Preliminary effort in developing the smoothed material point method for impact

He, Lisha; Gan, Yong; Chen, Zhen

doi:10.1007/s40571-018-0197-4

Cited by 8 publications

(4 citation statements)

References 22 publications

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“…To infer a target density p(x) with x ∈ R d , we can represent the gradient field of log p(x), also termed score [16,24] in statistics, as a time-invariant, external force field 21 , i.e. f ext (x) = ∇x log p(x), and use MPM to evolve the IPS under internal and external effects 22 . It is expected that, some transient or terminal (steady) configuration of the particles, i.e.…”

Section: Mpm-based Sampling: Methodologymentioning

confidence: 99%

“…Also, MPM simulation requires less tricky ad hoc parameters than SPH [13]; typical hyper-parameters for MPM are the mesh spacing and time step. A combined SPH-MPM method, which exhibits superior performance over SPH and MPM, has been developed [59,22]. There are efforts [86] to develop hybrid methods which couple MPM with other particle modelling methods for improved efficiency, e.g.…”

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confidence: 99%

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The Material Point Method

Zhang¹,

Chen²,

Liao³

et al. 2017

The Material Point Method

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Section: Mpm-based Sampling: Methodologymentioning

confidence: 99%

mentioning

confidence: 99%

The Material Point Method

Zhang¹,

Chen²,

Liao³

et al. 2017

The Material Point Method

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“…As material points act as quadrature points, moving arbitrarily across the background approximation, they often locate suboptimally for integration in the Galerkin weak form, leading to violations of Galerkin exactness [17], and resulting in low accuracy and suboptimal convergence properties. While approaches such as B-Spline basis [18], Generalized Interpolation Material Point (GIMP) [16], Isogeometric Analysis (IGA) [19], and others [20,21,22] can mitigate the cell-crossing instability, they do not consistently restore optimal accuracy and convergence properties because the integration scheme of the weak form still violates Galerkin exactness. Recently, Rodriguez and Huang [17] introduced the reproducing kernel (RK) approximation [23,24] into the MPM framework.…”

Section: Introductionmentioning

confidence: 99%

A Blended Variationally Consistent Phase Field Material Point Method for Material Fragmentation Problems

Tangade,

Huang,

Rodriguez

2024

Preprint

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The material point method (MPM) can effectively addresses material fragmentation issues over mesh-based method due to its meshfree nature but faces numerical inaccuracies such as cell-crossing instability and Galerkin inexactness inherent in its numerical framework. The utilization of previously developed variational consistent (VC) corrections with smooth reproducing kernel (RK) approximations has proven effective in preventing cell-crossing and ensuring Galerkin exactness, albeit limited to continuum bodies. In this study, we present a blended variationally consistent phase field material point method for modeling material fragmentation process. The phase field damage method is integrated into MPM to facilitate the tracking of damage/cracks during the fragmentation process. The incorporation of VC correction alongside smooth RK approximation offers benefits not only for non-oscillatory stress modes but also for robust phase field evolution. To address the complexities of VC in handling domain boundary tracking during fragmentation, we introduce a deformation-driven blending scheme to seamlessly blend non-VC for fragmented regions and VC for continuous domains with a smooth transition zone in the Galerkin MPM. This approach enhances the stability and robustness of the formulation for simulating fragmentation problems. Benchmark examples involving extreme deformation scenarios illustrate the effectiveness of the proposed MPM framework, confirming its consistency and stability.

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“…Impact problems (similar to the SHPB experiment) represent a well-suited use case for MPM because of the high deformations that occur, as shown, e.g. in [6,10].…”

mentioning

confidence: 99%

Modeling of the Split-Hopkinson-Pressure-Bar experiment with the explicit material point method

Niekamp

Bergmann²,

Pöhl

et al. 2021

Comp. Part. Mech.

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The material point method (MPM) represents an alternative discretization method for numerical simulations. It aims to combine the benefits of a Lagrangian representation of bodies and an Eulerian numerical solution approach. Therefore, especially at high material deformations the method is not prone to mesh distortions such as the finite element method (FEM). For this reason, the MPM is used to a great extent for modeling granular materials as in geo-mechanics. However, high deformations occur in many industrial processes on metallic materials. The Split-Hopkinson-Pressure-Bar (SHPB) experiment is used to characterize material properties at high deformation rates. Although widely used, this experiment is not yet standardized and shows a variety of sensitivities, e.g. to friction. Inter alia for this reason, simulations are conducted with the experiment to allow for a better evaluation of the measured data. The purpose of this work from an engineering point of view is to analyze the performance of the MPM on an SHPB experiment. In order to validate the experimental results for the material characterization under dynamic loading conditions we introduce frictional contact. We use arbitrary tri-linear brick domains in a 3D CPDI1 scheme, instead of originally used parallelepipeds. This allows for a more flexible geometry approximation using standard meshes. The results of the method are analyzed with respect to discretization sensitivity and discussed in the context of the experimental results for a 42CrMo4 steel. We were able to show that the method is capable to reproduce the SHPB experiment. Additionally the method shows convergency in the results with finer discretizations. Thus, the MPM has underlined its importance as an alternative simulation technique for problems with high deformation.

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Preliminary effort in developing the smoothed material point method for impact

Cited by 8 publications

References 22 publications

The Material Point Method

The Material Point Method

A Blended Variationally Consistent Phase Field Material Point Method for Material Fragmentation Problems

Modeling of the Split-Hopkinson-Pressure-Bar experiment with the explicit material point method

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