p-FEM for finite deformation powder compaction

The simulation of powder compaction problems (die-compaction and cold isostatic pressing) is considered herein by an implicit high-order (p-version) finite element method. In this class of problems use is made of a finite strain viscoplasticity model with evolution equations for internal variables developed for the highly compressible behavior in powder compaction processes. The classical approach of implicit finite elements applies the combination of Backward-Euler integration scheme and the Multilevel-Newton algorithm to solve the system of differential-algebraic equations resulting from the space-discretized weak formulation by means of p-version finite elements. This approach requires on Gauss-point level a robust stress-algorithm. The challenging investigations are the incorporation of the applied highly non-linear viscoplasticity model into a p-version finite element formulation using follower load applications. Several axisymmetric numerical examples show the feasibility and good performance of this p-version approach.