the bifurcation point.