Journal of Materials Processing Technology 177 (2006) 53–57 The extended finite element method (X-FEM) for powder forming problems A.R. Khoei ∗ , A. Shamloo, M. Anahid, K. Shahim Department of Civil Engineering, Sharif University of Technology, P.O. Box 11365-9313, Tehran, Iran Abstract In this paper, the eXtended Finite Element Method (X-FEM) is developed in pressure-sensitive plasticity of powder compaction process. In X-FEM, the need for mesh adaption to discontinuity interface is neglected and the process is accomplished by employing additional functions, which are added to approximate the displacement field of the elements located on the interface. The double-surface cap plasticity model is employed within the X-FEM framework in numerical simulation of powder 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 application of X-FEM technique in simulation of powder material is presented in an incremental manner. Finally, the numerical example of a shaped tablet component is analyzed numerically. © 2006 Elsevier B.V. All rights reserved. Keywords: Extended FEM; Partition of unity; Enrichment function; Cap plasticity; Powder compaction 1. Introduction Powder pressing process is the main part of many powder metallurgy manufacturing routes. The physical and mechanical properties of powder metallurgy (PM) components are closely related to their final density. The density distribution of the mate- rial in the as-poured condition has effects that are propagated throughout the subsequent PM processes. In powder compaction simulation, the note for mesh adaption in different stages of process is of great importance. The requirement of mesh adap- tation in this process may consume high expenses of capacity and time in computer simulation. Thus, it is necessary to per- form an innovative procedure to remove the limitation of the mesh conforming to the boundary conditions. In the eXtended Finite Element Method (X-FEM), the need for remeshing and mesh adaption can be neglected if discontinuity happens. In this technique, the standard displacement based approximation is enriched by incorporating discontinuous fields through a par- tition of unity method [1]. Mesh adaption process is therefore substituted by partitioning the domain with some triangular sub- elements whose Gauss points are used for integration of the domain of elements. ∗ Corresponding author. Tel.: +98 21 6005818; fax: +98 21 6014828. E-mail address: arkhoei@sharif.edu (A.R. Khoei). A number of computational modeling of X-FEM have been reported in elastic analysis of crack growth and crack propaga- tion [2–4]. The implementation of X-FEM in plasticity behavior of material is a pristine field. The aim of present study is to imple- ment the method in pressure-sensitive plasticity material, such as compaction forming of powder, as the necessity of remesh- ing can be observed in most conditions. Constitutive modeling of powder is also one of the main ingredients of successful quantita- tive solution possibilities, which can reproduce powder material behavior under complicated loading conditions [5]. In this study, a cap plasticity model is developed based on a combination of a convex yield surface consisting of a failure envelope and a hard- ening elliptical cap for non-linear behavior of powder materials in the concept of the generalized plasticity formulation. The cap plasticity together with frictional contact algorithm is performed within the framework of extended finite element method, in order to predict the non-uniform relative density distribution during powder die pressing. The discontinuity between tool and pow- der is modeled using the enrichment functions, whose geometry is not dependent on the topology of the mesh. 2. The extended finite element method The X-FEM is a powerful and accurate approach to model discontinuity without considering its geometries. In this method, the discontinuity is not considered in mesh generation operation 0924-0136/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2006.03.182