Meshfree and particle methods and their applications - TAM ...

18 Li and Liu: Meshfree and particle methods and applications Appl Mech Rev vol 55, no 1, January 2002
It is worth mentioning that Hao et al 280 used RKPM
combined with finite element method in a micro-mechanics
damage simulation. In that study, a multiple scale RKPM is
used to simulate a ductile fracture process involving damage
evolution, and multiresolution analysis has also been performed
on shear bands formation. The numerical results
show that the multiple scale RKPM possesses a strong ability
to capture physical phenomena such as shear band, large
deformation, and the material instability during damage evolution.
Zhang et al 283 used EFG to model the jointed rock
structures; Aluru 96 used RKPM to analyze microelectromechanical
system. Danielson et al 284,285 has been developing
a new communication scheme for parallel implementation
of RKPM formulation. They have tested a quarter
million particle computations in Cray T3E supercomputer in
simulations of shear band and fracture. Recently, Zhang et al
286 have developed a parallel version of 3D RKPM code
in implicit CFD calculation, which has the capacity to deal
with more than one million particles. A novel procedure of
implementing the essential boundary condition by using the
bridging scale hierarchical enrichment, and the associated
parallel communication with different processors is presented
in that paper.
A simple illustration of the multiresolution meshfree
method is given in Figs. 12 and 13. Figure 12 depicts the
analysis of large deformation solids and the plastic deformation
of a notched bar. The high scale solution Fig. 12c is an
extraction from the total solution Fig. 12b. It shows the
crack tip field and the localized shear bands. The quantitative
experimental result is given in Fig. 12a. Similarly, Fig. 13a
depicts the high scale solution obtained by wavelets decomposition
of the total scale solution for the pressure from the
analysis of the compressible flow-structure interaction. This
figure, labeled High scale clearly indicates the shock location
and this solution can be used as an error indicator to guide
the adaptivity which is simply implemented by addition of
appropriately placed particles in the meshfree method. The
total solution is given in Fig. 13b.
Due to the difficulties in imposing essential boundary
conditions, a special meshfree contact algorithm is needed
Fig. 11
Meshfree simulation of curved dynamic shear band: a experimental observation; b meshfree calculation 248
Fig. 12
Multi-scale Meshfree Simulation of strain localization of three point bending test