Comparison between incremental deformation theory and flow rule to simulate sheet-metal forming processes

Numerical simulation of the deep drawing process for the manufacture of aeronautical or automotive components should predict with good accuracy the behaviour during the forming operation, taking into account, the material and the process parameters. Existing simulation strategies give good results, however calculation time are long due to the high degree of non-linearities of these problems. The objective of this work is therefore to decrease the calculation time, resulting from the non-linear material behaviour. A new algorithm based on incremental deformation theory (related to Hencky Theory) is presented, in order to compute the plasticity rule in a finite element code (ABAQUS). This algorithm is used to simulate two sheet-metal forming processes: typical stretch forming operation and incremental single point sheet forming. For each case the new algorithm is compared with a classical flow rule plasticity law. In order to have a valid comparison in terms of CPU time, the two material behaviour laws have been implemented in ABAQUS EXPLICIT using the material user function (VUMAT). Good agreement in terms of the stress state and thickness distribution is obtained with the new approach. A significant decrease in CPU time is observed when the major source of non-linearity comes from the material behaviour.