Application of block Newton method to elastoplastic problems under plane stress state

Abstract

The simultaneously iterative procedure for elastic-plastic boundary value problems proposed by the authors is extended to elastoplastic problems under plane stress state. The authors define a coupled problem of the equilibrium equation, the yield equation, and the plane stress condition at every material points, and develop a numerical procedure based on the block Newton method to solve them with simultaneous linearization. In the proposed block Newton method, the tangent moduli can be constructed algebraically by eliminating the internal variables, which are also updated algebraically without local iterative calculation. In addition, the residuals of yield criterion and plane stress state are incorporated into the linearized equilibrium equation. Hence, the proposed procedure enables us to decrease the residuals in the coupled boundary value problems simultaneously. Some numerical examples illustrate the validity and the effectiveness of the procedures under plane stress state with material nonlinearity.