The incremental plasticity condition application for pure bending of a curved bar (Golovin problem)

Abstract

The limiting elastic state of a bar with large curvature under pure bending is considered on the basis of the elasticity theory exact solution. As a criterion for the limiting state, the gradient plasticity condition is used, which determines the yield onset in an inhomogeneous stress state. Analytical expressions for calculating the corresponding stresses are obtained. The results comparison with a simplified solution is given.