A Smoothed Particle Galerkin Formulation for Extreme Material Flow Analysis in Bulk Forming Applications

This paper presents a new particle formulation for extreme material flow analyses in the bulk forming applications. The new formulation is first established by an introduction of a smoothed displacement field to the standard Galerkin formulation to eliminate zero-energy modes in conventional particle methods. The discretized system of linear equations is consistently derived and integrated using a direct nodal integration scheme. The linear formulation is next extended to the large deformation quasi-static analysis of inelastic materials. As quasi-static Lagrangian simulation proceeds in the severe deformation range, the analysis method is switched to explicit dynamics formulation and an adaptive Lagrangian kernel approach is preformed to reset the reference configuration and maintain the injective deformation mapping at the particles. Both nonconvex and convex meshfree approximations are investigated in this study. Several numerical benchmarks are provided to demonstrate the effectiveness and accuracy of...

[1]  N. Sukumar.  Construction of polygonal interpolants: a maximum entropy approach , 2004 .

[2]  S. A. Medin,et al.  Smoothed Particle Hydrodynamics Using Interparticle Contact Algorithms , 2002 .

[3]  Yong-Ming Guo,et al.  Numerical modeling of composite solids using an immersed meshfree Galerkin method , 2013 .

[4]  Guirong Liu.  A GENERALIZED GRADIENT SMOOTHING TECHNIQUE AND THE SMOOTHED BILINEAR FORM FOR GALERKIN FORMULATION OF A WIDE CLASS OF COMPUTATIONAL METHODS , 2008 .

[5]  Damien Violeau,et al.  Fluid Mechanics and the SPH Method: Theory and Applications , 2012 .

[6]  Larry D. Libersky,et al.  Recent improvements in SPH modeling of hypervelocity impact , 1997 .

[7]  Hui-Ping Wang,et al.  An enhanced cell‐based smoothed finite element method for the analysis of Reissner–Mindlin plate bending problems involving distorted mesh , 2013 .

[8]  Rade Vignjevic,et al.  A treatment of zero-energy modes in the smoothed particle hydrodynamics method , 2000 .

[9]  T. Belytschko,et al.  Nodal integration of the element-free Galerkin method , 1996 .

[10]  Jiun-Shyan Chen,et al.  An arbitrary order variationally consistent integration for Galerkin meshfree methods , 2013 .

[11]  M. Koishi,et al.  Three‐dimensional meshfree‐enriched finite element formulation for micromechanical hyperelastic modeling of particulate rubber composites , 2012 .

[12]  Michael A. Puso,et al.  Meshfree and finite element nodal integration methods , 2008 .

[13]  Guirong Liu,et al.  Upper bound solution to elasticity problems: A unique property of the linearly conforming point interpolation method (LC‐PIM) , 2008 .

[14]  Wing Kam Liu,et al.  Reproducing Kernel Particle Methods for large deformation analysis of non-linear structures , 1996 .

[15]  Guirong Liu.  Meshfree Methods: Moving Beyond the Finite Element Method, Second Edition , 2009 .

[16]  T. Belytschko,et al.  Stable particle methods based on Lagrangian kernels , 2004 .

[17]  Antonio Huerta,et al.  Stabilized updated Lagrangian corrected SPH for explicit dynamic problems , 2007 .

[18]  Guirong Liu,et al.  A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems , 2009 .

[19]  Wei Hu,et al.  Bubble‐enhanced smoothed finite element formulation: a variational multi‐scale approach for volume‐constrained problems in two‐dimensional linear elasticity , 2014 .

[20]  Dongdong Wang,et al.  Locking-free stabilized conforming nodal integration for meshfree Mindlin-Reissner plate formulation , 2004 .

[21]  J.S. Chen,et al.  A meshfree‐enriched finite element method for compressible and near‐incompressible elasticity , 2012 .

[22]  Magdalena Ortiz,et al.  Local maximum‐entropy approximation schemes: a seamless bridge between finite elements and meshfree methods , 2006 .

[23]  A. Rosolen,et al.  An adaptive meshfree method for phase-field models of biomembranes. Part II: A Lagrangian approach for membranes in viscous fluids , 2013, J. Comput. Phys..

[24]  T. Belytschko,et al.  Element‐free Galerkin methods , 1994 .

[25]  Wing Kam Liu,et al.  Reproducing kernel particle methods , 1995 .

[26]  C. T. Wu,et al.  A generalized approximation for the meshfree analysis of solids , 2011 .

[27]  Multi-scale finite element analysis of acoustic waves using global residual-free meshfree enrichments , 2013 .

[28]  Guirong Liu,et al.  A face‐based smoothed finite element method (FS‐FEM) for 3D linear and geometrically non‐linear solid mechanics problems using 4‐node tetrahedral elements , 2009 .

[29]  J. Monaghan.  Why Particle Methods Work , 1982 .

[30]  Jiun-Shyan Chen,et al.  A stabilized conforming nodal integration for Galerkin mesh-free methods , 2001 .

[31]  J. Monaghan.  SPH without a Tensile Instability , 2000 .

[32]  K. Y. Dai,et al.  A Smoothed Finite Element Method for Mechanics Problems , 2007 .

[33]  K. K. Pandey,et al.  Effect of the surfactant CTAB on the high pressure behavior of CdS nano particles , 2012 .

[34]  C. T. Wu,et al.  On the analysis of dispersion property and stable time step in meshfree method using the generalized meshfree approximation , 2011 .

[35]  L. Libersky,et al.  High strain Lagrangian hydrodynamics: a three-dimensional SPH code for dynamic material response , 1993 .

[36]  Jiun-Shyan Chen,et al.  Non‐linear version of stabilized conforming nodal integration for Galerkin mesh‐free methods , 2002 .

[37]  T. Belytschko,et al.  Consistent pseudo-derivatives in meshless methods , 1997 .

[38]  C. T. Wu,et al.  Meshfree-enriched simplex elements with strain smoothing for the finite element analysis of compressible and nearly incompressible solids , 2011 .

[39]  Yong Guo,et al.  A Coupled Meshfree/Finite Element Method for Automotive Crashworthiness Simulations , 2009 .

[40]  Thomas Slawson,et al.  Semi-Lagrangian reproducing kernel particle method for fragment-impact problems , 2011 .

[41]  Sivakumar Kulasegaram,et al.  Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulations , 2000 .

[42]  R. P. Ingel,et al.  An approach for tension instability in smoothed particle hydrodynamics (SPH) , 1995 .

[43]  Ted Belytschko,et al.  A unified stability analysis of meshless particle methods , 2000 .

[44]  S. Attaway,et al.  Smoothed particle hydrodynamics stability analysis , 1995 .