Stability and extremum principles for post yield analysis of finite plasticity

The post yield behavior of rigid-perfectly plastic solids at the collapse load is studied based on the finite deformation theory. By using the general duality theory developed by Gao-Strang (1989), a global stability criteria is proposed and a pair of dual extremum principles, expressed in terms of displacements, displacement rates and the Kirchhoff stresses are established for plastic collapse analysis. It is proved that under large deformations, the existence of the plastic limit state at the collapse load depends on the directional derivative of a so-called complementary gap function. The application to the nonlinear plastic collapse theory yields a pair of dual bounding theorems for limit loading factor associated with any transient displacement of the deformed body when the global extremum criteria are satisfied. Dedicated to Professor Y.K. Cheung on the occasion of his 60th birthday