Dynamic Meshing for Material Point Method Computations
This paper presents strategies for dynamically creating, managing and removing mesh cells during computations in the context of the Material Point Method (MPM). The dynamic meshing approach has been developed to help address problems involving motion of a finite size body in unbounded domains in which the extent of material travel and deformation is unknown a priori, such as in the case of landslides and debris flows. The key idea is to efficiently instantiate and search only cells that contain material points, thereby avoiding unneeded storage and computation. Mechanisms for doing this efficiently are presented, and example problems are used to demonstrate the effectiveness of dynamic mesh management relative to alternative approaches.
[1] D. Sulsky, Z. Chen, and H. L. Schreyer, "A particle method for historydependent
materials," Computer Methods in Applied Mechanics and
Engineering, vol. 118, no. 1-2, pp. 179-196, 1994.
[2] D. Sulsky, S. Zhou, and H. L. Schreyer, "Application of a particle-incell
method to solid mechanics," Computer Physics Communications,
vol. 87, no. 1-2, pp. 236-252, 1995.
[3] W.-K. Shin, "Numerical simulation of landslides and debris flows using
an enhanced material point method," Ph.D. dissertation, University of
Washington, 2009.
[4] P. Mackenzie-Helnwein, P. Arduino, W. Shin, J. A. Moore, and G. R.
Miller, "Modeling strategies for multiphase drag interactions using the
material point method," International Journal for Numerical Methods in
Engineering, 2010, in print.
[5] S. Bardenhagen, J. U. Brackbill, and D. Sulsky, "The material point
method for granular materials," Computer Methods in Applied Mechanics
and Engineering, vol. 187, no. 3-4, pp. 529-541, 2000.
[6] S. Bardenhagen, J. Guilkey, K. Roessig, J. Brackbill, W. Witzel, and
J. Foster, "An improved contact algorithm for the material point method
and application to stress propagation in granular material," Computer
Modeling in Engineering & Sciences, vol. 2, pp. 509-522, 2001.
[7] W. Hu and Z. Chen, "A multi-mesh MPM for simulating the meshing
process of spur gears," Computers & Structures, vol. 81, no. 20, pp.
1991-2002, 2003.
[8] J. A. Nairn, "Material point method calculations with explicit cracks,"
Computer Modeling in Engineering and Sciences, vol. 4, pp. 649-664,
2003.
[9] M. Steffen, R. M. Kirby, and M. Berzins, "Analysis and reduction of
quadrature error in the material point method (MPM)," Int. J. Numer.
Meth. Engng., vol. 76, no. 6, pp. 922-948, 2008.
[10] Y. Zhang, J. Guilkey, J. Hoying, and W. J.A., "Mechanical simulation
of multicellular structures with the material point method," in c-
CMBBE2004, March 2004, p. (6 pages).
[11] J. Bentley and J. H. Friedman, "Data structures for range searching,"
Computing Surveys, vol. 11, no. 4, pp. 397-409, 1979.
[12] S. Lefebvre and H. Hoppe, "Perfect spatial hashing," ACM SIGGRAPH,
pp. 579-588, 2006.
[13] T. Harada, S. Koshizuka, and Y. Kawaguchi, "Sliced data structure for
particle-based simulations on gpus," in GRAPHITE -07: Proceedings of
the 5th international conference on Computer graphics and interactive
techniques in Australia and Southeast Asia. New York, NY, USA:
ACM, 2007, pp. 55-62.
[14] D. A.Watt, Programming Language Concepts and Paradigms. Prentice-
Hall, 1990.
[15] B. Stroustrup, The C++ Programming Language, 3rd ed. Addison-
Wesley Professional, 1997.
[1] D. Sulsky, Z. Chen, and H. L. Schreyer, "A particle method for historydependent
materials," Computer Methods in Applied Mechanics and
Engineering, vol. 118, no. 1-2, pp. 179-196, 1994.
[2] D. Sulsky, S. Zhou, and H. L. Schreyer, "Application of a particle-incell
method to solid mechanics," Computer Physics Communications,
vol. 87, no. 1-2, pp. 236-252, 1995.
[3] W.-K. Shin, "Numerical simulation of landslides and debris flows using
an enhanced material point method," Ph.D. dissertation, University of
Washington, 2009.
[4] P. Mackenzie-Helnwein, P. Arduino, W. Shin, J. A. Moore, and G. R.
Miller, "Modeling strategies for multiphase drag interactions using the
material point method," International Journal for Numerical Methods in
Engineering, 2010, in print.
[5] S. Bardenhagen, J. U. Brackbill, and D. Sulsky, "The material point
method for granular materials," Computer Methods in Applied Mechanics
and Engineering, vol. 187, no. 3-4, pp. 529-541, 2000.
[6] S. Bardenhagen, J. Guilkey, K. Roessig, J. Brackbill, W. Witzel, and
J. Foster, "An improved contact algorithm for the material point method
and application to stress propagation in granular material," Computer
Modeling in Engineering & Sciences, vol. 2, pp. 509-522, 2001.
[7] W. Hu and Z. Chen, "A multi-mesh MPM for simulating the meshing
process of spur gears," Computers & Structures, vol. 81, no. 20, pp.
1991-2002, 2003.
[8] J. A. Nairn, "Material point method calculations with explicit cracks,"
Computer Modeling in Engineering and Sciences, vol. 4, pp. 649-664,
2003.
[9] M. Steffen, R. M. Kirby, and M. Berzins, "Analysis and reduction of
quadrature error in the material point method (MPM)," Int. J. Numer.
Meth. Engng., vol. 76, no. 6, pp. 922-948, 2008.
[10] Y. Zhang, J. Guilkey, J. Hoying, and W. J.A., "Mechanical simulation
of multicellular structures with the material point method," in c-
CMBBE2004, March 2004, p. (6 pages).
[11] J. Bentley and J. H. Friedman, "Data structures for range searching,"
Computing Surveys, vol. 11, no. 4, pp. 397-409, 1979.
[12] S. Lefebvre and H. Hoppe, "Perfect spatial hashing," ACM SIGGRAPH,
pp. 579-588, 2006.
[13] T. Harada, S. Koshizuka, and Y. Kawaguchi, "Sliced data structure for
particle-based simulations on gpus," in GRAPHITE -07: Proceedings of
the 5th international conference on Computer graphics and interactive
techniques in Australia and Southeast Asia. New York, NY, USA:
ACM, 2007, pp. 55-62.
[14] D. A.Watt, Programming Language Concepts and Paradigms. Prentice-
Hall, 1990.
[15] B. Stroustrup, The C++ Programming Language, 3rd ed. Addison-
Wesley Professional, 1997.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:59287", author = "Wookuen Shin and Gregory R. Miller and Pedro Arduino and Peter Mackenzie-Helnwein", title = "Dynamic Meshing for Material Point Method Computations", abstract = "This paper presents strategies for dynamically creating, managing and removing mesh cells during computations in the context of the Material Point Method (MPM). The dynamic meshing approach has been developed to help address problems involving motion of a finite size body in unbounded domains in which the extent of material travel and deformation is unknown a priori, such as in the case of landslides and debris flows. The key idea is to efficiently instantiate and search only cells that contain material points, thereby avoiding unneeded storage and computation. Mechanisms for doing this efficiently are presented, and example problems are used to demonstrate the effectiveness of dynamic mesh management relative to alternative approaches.
", keywords = "Numerical Analysis, Material Point Method, Large Deformations, Moving Boundaries.", volume = "4", number = "8", pages = "1170-9", }
