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

• Published in: International journal for numerical methods in engineering Vol. 75; no. 12; pp. 1457 - 1491
• Main Authors: Rossi, Rodrigo, Alves, Marcelo Krajnc, Al-Qureshi, Hazim Ali
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 17.09.2008; Wiley
• Subjects: Cap model; Cross-disciplinary physics: materials science; rheology; Exact sciences and technology; finite strains; Fundamental areas of phenomenology (including applications); Inelasticity (thermoplasticity, viscoplasticity...); Materials science; Materials synthesis; materials processing; mesh-free methods; Physics; powder compaction; Solid mechanics; Structural and continuum mechanics; Constitutive equation; Cold process; High strain; Multiplication; Cold pressing; Logarithmic function; Signorini problem; Stress tensor; Modeling; finite strains; Powder technology; Friction; Least squares method; Strain gradient; Meshless method; Augmented Lagrangian; Operator splitting; Powder compaction; mesh-free methods; Smooth surface; Structural analysis; Cap model
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.2307

This paper presents a detailed framework for simulation of cold powder compaction process. This framework consists of the following main assumptions: The total Lagrangian description is employed; the powder is assumed to be isotropic and it is modeled by a complete, smooth three‐surface Cap model; the constitutive formulation is based on the multiplicative decomposition of the deformation gradient and on stress–strain pair formed by the Hencky logarithmic strain and the rotated Kirchhoff stress tensor; the elastic constitutive relationship considers that some parameters are dependent upon the relative density of the powder; the contact formulation is based on the Signorini condition and the friction is modeled by using a regularized Coulomb model; and the spatial discretization is made by the element‐free Galerkin method where the essential boundary conditions are enforced via an augmented Lagrangian method. Details concerning the discretization and the linearization of the weak form are presented and a master algorithm is proposed. Some key examples already investigated by other authors, but with somewhat different approaches, are revisited in this paper in order to investigate the adequacy of the proposed model and attest the performance of the proposed numerical scheme. Copyright © 2008 John Wiley & Sons, Ltd.