Meshless Methods for Large Deformation Elastodynamics

Meshless methods are a promising candidate to reliably simulate materials undergoing large deformations. Unlike mesh based methods like the FEM, meshless methods are not limited in the amount of deformation they can reproduce since there are no mesh regularity constraints to consider. However, other numerical issues like zero energy modes, the tensile instability and disorder of the discretization points due to the deformation may impose limits on the deformations possible. It is thus worthwhile to benchmark a wide array of these methods since a proper review to this end has been missing from the literature so far. In the interest of reproducibility, the complete source code of all methods considered is made public.

[1]  Soheil Mohammadi,et al.  A STABILIZED PARTICLE METHOD FOR LARGE DEFORMATION DYNAMIC ANALYSIS OF STRUCTURES , 2012 .

[2]  Renato Pajarola,et al.  A unified particle model for fluid–solid interactions , 2007, Comput. Animat. Virtual Worlds.

[3]  A. Connolly,et al.  Godunov SPH with an operator-splitting procedure for materials with strength , 2014 .

[4]  G. R. Johnson,et al.  NORMALIZED SMOOTHING FUNCTIONS FOR SPH IMPACT COMPUTATIONS , 1996 .

[5]  Paul W. Cleary,et al.  Modelling of metal forging using SPH , 2012 .

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

[7]  K. Miller,et al.  A meshless Total Lagrangian explicit dynamics algorithm for surgical simulation , 2010 .

[8]  Petros Koumoutsakos,et al.  Remeshed smoothed particle hydrodynamics simulation of the mechanical behavior of human organs. , 2004, Technology and health care : official journal of the European Society for Engineering and Medicine.

[9]  L. Lucy.  A numerical approach to the testing of the fission hypothesis. , 1977 .

[10]  J. K. Chen,et al.  A generalized smoothed particle hydrodynamics method for nonlinear dynamic problems , 2000 .

[11]  Karol Miller,et al.  A three-dimensional nonlinear meshfree algorithm for simulating mechanical responses of soft tissue , 2014 .

[12]  J. Owen,et al.  Adaptive Smoothed Particle Hydrodynamics: Methodology. II. , 1995, astro-ph/9512078.

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

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

[15]  P. W. Randles,et al.  Normalized SPH with stress points , 2000 .

[16]  Petros Koumoutsakos,et al.  Vortex Methods: Theory and Practice , 2000 .

[17]  Daniel J. Price,et al.  Smoothed Particle Magnetohydrodynamics – II. Variational principles and variable smoothing-length terms , 2003, astro-ph/0310790.

[18]  Konrad Wegener,et al.  Simulation of single grain cutting using SPH method , 2010 .

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

[20]  Matthias Teschner,et al.  Corotated SPH for Deformable Solids , 2009, NPH.

[21]  Daniel J. Price.  Smoothed particle hydrodynamics and magnetohydrodynamics , 2010, J. Comput. Phys..

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

[23]  Ted Belytschko,et al.  Material stability analysis of particle methods , 2005, Adv. Comput. Math..

[24]  Vishal Mehra,et al.  Tensile Instability and Artificial Stresses in Impact Problems in SPH , 2012 .

[25]  J. Monaghan,et al.  SPH elastic dynamics , 2001 .

[26]  Nader A. Issa,et al.  Fluid motion generated by impact , 2003 .

[27]  J. Monaghan.  Smoothed particle hydrodynamics , 2005 .

[28]  P. M. Naghdi,et al.  On the time derivative of tensors in mechanics of continua , 1961 .

[29]  Marc Duflot,et al.  Meshless methods: A review and computer implementation aspects , 2008, Math. Comput. Simul..

[30]  Marc Alexa,et al.  Point based animation of elastic, plastic and melting objects , 2004, SCA '04.

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

[32]  Daniel J. Price,et al.  Smoothed particle magnetohydrodynamics - III. Multidimensional tests and the B = 0 constraint , 2005, astro-ph/0509083.

[33]  D. J. Pope,et al.  SECOND ORDER GODUNOV SPH FOR HIGH VELOCITY IMPACT DYNAMICS , 2013 .

[34]  Li Guangyao,et al.  3D adaptive RKPM method for contact problems with elastic–plastic dynamic large deformation , 2009 .

[35]  Wing Kam Liu,et al.  Nonlinear Finite Elements for Continua and Structures , 2000 .

[36]  Rade Vignjevic,et al.  A Frictionless Contact Algorithm for Meshless Methods , 2007 .

[37]  Rade Vignjevic,et al.  A contact algorithm for smoothed particle hydrodynamics , 2000 .

[38]  Martin W. Heinstein,et al.  An analysis of smoothed particle hydrodynamics , 1994 .

[39]  J. K. Chen,et al.  A corrective smoothed particle method for transient elastoplastic dynamics , 2001 .

[40]  V. Springel,et al.  Cosmological smoothed particle hydrodynamics simulations: the entropy equation , 2001, astro-ph/0111016.

[41]  Adnan Eghtesad,et al.  Study of dynamic behavior of ceramic–metal FGM under high velocity impact conditions using CSPM method , 2012 .

[42]  Prabhu Ramachandran,et al.  Approximate Riemann solvers for the Godunov SPH (GSPH) , 2014, J. Comput. Phys..

[43]  J. K. Chen,et al.  Completeness of corrective smoothed particle method for linear elastodynamics , 1999 .

[44]  Jon Louis Bentley,et al.  Multidimensional binary search trees used for associative searching , 1975, CACM.

[45]  N. Aluru,et al.  On the Equivalence Between Least-Squares and Kernel Approximations in Meshless Methods , 2001 .

[46]  Joseph John Monaghan,et al.  SPH and Riemann Solvers , 1997 .

[47]  Juan R. Reveles.  Development of a total Lagrangian SPH code for the simulation of solids under dynamic loading , 2007 .

[48]  H. Wang,et al.  Development of parallel 3D RKPM meshless bulk forming simulation system , 2007, Adv. Eng. Softw..

[49]  Markus H. Gross,et al.  Meshless deformations based on shape matching , 2005, ACM Trans. Graph..

[50]  J. Bonet,et al.  Variational and momentum preservation aspects of Smooth Particle Hydrodynamic formulations , 1999 .

[51]  Larry D. Libersky,et al.  Smooth particle hydrodynamics with strength of materials , 1991 .

[52]  L. Libersky,et al.  Smoothed Particle Hydrodynamics: Some recent improvements and applications , 1996 .

[53]  Isaac Fried,et al.  A note on elastic energy density functions for largely deformed compressible rubber solids , 1988 .

[54]  P. M. Naghdi,et al.  SOME REMARKS ON ELASTIC-PLASTIC DEFORMATION AT FINITE STRAIN , 1971 .

[55]  Konrad Wegener,et al.  Simulation of Hexa-Octahedral Diamond Grain Cutting Tests Using the SPH Method☆ , 2013 .

[56]  Ted Belytschko,et al.  ON THE COMPLETENESS OF MESHFREE PARTICLE METHODS , 1998 .

[57]  J. Monaghan.  Simulating Free Surface Flows with SPH , 1994 .

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

[59]  J. Monaghan.  SPH compressible turbulence , 2002, astro-ph/0204118.

[60]  S. Miyama,et al.  Numerical Simulation of Viscous Flow by Smoothed Particle Hydrodynamics , 1994 .

[61]  Mark A Fleming,et al.  Meshless methods: An overview and recent developments , 1996 .

[62]  J. Monaghan,et al.  Shock simulation by the particle method SPH , 1983 .

[63]  Soheil Mohammadi,et al.  A field smoothing stabilization of particle methods in elastodynamics , 2008 .

[64]  P. Koumoutsakos,et al.  A Lagrangian particle level set method. , 2005 .

[65]  Daniel J. Price,et al.  Smoothed Particle Magnetohydrodynamics , 2004 .

[66]  P. W. Randles,et al.  On Neighbors, Derivatives, and Viscosity in Particle Codes , 1999 .

[67]  D. Shepard.  A two-dimensional interpolation function for irregularly-spaced data , 1968, ACM National Conference.

[68]  Guangyao Li,et al.  Element‐free Galerkin method for contact problems in metal forming analysis , 2001 .

[69]  J. K. Chen,et al.  An improvement for tensile instability in smoothed particle hydrodynamics , 1999 .

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

[71]  Ted Belytschko,et al.  Explicit Reproducing Kernel Particle Methods for large deformation problems , 1998 .

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

[73]  Not Available Not Available.  Meshfree particle methods , 2000 .

[74]  J. K. Chen,et al.  A corrective smoothed particle method for boundary value problems in heat conduction , 1999 .

[75]  G. R. Johnson,et al.  A CONSTITUTIVE MODEL AND DATA FOR METALS SUBJECTED TO LARGE STRAINS, HIGH STRAIN RATES AND HIGH TEMPERATURES , 2018 .

[76]  J. Monaghan.  On the problem of penetration in particle methods , 1989 .

[77]  J. Michael Owen,et al.  Adaptive smoothed particle hydrodynamics, with application to cosmology: Methodology , 1996 .

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

[79]  Petros Koumoutsakos,et al.  A Lagrangian particle method for the simulation of linear and nonlinear elastic models of soft tissue , 2008, J. Comput. Phys..