A unified approach for displacement, equilibrium and hybrid finite element models in elasto-plasticity (original) (raw)

Finite element models for elasto-plastic incremental analysis are derived from a three-field variational principle. The Newton-Raphson method is applied to solve the nonlinear system of equations which is obtained from the stationarity condition of this principle. The iterative schemes are discussed in detail for pure displacement and for pure equilibrium models from which iterative schemes for hybrid models folfow directly. In the displacement model, the compatibility of the strains and the plasticity criterium are satisfied during the whole iterative process, while the equilibrium of the stresses is restored only in the mean after convergence. In the equilibrium model, the plasticity criterium and the compatibility of the strains are verified in the mean during the iterative process; when convergence is achieved, the stresses are locally in equilibrium with the applied external loads. In both cases, a tangential stiffness matrix can be constructed, even for perfectly plastic materials and it allowsone to obtain always very good convergence properties. Examples are shown for plane stress and axisymmetric cases.