Abstract
A multiscale meshfree particle method is developed, which includes recent advances in SPH and other meshfree research efforts. Key features will include linear consistency, stability, and both local and global conservation properties. In addition, through the incorporation of Reproducing Kernal Particle Method (RKPM), standard moving least squares (MLS) enhancement and wavelet techniques, the method have the flexibility of resolving multiple scales in the solution of complex, multiple physics processes. We present the application of this approach in the following areas: 1) simulations on propagation of dynamic fracture and shear band; 2) impact and penetration; 3) fluid dynamics and 4) nano-mechanics.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
M. Bar-Lev and H.T. Yang. Initial flow field over an impulsively started circular cylinder. Journal of Fluid Mechanics, 72:625–647, 1975.
T. Belytschko and T. Tabbara. Dynamic fracture using efg. IJNME, 39:3, 1996.
J.S. Chen, C. Pan, C.T. Wu, and W.K. Liu. Reproducing kernel particle methods for large deformation analysis of nonlinear structures. Computer Methods in Applied Mechanics and Engineering, 139:195–227, 1996.
W.M. Collins and S.C.R. Dennis. The initial flow past an impulsively started circular cylinder. Quarterly Journal of Mechanics and Applied Mathematics, 26:53–75, 1973a.
W.M. Collins and S.C.R. Dennis. Flow past an impulsively started circular cylinder. Journal of Fluid Mechanics, 60:105–127, 1973b.
S. Hao, W.K. Liu, P. Klein, and D. Qian. Multi-scale damage model, manuscript to be submitted, 2001.
S. Hao, H. Park, and W.K. Liu. Moving particle finite element method, submitted, 2001.
S. Jun, W.K. Liu, and T. Belytschko. Explicit reproducing kernel particle methods for large deformation problems. International Journal for Numerical Methods in Engineering, 41:137–166, 1998.
J.F. Kalthoff and S. Winkler. Failure mode transition at high rates of shear loading. C. Y. Chiem, H.D. Kunze and L. W. Meyer, edts., Impact Loading and Dynamic Behavior of Materials, 1:185–195, 1987a.
P.A. Klein. Technical Report. Sandia National Laboratories, 1999.
S. Li and W.K. Liu. Meshfree and particle methods and their applications. accepted for publication in Applied Mechanics Review, 2001.
12. S. Li, W.K. Liu, D. Qian, P. Guduru, and R. Rosakis. Dynamic shear band propogation and micro-structure of adiabatic shear band. Comp. Meth. In Applied Mech. Engrg, in press, 2001.
S. Li, W.K. Liu, A. Rosakis, T. Belytschko, and W. Hao. Meshfree galerkin simulations of dynamic shear band propagation and failure mode transition. accepted for publication in Journal of Mechanics and Physics of Solids, 2000.
W.K. Liu and Y. Chen. Wavelet and multiple scale reproducing kernel methods. International Journal for Numerical Methods in Engineering, 21:901-931, 1995.
W.K. Liu, Y. Chen, R.A. Uras, and C.T. Chang. Generalized multiple scale reproducing kernel particle methods. Computer Methods in Applied Mechanics and Engineering, 139:91–158, 1996.
W.K. Liu and S. Jun. Multiple scale reproducing kernel particle methods for large deformation problems. International Journal for Numerical Methods in Engineering, 41:1339–1362, 1998.
W.K. Liu, S. Jun, J. Adee, and T. Belytschko. Reproducing kernel particle methods for structural dynamics. International Journal for Numerical Methods in Engineering, 38:1655–1680, 1995.
W.K. Liu, S, Jun, D.T. Sihling, Y. Chen, and W. Hao. Multiresolution reproducing kernel particle method for computational fluid dynamics. International Journal of Numerical Method in Fluids, 24:1391–1415, 1997.
W.K. Liu, S. Jun, and Y.F. Zhang. Reproducing kernel particle methods. International Journal for Numerical Methods in Engineering, 20:1081-1106, 1995.
W.K. Liu, R.A. Uras, and Y. Chen. Enrichment of the finite element method with the reproducing kernel particle method. Journal of Applied Mechanics, ASME, 64:861–870, 1997.
J.J. Mason, A.J. Rosakis, and G. Ravinchandran. Full field measurement of the dynamic deformation field around a growing adiabatic shear band at the tip of a dynamically loaded crack or notch. Journal of Mechanics and Physics of Solids, 42:1679–1697, 1994.
D. Qian, W.K. Liu, and R.S. Ruoff. Mechanics of nanotubes filled with fullerenes. accepted for publication in Journal of Physical Chemistry B, 2001.
K. Ravi-Chandar. On the failure mode transition in polycarbonate dynamic mixed-mode loading. International Journal of Solids and Structures, 32:925–938, 1995.
A.J. Rosakis. Private communication. 2000,
J. Sloan, R.E. Dunin-Borkowski, J.L. Hutchinson, K.S. Coleman, V.C. Williams, J.B. Claridge, A.P.E. York, C. Xu, S.R. Bailey, G. Brown, S. Fridrichs, and M.L.H. Green. The size distribution, imaging and obstructing properties of c60 and higher fullerenes formed within arc-growth single walled carbon nanotubes. Chemical Physics Letters, 316:191–198, 2000.
B.W. Smith, M. Monthoux, and D.E. Luzzi. Encapsulated c60 in carbon nanotubes. Nature, 336:323, 1998.
G. J. Wagner and W.K. Liu. Application of essential boundary conditions in mesh-free methods: a corrected collocation method. International Journal for Numerical Methods in Engineering, 47:1367–1379, 2000.
G.J. Wagner and W.K. Liu. Hierachical enrichment for bridging scales and meshfree boundary conditions. International Journal for Numerical Methods in Engineering, 50:507–524, 2000.
M.F. Yu, M.J. Dyer, D. Qian, W.K. Liu, and R.S. Ruoff. Locked twist in multi-walled carbon nanotube ribbons, accepted for publication in Physical Review B, Rapid Communications, 2001.
L.T. Zhang, G.J. Wagner, and W.K. Liu. A parallelized meshfree method with boundary enrichment for large-scale cfd. submitted to Journal of Computational Physics, 2000.
Y. Zhang, S. Iijima, Z. Shi, and Z. Gu. Defects in arc-discharg-produced single-walled carbon nanotubes. Philosophical Magazine Letters, 79:473–479, 1999.
M. Zhou, A.J. Rosakis, and G. Ravichandran. Dynamically propagating shear bands in impact-loaded prenotched plates -i, experimental investigations of temperature signatures and propagation speed. Journal of Mechanics of Physics and Solids, 44:981–1006, 1996a.
M. Zhou, A.J. Rosakis, and G. Ravichandran. Dynamically propagating shear bands in impact-loaded prenotched plates -ii, numerical simulations. Journal of Mechanics of Physics and Solids, 44:1007–1032, 1996b.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhang, L.T., Liu, W.K., Li, S.F., Qian, D., Hao, S. (2003). Survey of Multi-Scale Meshfree Particle Methods. In: Griebel, M., Schweitzer, M.A. (eds) Meshfree Methods for Partial Differential Equations. Lecture Notes in Computational Science and Engineering, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56103-0_30
Download citation
DOI: https://doi.org/10.1007/978-3-642-56103-0_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43891-5
Online ISBN: 978-3-642-56103-0
eBook Packages: Springer Book Archive