A BDF2 integration method with step size control for elasto-plasticity

When describing elastic-plastic material behavior with the finite element method (FEM), a system of differential-algebraic equations (DAE) has to be solved. In contrast to the classical 'elastic predictor-plastic corrector' method, a unified approach is applied, where all unknowns are treated as global quantities. Therefore the DAE-system has to be linearized with respect to the complete set of unknowns, coupling the displacements and the internal variables. Together with a higher order time integration method (BDF2), an automatic time step size control is presented. Comparison of numerical calculations show the potential of the presented approach to reduce CPU-time considerably.