A three-invariant hardening plasticity for numerical simulation of powder forming processes via the arbitrary Lagrangian-Eulerian FE model

In this paper, a three-invariant cap plasticity model with an isotropic hardening rule is presented for numerical simulation of powder compaction processes. A general form is developed for single-cap plasticity which can be compared with some common double-surface plasticity models proposed for powders in literature. The constitutive elasto-plastic matrix and its components are derived based on the definition of yield surface, hardening parameter and non-linear elastic behaviour, as function of relative density of powder. Different aspects of the new single plasticity are illustrated by generating the classical plasticity models as special cases of the proposed model. The procedure for determination of powder parameters is described by fitting the model to reproduce data from triaxial compression and confining pressure experiments. The three-invariant cap plasticity is performed within the framework of an arbitrary Lagrangian–Eulerian formulation, in order to predict the non-uniform relative density distribution during large deformation of powder die pressing. In ALE formulation, the reference configuration is used for describing the motion, instead of material configuration in Lagrangian, and spatial configuration in Eulerian formulation. This formulation introduces some convective terms in the finite element equations and consists of two phases. Each time step is analysed according to Lagrangian phase until required convergence is attained. Then, the Eulerian phase is applied to keep mesh configuration regular. Because of relative displacement between mesh and material, all dependent variables such as stress and strain are converted through the Eulerian phase. Finally, the numerical schemes are examined for efficiency and accuracy in the modelling of a rotational flanged component, an automotive component, a conical shaped-charge liner and a connecting-rod