Elastic-plastic return algorithms for sheet metal forming simulations and springback analysis

The Backward Euler and the Tangent Cutting Plane algorithms for elasto-plastic analysis were programmed and compared as stand-alone routines and after implementation in a finite element program written for the simulation of sheet metal forming operations. Comparisons are made between the two return algorithms and with an implementation of a rigid-plastic material law. The implementation assumes a plane stress state and therefore abandons the usual deviatoric formulation in favor of a principal stress state formulation. The algorithm comparison was performed for isotropic and anisotropic plasticity and perfectly plastic, kinematically hardening as well as power-law hardening materials. A subincrementation scheme was implemented and the impact of subincrementation on the accuracy as well as the computing time was assessed. Algorithm accuracy is evaluated in the standard way using contour error maps detailing angular and radial integration errors for a large number of strain increments.; It is found that as stand-alone routines, the Backward Euler algorithm has the edge in accuracy while the Tangent Plane algorithm is more economic since it consumes only approximately one third of the computing time.; The developed constitutive models were implemented in a finite element program developed for modelling two-dimensional sheet metal forming operations. Two sets of test runs simulating actual and meaningful forming operations were performed.; The first set of test runs involved the air bending of aluminum strips using a plane-strain three-point bending set-up. The program results, i.e. the computed punch force-displacement curve and the strain evolution at a particular location in the sheet strip, were compared with measurements obtained from experiments. The accuracy of the elastic-plastic constitutive routines was proven in a comparison of computed springback angles at various punch heights. The computed elastic-plastic results agreed very closely with measurements obtained from experiments.; The second set of test runs was performed on an industrial forming operation, namely the deep drawing of plane strain channel sections. The program was able to simulate this forming operation for two different strip materials to the full drawing depth of 70 mm. A punch force-displacement curve and the strain distribution at full drawing depth are given.