An Arbitrary Lagrangian-eulerian Finite Element Method for Cone-cap Plasticity; Application to Powder Compaction Simulation

The compaction forming of metal powder is a process involving large deformations, large strain, non-linear material behavior and friction. Consequently, the numerical analysis of such a highly non-linear process is a formidable computational problem. In this paper, an ALE technique is presented based on a generalized cap plasticity model in simulation of powder forming processes. 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 analyzed 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. In order to describe the constitutive model of the highly non-linear behavior of powder materials, a single cone-cap plasticity model is developed based on a hardening rule to define the dependence of the yield surface on the degree of plastic straining. This model reflects the yielding, frictional and densification characteristics of powder along with strain and geometrical hardening, which occur during the compaction process. Finally, the powder behavior during the compaction of several components is numerically simulated. It is shown that the proposed ALE model using cap plasticity theory is capable of simulating the metal powder during compaction. A.R. Khoei , M. Anahid , A.R. Azami and S. Azizi 2