Efficient elastic-plastic finite element analysis with higher order stress-point algorithms

The treatment of elastic-plastic problems with finite elements depends essentially on the methods used for state determination and the solution of the nonlinear equations. A systematic formulation of the state determination leads to higher order algorithms, which can better satisfy demands on accuracy and computational costs. The state determination influences highly the solution method for the system of nonlinear equations. In a comparison between Newton and a quasi-Newton method it is shown, that quasi-Newton methods are more suited for an efficient computation in combination with accurate path independent state determination algorithms.