An evaluation of explicit time integration schemes for use with the generalized interpolation material point method

Wallstedt, P. C.; Guilkey, James

doi:10.1016/j.jcp.2008.07.019

Cited by 106 publications

(84 citation statements)

References 15 publications

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“…Using the cpGIMP, Wallstedt and Guilkey [23] demonstrated that the USL scheme performs dramatically better than an alternative 'update stress first (USF)' scheme.…”

Section: Review Of the Mpm And Gimp Methodsmentioning

confidence: 99%

“…This allows verification of nonlinear codes or algorithms by running them with the computed external force and demonstrating that the assumed solution is recovered. Two examples constructed based on the MMS in this paper are similar to those that were constructed and described by Wallstedt and Guilkey [23] for studying the effects of different time integration schemes in the GIMP algorithm. The following error norm was adopted to investigate spatial convergence of these two examples: (27) in which N t and N p are total number of particles and time steps, respectively, u app (x p , t i ) and u exact (x p , t i ) are the calculated and analytical displacement vectors, respectively.…”

Section: Numerical Examplesmentioning

confidence: 97%

“…The first two examples were constructed based on the method of manufactured solutions (MMS) [23,30]. In the MMS, the solution of the model equations is assumed a priori, then the external force required to achieve this solution is analytically determined.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Another method for changing particle size has been proposed and is described in [21]. This method is not investigated here because it likewise has the shortcoming of neglecting shear distortion and has some challenging issues reported in [23] even in comparison to cpGIMP.…”

Section: Introductionmentioning

confidence: 99%

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A convected particle domain interpolation technique to extend applicability of the material point method for problems involving massive deformations

Sadeghirad

Brannon

Burghardt

2011

Numerical Meth Engineering

302

243

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SUMMARYA new algorithm is developed to improve the accuracy and efficiency of the material point method for problems involving extremely large tensile deformations and rotations. In the proposed procedure, particle domains are convected with the material motion more accurately than in the generalized interpolation material point method. This feature is crucial to eliminate instability in extension, which is a common shortcoming of most particle methods. Also, a novel alternative set of grid basis functions is proposed for efficiently calculating nodal force and consistent mass integrals on the grid. Specifically, by taking advantage of initially parallelogram-shaped particle domains, and treating the deformation gradient as constant over the particle domain, the convected particle domain is a reshaped parallelogram in the deformed configuration. Accordingly, an alternative grid basis function over the particle domain is constructed by a standard 4-node finite element interpolation on the parallelogram. Effectiveness of the proposed modifications is demonstrated using several large deformation solid mechanics problems.

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“…Using the cpGIMP, Wallstedt and Guilkey [23] demonstrated that the USL scheme performs dramatically better than an alternative 'update stress first (USF)' scheme.…”

Section: Review Of the Mpm And Gimp Methodsmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 97%

Section: Numerical Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A convected particle domain interpolation technique to extend applicability of the material point method for problems involving massive deformations

Sadeghirad

Brannon

Burghardt

2011

Numerical Meth Engineering

302

243

View full text Add to dashboard Cite

show abstract

“…Compared to the original Update-Stress-First algorithm by Wallstedt and Guilkey (2008), a large gain in numerical stability and accuracy is obtained at the cost of slightly increased computational effort, for more details see Nairn (2003). In a first step, the new particle velocities are again interpolated to the grid nodes:…”

Section: Computation Of Velocity Gradientmentioning

confidence: 99%

Development and validation of a meshless 3D material point method for simulating the micro-milling process

Leroch¹,

Eder²,

Ganzenmüller³

et al. 2018

Preprint

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A meshless Generalized Interpolation Material Point Method for simulating the micro-milling process was developed. This method has several advantages over well-established approaches (such as finite elements) when it comes to large plastic strains and deformations, since it inherently does not suffer from tensile instability problems. The feasibility of the developed material point model for simulating micro-milling is verified against finite element simulations and experimental data. The model is able to successfully predict experimentally measured cutting forces and determine chip temperatures in agreement with conventional finite element simulations. After having verified the approach, the model was applied to perform extensive numerical 3D simulations of the micro-milling process. The goal is to evaluate the response of the micromilling cutting forces as function of the hardening behavior of the micro-milled material. The meshless 3D simulations reveal a dependency of tool force slopes (with respect to the uncut chip thickness) on the hardening parameters. Based on these findings, a new approach is outlined to determine hardening parameters directly from two micro-milling experiments with distinct, sufficiently large uncut chip thicknesses.

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Numerical simulation of granular mixing in a rotary drum using a generalized interpolation material point method

Zuo

Gong

Xie

2020

Asia-Pacific J Chem Eng

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Numerical simulations using a generalized interpolation material point method (GIMP) and material point method were introduced into the studying of granular mixing in a rotary drum. A Drucker–Prager model that has an equal size with a Mohr–Coulomb criterion was adopted to predict the failure behavior of granular matter. Experiments and discrete element method simulations were conducted to validate the models, and GIMP was finally used due to its accuracy and the ability for eliminating the crossing boundary noise. Velocity field of bed surface and standard deviation were used to measure the mixing performance. In particular, the influence of mesh size, elastic modulus, cohesion, and filling level were investigated. The results of simulations show that the utilization of GIMP significantly reduces the computing cost of simulation. The analysis of mixing performance shows that mixing performance decreases with the increase of elastic moduli, cohesion of granular matter, and filling levels.

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An evaluation of explicit time integration schemes for use with the generalized interpolation material point method

Cited by 106 publications

References 15 publications

A convected particle domain interpolation technique to extend applicability of the material point method for problems involving massive deformations

A convected particle domain interpolation technique to extend applicability of the material point method for problems involving massive deformations

Development and validation of a meshless 3D material point method for simulating the micro-milling process

Numerical simulation of granular mixing in a rotary drum using a generalized interpolation material point method

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