New and Advanced Numerical Strategies for the Simulation of Material Forming

In recent years new and advanced numerical strategies have opened new possibilities in the simulation of forming processes. Multiscale descriptions, meshless methods and enhanced finite element approaches are some techniques that have contributed to the enhancement of forming process simulations. These approaches will be revisited in this chapter.

[1]  Mark A Fleming,et al.  Smoothing and accelerated computations in the element free Galerkin method , 1996 .

[2]  Alex M. Andrew,et al.  Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (2nd edition) , 2000 .

[3]  D. Ryckelynck,et al.  A priori hyperreduction method: an adaptive approach , 2005 .

[4]  Icíar Alfaro,et al.  Updated Lagrangian free surface flow simulations with natural neighbour Galerkin methods , 2004 .

[5]  Martin J. Mohlenkamp,et al.  Algorithms for Numerical Analysis in High Dimensions , 2005, SIAM J. Sci. Comput..

[6]  Francisco Chinesta,et al.  Accounting for incompressibility in reproducing kernel particle meshless approximations , 2006 .

[7]  Jie Zhou,et al.  3D FEM simulation of the whole cycle of aluminium extrusion throughout the transient state and the steady state using the updated Lagrangian approach , 2003 .

[8]  B. Nayroles,et al.  Generalizing the finite element method: Diffuse approximation and diffuse elements , 1992 .

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

[10]  Grégory Legrain,et al.  Fracture with large deformation using X-FEM , 2004 .

[11]  Eugenio Oñate,et al.  The particle finite element method: a powerful tool to solve incompressible flows with free‐surfaces and breaking waves , 2004 .

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

[13]  Eugenio Oñate,et al.  The meshless finite element method , 2003 .

[14]  David Ryckelynck,et al.  Deterministic Approach of the Multi Bead-Spring Polymer Models , 2005 .

[15]  O. Pironneau,et al.  Computational Methods for Option Pricing (Frontiers in Applied Mathematics) (Frontiers in Applied Mathematics 30) , 2005 .

[16]  Francisco Chinesta,et al.  A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modelling of complex fluids - Part II: Transient simulation using space-time separated representations , 2007 .

[17]  Jiun-Shyan Chen,et al.  Analysis of metal forming process based on meshless method , 1998 .

[18]  Bamin Khomami,et al.  Brownian dynamics simulations of bead-rod and bead-spring chains: numerical algorithms and coarse-graining issues , 2002 .

[19]  Francisco Chinesta,et al.  On the Reduction of Kinetic Theory Models Related to Finitely Extensible Dumbbells , 2006 .

[20]  Elías Cueto,et al.  Natural element meshless simulation of flows involving short fiber suspensions , 2003 .

[21]  Philippe Lorong,et al.  Meshless Methods and Partition of Unity Finite Elements , 2005 .

[22]  T. Hughes,et al.  The variational multiscale method—a paradigm for computational mechanics , 1998 .

[23]  Åke Björck,et al.  The calculation of linear least squares problems , 2004, Acta Numerica.

[24]  T. Belytschko,et al.  THE NATURAL ELEMENT METHOD IN SOLID MECHANICS , 1998 .

[25]  M. Ortiz,et al.  An adaptive finite element approach to atomic-scale mechanics—the quasicontinuum method , 1997, cond-mat/9710027.

[26]  Hans-Joachim Bungartz,et al.  Acta Numerica 2004: Sparse grids , 2004 .

[27]  Cédric Chauvière,et al.  Simulation of dilute polymer solutions using a Fokker–Planck equation , 2004 .

[28]  Miguel Ángel Martínez,et al.  Overview and recent advances in natural neighbour galerkin methods , 2003 .

[29]  I. Babuska,et al.  The generalized finite element method , 2001 .

[30]  F. Chinesta,et al.  A new extension of the natural element method for non‐convex and discontinuous problems: the constrained natural element method (C‐NEM) , 2004 .

[31]  Manuel Laso,et al.  “SMART” POLYMERS IN FINITE-ELEMENT CALCULATIONS , 1992 .

[32]  H. Bungartz,et al.  Sparse grids , 2004, Acta Numerica.

[33]  Wing Kam Liu,et al.  Reproducing kernel particle methods for structural dynamics , 1995 .

[34]  Yves Achdou,et al.  Computational Methods for Option Pricing (Frontiers in Applied Mathematics) (Frontiers in Applied Mathematics 30) , 2005 .

[35]  Cédric Chauvière,et al.  A fast solver for Fokker-Planck equation applied to viscoelastic flows calculations , 2003 .

[36]  Paulo A.F. Martins,et al.  Steady and non-steady state analysis of bulk forming processes by the reproducing kernel particle method , 2005 .

[37]  L. Gary Leal,et al.  Smoothed particle hydrodynamics techniques for the solution of kinetic theory problems: Part 2. The effect of flow perturbations on the simple shear behavior of LCPs , 1999 .

[38]  Manuel Doblaré,et al.  Imposing essential boundary conditions in the natural element method by means of density-scaled?-shapes , 2000 .

[39]  Ashok Srinivasan,et al.  Smoothed particle hydrodynamics techniques for the solution of kinetic theory problems Part 1: Method , 1997 .

[40]  Francisco Chinesta,et al.  Deterministic particle approach of Multi Bead-Spring polymer models , 2006 .

[41]  Elías Cueto,et al.  Induced Anisotropy in Foams Forming Processes: Modelling and Simulation , 2004 .

[42]  J. Rojek,et al.  Numerical simulation of sand mould manufacture for Lost Foam Casting process , 2003 .

[43]  Ted Belytschko,et al.  A finite element method for crack growth without remeshing , 1999 .

[44]  Elías Cueto,et al.  10th Esaform Conference on Material Forming , 2007 .

[45]  Francisco Chinesta,et al.  Thermomechanical Cutting Model Discretisation. Eulerian or Lagrangian, Mesh or Meshless? , 2004 .

[46]  R. Keunings.  MICRO-MACRO METHODS FOR THE MULTISCALE SIMULATION OF VISCOELASTIC FLOW USING MOLECULAR MODELS OF KINETIC THEORY , 2004 .

[47]  I. Babuska,et al.  ON THE ANGLE CONDITION IN THE FINITE ELEMENT METHOD , 1976 .