IGA-MPM: The Isogeometric Material Point Method

Moutsanidis, Georgios; Long, Christopher C.; Bazilevs, Yuri

doi:10.1016/j.cma.2020.113346

IGA-MPM: The Isogeometric Material Point Method

Journal Article · Sat Aug 22 00:00:00 EDT 2020 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2020.113346· OSTI ID:1711396

^[1]; ^[2]; Bazilevs, Yuri ^[3]

Stony Brook Univ., NY (United States)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Brown Univ., Providence, RI (United States)

In this work, we propose the use of Isogeometric Analysis (IGA) within the context of the Material Point Method (MPM), and refer to the approach as IGA-MPM. We use the idea of IGA, and its instantiation based on Non-Uniform Rational B-Splines (NURBS), to build higher-order accurate and smooth approximation for MPM. Higher-order smoothness yields a continuous representation of the strain rate, and, as a result, prevents jumps in the stress and other history variables as the material points cross the element boundaries. Furthermore, NURBS can exactly represent all conic sections and the corresponding symmetries in the solution, which may be important in some applications. Several numerical examples of increasing complexity are presented, and show the ability of IGA-MPM to eliminate the well known cell-crossing instability of the conventional MPM. In addition, the examples presented demonstrate improved accuracy, convergence, and symmetry preservation of IGA-MPM compared to the conventional MPM, both for rectilinear and curved geometries.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA). Office of Defense Nuclear Nonproliferation R&D (NA-22)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1711396

Alternate ID(s):: OSTI ID: 1809310

Report Number(s):: LA-UR--20-23322

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Vol. 372; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (33)

Fluid-membrane interaction based on the material point method York, Allen R.; Sulsky, Deborah; Schreyer, Howard L. International Journal for Numerical Methods in Engineering, Vol. 48, Issue 6 https://doi.org/10.1002/(SICI)1097-0207(20000630)48:6<901::AID-NME910>3.0.CO;2-T	journal	June 2000
Analysis and reduction of quadrature errors in the material point method (MPM) Steffen, Michael; Kirby, Robert M.; Berzins, Martin International Journal for Numerical Methods in Engineering, Vol. 76, Issue 6 https://doi.org/10.1002/nme.2360	journal	November 2008
A convected particle domain interpolation technique to extend applicability of the material point method for problems involving massive deformations Sadeghirad, A.; Brannon, R. M.; Burghardt, J. International Journal for Numerical Methods in Engineering, Vol. 86, Issue 12 https://doi.org/10.1002/nme.3110	journal	March 2011
An accelerated, convergent, and stable nodal integration in Galerkin meshfree methods for linear and nonlinear mechanics: ACCELERATED, CONVERGENT, STABLE NODAL INTEGRATION IN MESHFREE METHODS Hillman, Michael; Chen, Jiun-Shyan International Journal for Numerical Methods in Engineering, Vol. 107, Issue 7 https://doi.org/10.1002/nme.5183	journal	December 2015
Field-gradient partitioning for fracture and frictional contact in the material point method: Field-gradient partitioning for fracture and frictional contact in the material point method Homel, Michael A.; Herbold, Eric B. International Journal for Numerical Methods in Engineering, Vol. 109, Issue 7 https://doi.org/10.1002/nme.5317	journal	August 2016
Enhancement of the material point method using B-spline basis functions Gan, Yong; Sun, Zheng; Chen, Zhen International Journal for Numerical Methods in Engineering, Vol. 113, Issue 3 https://doi.org/10.1002/nme.5620	journal	July 2017
A new formulation for air-blast fluid–structure interaction using an immersed approach. Part I: basic methodology and FEM-based simulations Bazilevs, Y.; Kamran, K.; Moutsanidis, G. Computational Mechanics, Vol. 60, Issue 1 https://doi.org/10.1007/s00466-017-1394-3	journal	March 2017
A new formulation for air-blast fluid–structure interaction using an immersed approach: part II—coupling of IGA and meshfree discretizations Bazilevs, Y.; Moutsanidis, G.; Bueno, J. Computational Mechanics, Vol. 60, Issue 1 https://doi.org/10.1007/s00466-017-1395-2	journal	March 2017
Modelling of landslides with the material-point method Andersen, S.; Andersen, L. Computational Geosciences, Vol. 14, Issue 1 https://doi.org/10.1007/s10596-009-9137-y	journal	April 2009
Application of a particle-in-cell method to solid mechanics Sulsky, Deborah; Zhou, Shi-Jian; Schreyer, Howard L. Computer Physics Communications, Vol. 87, Issue 1-2 https://doi.org/10.1016/0010-4655(94)00170-7	journal	May 1995
On calculating with B-splines de Boor, Carl Journal of Approximation Theory, Vol. 6, Issue 1 https://doi.org/10.1016/0021-9045(72)90080-9	journal	July 1972
Mass matrix formulation of the FLIP particle-in-cell method Burgess, D.; Sulsky, D.; Brackbill, J. U. Journal of Computational Physics, Vol. 103, Issue 1 https://doi.org/10.1016/0021-9991(92)90323-Q	journal	November 1992
A particle method for history-dependent materials Sulsky, D.; Chen, Z.; Schreyer, H. L. Computer Methods in Applied Mechanics and Engineering, Vol. 118, Issue 1-2 https://doi.org/10.1016/0045-7825(94)90112-0	journal	September 1994
Reproducing Kernel Particle Methods for large deformation analysis of non-linear structures Chen, Jiun-Shyan; Pan, Chunhui; Wu, Cheng-Tang Computer Methods in Applied Mechanics and Engineering, Vol. 139, Issue 1-4 https://doi.org/10.1016/S0045-7825(96)01083-3	journal	December 1996
The material-point method for granular materials Bardenhagen, S. G.; Brackbill, J. U.; Sulsky, D. Computer Methods in Applied Mechanics and Engineering, Vol. 187, Issue 3-4 https://doi.org/10.1016/S0045-7825(99)00338-2	journal	July 2000
Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement Hughes, T. J. R.; Cottrell, J. A.; Bazilevs, Y. Computer Methods in Applied Mechanics and Engineering, Vol. 194, Issue 39-41 https://doi.org/10.1016/j.cma.2004.10.008	journal	October 2005
Isogeometric analysis using T-splines Bazilevs, Y.; Calo, V. M.; Cottrell, J. A. Computer Methods in Applied Mechanics and Engineering, Vol. 199, Issue 5-8 https://doi.org/10.1016/j.cma.2009.02.036	journal	January 2010
Isogeometric analysis using LR B-splines Johannessen, Kjetil André; Kvamsdal, Trond; Dokken, Tor Computer Methods in Applied Mechanics and Engineering, Vol. 269 https://doi.org/10.1016/j.cma.2013.09.014	journal	February 2014
PetIGA: A framework for high-performance isogeometric analysis Dalcin, L.; Collier, N.; Vignal, P. Computer Methods in Applied Mechanics and Engineering, Vol. 308 https://doi.org/10.1016/j.cma.2016.05.011	journal	August 2016
Modeling strong discontinuities in the material point method using a single velocity field Moutsanidis, Georgios; Kamensky, David; Zhang, Duan Z. Computer Methods in Applied Mechanics and Engineering, Vol. 345 https://doi.org/10.1016/j.cma.2018.11.005	journal	March 2019
Analysis of spatial interpolation in the material-point method Andersen, S.; Andersen, L. Computers & Structures, Vol. 88, Issue 7-8 https://doi.org/10.1016/j.compstruc.2010.01.004	journal	April 2010
Material point method applied to multiphase flows Zhang, Duan Z.; Zou, Qisu; VanderHeyden, W. Brian Journal of Computational Physics, Vol. 227, Issue 6, p. 3159-3173 https://doi.org/10.1016/j.jcp.2007.11.021	journal	March 2008
An evaluation of explicit time integration schemes for use with the generalized interpolation material point method Wallstedt, P. C.; Guilkey, J. E. Journal of Computational Physics, Vol. 227, Issue 22 https://doi.org/10.1016/j.jcp.2008.07.019	journal	November 2008
Material point method enhanced by modified gradient of shape function Zhang, Duan Z.; Ma, Xia; Giguere, Paul T. Journal of Computational Physics, Vol. 230, Issue 16 https://doi.org/10.1016/j.jcp.2011.04.032	journal	July 2011
Isogeometric analysis of Lagrangian hydrodynamics: Axisymmetric formulation in the rz-cylindrical coordinates Bazilevs, Y.; Long, C. C.; Akkerman, I. Journal of Computational Physics, Vol. 262 https://doi.org/10.1016/j.jcp.2014.01.001	journal	April 2014
Hyperbolic phase field modeling of brittle fracture: Part II—immersed IGA–RKPM coupling for air-blast–structure interaction Moutsanidis, Georgios; Kamensky, David; Chen, J. S. Journal of the Mechanics and Physics of Solids, Vol. 121 https://doi.org/10.1016/j.jmps.2018.07.008	journal	December 2018
An Implicit High-order Material Point Method Motlagh, Yousef G.; Coombs, William M. Procedia Engineering, Vol. 175 https://doi.org/10.1016/j.proeng.2017.01.003	journal	January 2017
A High Order Material Point Method Tielen, Roel; Wobbes, Elizaveta; Möller, Matthias Procedia Engineering, Vol. 175 https://doi.org/10.1016/j.proeng.2017.01.022	journal	January 2017
Impact of cylinders on a rigid boundary Wilkins, Mark L.; Guinan, Michael W. Journal of Applied Physics, Vol. 44, Issue 3 https://doi.org/10.1063/1.1662328	journal	March 1973
The Numerical Evaluation of B -Splines Cox, M. G. IMA Journal of Applied Mathematics, Vol. 10, Issue 2 https://doi.org/10.1093/imamat/10.2.134	journal	January 1972
ISOGEOMETRIC ANALYSIS: APPROXIMATION, STABILITY AND ERROR ESTIMATES FOR h-REFINED MESHES Bazilevs, Y.; BeirÃO Da Veiga, L.; Cottrell, J. A. Mathematical Models and Methods in Applied Sciences, Vol. 16, Issue 07 https://doi.org/10.1142/S0218202506001455	journal	July 2006
Adaptive isogeometric methods with hierarchical splines: Error estimator and convergence Buffa, Annalisa; Giannelli, Carlotta Mathematical Models and Methods in Applied Sciences, Vol. 26, Issue 01 https://doi.org/10.1142/S0218202516500019	journal	November 2015
A material point method for snow simulation Stomakhin, Alexey; Schroeder, Craig; Chai, Lawrence ACM Transactions on Graphics, Vol. 32, Issue 4 https://doi.org/10.1145/2461912.2461948	journal	July 2013

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42 ENGINEERING
Cell-Crossing Instability
Isogeometric Analysis
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