Reproducing Kernel Particle Method in Plasticity of Pressure-Sensitive Material with Reference to Powder Forming Process

Abstract

In this paper, an application of the reproducing kernel particle method (RKPM) is presented in plasticity behavior of pressure-sensitive material. The RKPM technique is implemented in large deformation analysis of powder compaction process. The RKPM shape function and its derivatives are constructed by imposing the consistency conditions. The essential boundary conditions are enforced by the use of the penalty approach. The support of the RKPM shape function covers the same set of particles during powder compaction, hence no instability is encountered in the large deformation computation. A double-surface plasticity model is developed in numerical simulation of pressuresensitive material. The plasticity model includes a failure surface and an elliptical cap, which closes the open space between the failure surface and hydrostatic axis. The moving cap expands in the stress space according to a specified hardening rule. The cap model is presented within the framework of large deformation RKPM analysis in order to predict the non-uniform relative density distribution during powder die pressing. Numerical computations are performed to demonstrate the applicability of the algorithm in modeling of powder forming processes and the results are compared to those obtained from finite element simulation to demonstrate the accuracy of the proposed model.

A total Lagrangian framework for simulation of powder compaction process based on a smooth three‐surface Cap model and a mesh‐free method

“…Figure 13 shows the deformed configuration at the end of the analysis. This example was also investigated in the works [7,11,12,49,56]. Again, there are differences between the boundary condition used by these authors and those used in the present simulation.…”

“…In Figure 17 was also considered by Lewis and Khoei [12]; however, these authors restricted the movement of the nodes in contact with the top and bottom mold walls. This example is also investigated in Reference [49].…”

“…Particularly regarding the simulation of powder compaction process using mesh-free methods, one can find the work presented by Khoei et al [49]. In this work, the authors use the reproducing kernel particle method to perform the spatial discretization of the medium and the penalty method to enforce the essential boundary conditions.…”

“…Here, an effective contact between the powder and all mold walls is considered. In [7,11,12,49,56], some degrees of freedom at the boundary had been restricted radially and the effect of the friction over some walls was neglected as well.…”