Zone estimates in the elastic-plastic torsion problem

Using continuity and jump conditions across the elastic-plastic interface, we show that the curvature of the shearing stress lines in the plastic zone of a simply connected bar under torsion is bounded above by a number proportionate to the twisting angle. For sufficiently large torsion the above geometrical condition defines a region in the cross-section which is a priori elastic. This lower bound for the elastic zone in the sense of set inclusion is supplemented by an upper bound for the zone area.