A new method for material point method particle updates that reduces noise and enhances stability

Abstract Current material point method (MPM) particle updates use a PIC approach, a FLIP approach, or a linear combination of PIC and FLIP. A PIC update filters velocity in each time step, which causes unwanted numerical diffusion, while FLIP eliminates that diffusion, but may retain too much noise. This paper develops a new particle update termed XPIC( m ) (for eXtended PIC of order m ) because it generalizes PIC updates. XPIC(1) is identical to current PIC methods, but higher orders of XPIC( m ) address the over filtering and numerical diffusion of PIC, while still filtering out noise caused by the nontrivial null space of the extrapolation matrix used in MPM. As m → ∞ , XPIC( m ) converges to a modified FLIP update with orthogonal removal of null space noise. The frequency response and filtering properties of XPIC( m ) are investigated and several numerical examples demonstrate its advantages over other update methods.

[1]  Huang Yuan,et al.  Application of material point methods for cutting process simulations , 2012 .

[2]  Song Lin,et al.  Numerical simulation of explosive welding using the material point method , 2011 .

[3]  D. Sulsky,et al.  A particle method for history-dependent materials , 1993 .

[4]  Alexey Stomakhin,et al.  A material point method for snow simulation , 2013, ACM Trans. Graph..

[5]  Pedro Arduino,et al.  Avalanche and landslide simulation using the material point method: flow dynamics and force interaction with structures , 2014, Computational Geosciences.

[6]  J. Nairn.  Numerical Simulations of Transverse Compression and Densification in Wood , 2006 .

[7]  J. Nairn,et al.  Modeling Imperfect Interfaces in the Material PointMethod using Multimaterial Methods , 2013 .

[8]  John A. Nairn,et al.  Simulation of dynamic fracture with the Material Point Method using a mixed J-integral and cohesive law approach , 2011 .

[9]  James B Hoying,et al.  Computational modeling of multicellular constructs with the material point method. , 2006, Journal of biomechanics.

[10]  Jacques Laskar,et al.  Recent formation and evolution of northern Martian polar layered deposits as inferred from a Global Climate Model , 2007 .

[11]  Martin Berzins,et al.  Examination and Analysis of Implementation Choices within the Material Point Method (MPM) , 2008 .

[12]  R. Ogden.  Non-Linear Elastic Deformations , 1984 .

[13]  John A. Nairn,et al.  Material Point Method Calculations with Explicit Cracks , 2003 .

[14]  S. Bardenhagen,et al.  The Generalized Interpolation Material Point Method , 2004 .

[15]  John A. Nairn,et al.  Material point method simulations of transverse fracture in wood with realistic morphologies , 2007 .

[16]  D. Sulsky,et al.  Using the material‐point method to model sea ice dynamics , 2007 .

[17]  J. Brackbill,et al.  FLIP: A method for adaptively zoned, particle-in-cell calculations of fluid flows in two dimensions , 1986 .

[18]  P. Wriggers,et al.  IMPROVING ACCURACY IN PARTICLE METHODS USING NULL SPACES AND FILTERS , 2015 .

[19]  Philipp Birken,et al.  Numerical Linear Algebra , 2011, Encyclopedia of Parallel Computing.

[20]  James E. Guilkey,et al.  An Improved Contact Algorithm for the Material Point Method and Application to Stress Propagation in Granular Material , 2001 .

[21]  A. Sadeghirad,et al.  A convected particle domain interpolation technique to extend applicability of the material point method for problems involving massive deformations , 2011 .

[22]  J. Brackbill,et al.  Flip: A low-dissipation, particle-in-cell method for fluid flow , 1988 .

[23]  John A. Nairn,et al.  Numerical Simulation of Orthogonal Cutting using the Material Point Method , 2015 .

[24]  J. Brackbill,et al.  The material-point method for granular materials , 2000 .

[25]  Xavier Frank,et al.  New modelling approaches to predict wood properties from its cellular structure: image-based representation and meshless methods , 2015, Annals of Forest Science.

[26]  Adi Ben-Israel,et al.  Generalized inverses: theory and applications , 1974 .