2008
DOI: 10.1002/nme.2360
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Analysis and reduction of quadrature errors in the material point method (MPM)

Abstract: SUMMARYThe material point method (MPM) has demonstrated itself as a computationally effective particle method for solving solid mechanics problems involving large deformations and/or fragmentation of structures, which are sometimes problematic for finite element methods (FEMs). However, similar to most methods that employ mixed Lagrangian (particle) and Eulerian strategies, analysis of the method is not straightforward. The lack of an analysis framework for MPM, as is found in FEMs, makes it challenging to exp… Show more

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Cited by 244 publications
(221 citation statements)
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“…while this is a reasonable approximation for compressible flow, and was first used by Kim [11], it represents a departure from the standard MPM approach for solid mechanics, in which the volumes associated with particles are tracked, see [16], for an analysis of this case. The particle's mass is calculated from the density and the volume of the particle as…”
Section: Application To Gas Dynamicsmentioning
confidence: 99%
See 1 more Smart Citation
“…while this is a reasonable approximation for compressible flow, and was first used by Kim [11], it represents a departure from the standard MPM approach for solid mechanics, in which the volumes associated with particles are tracked, see [16], for an analysis of this case. The particle's mass is calculated from the density and the volume of the particle as…”
Section: Application To Gas Dynamicsmentioning
confidence: 99%
“…This method of force calculation has been developed here as being more appropriate for compressible gas dynamics as it assumes that the particles within a cell have the same volume. Analysis and investigation of alternative methods for solid mechanics and different approaches to gas dynamics are provided by [6,13,16].…”
Section: Application To Gas Dynamicsmentioning
confidence: 99%
“…For example, B-splines have been shown to decrease quadrature errors and improve the spatial convergence rates for many MPM problems [11]. A typical one-dimensional quadratic B-spline can be constructed by convolving piecewise-constant basis functions with themselves:…”
Section: Standard Mpmmentioning
confidence: 99%
“…While CD was shown to have the lowest error of the time-stepping methods in their tests, the method showed no temporal error convergence in the regions of time-step selection where their simulations were stable. This paper seeks to use and extend the perspective on the spatial errors gained in [11,12] to understand the lack of temporal convergence demonstrated in [7]. The inspiration for connecting the spatial error characteristics with the temporal error characteristics lies outside the MPM literature.…”
Section: Introductionmentioning
confidence: 99%
“…In this work the shape functions used are cubic BSplines [4], [5] . They have been shown to reduce the quadrature errors and the grid crossing errors associated with discontinuous shape functions.…”
Section: Ifmentioning
confidence: 99%