Modified Admissible Criterion for the Collapse of Unique Solution as the Limit of Ductility.

Abstract

In general, there are two situations bringing about multiplicity : one is statically admissible multiplicity and the other is kinematically admissible multiplicity. The former appears first, followed by the latter. They correspond to diffuse and localized neckings, respectively. When the plastic deformation of the element in a body is not largely constrained such as under plain stress, there is the possibility that multiplicity appears at the stage that the load in first principal direction becomes stationary. The condition for statical collapse of unique solution is discussed here from the phenomenal aspects of view, especially, in the case that the loading path is restricted by surrounding constraint. Then, the modified criterion is proposed which describes plastic instability occurring under the condition that maximum principal nominal stress becomes stationary. It gives multiplicity having plastic and rigid solutions on a restricted loading path. The statical collapse is demonstrated on the process of sheet formability with straight strain path.