Energy conservation and accuracy of some MPM formulations

Berzins, Martin

doi:10.1007/s40571-021-00457-3

Cited by 8 publications

(3 citation statements)

References 14 publications

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“…For example, when combined with a lumped mass matrix, the USL approach leads to excessive energy dissipation 22 . However, the USL approach is often preferred as the dissipation is consistent with the accuracy of the solution and it tends to damped unresolved modes 22,43 . Differences between USF and USL, alongside the MUSL approach, 18 will be explored in more detail as part of the numerical analyses presented in Section 5, including a study on the energy conserving nature of the approaches with both lumped and consistent mass matrices.…”

Section: Materials Point Methodsmentioning

confidence: 99%

Ghost stabilisation of the material point method for stable quasi‐static and dynamic analysis of large deformation problems

Coombs

2023

Numerical Meth Engineering

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The unstable nature of the material point method (MPM) is widely documented and is a barrier to the method being used for routine engineering analyses of large deformation problems. The vast majority of articles concerning this issue are focused on the instabilities that manifest when a material point crosses between background grid cells. However, there are other issues related to the stability of MPMs. This article focuses on the issue of the conditioning of the global system of equations caused by the arbitrary nature of the position of the physical domain relative to the background computational grid. The issue is remedied here via the use of a ghost stabilisation technique that penalises variations in the gradient of the solution field near the boundaries of the physical domain. This technique transforms the stability of the MPM, providing a robust computational framework for large deformation explicit dynamic and implicit quasi‐static analysis.

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Section: Materials Point Methodsmentioning

confidence: 99%

Ghost stabilisation of the material point method for stable quasi‐static and dynamic analysis of large deformation problems

Coombs

2023

Numerical Meth Engineering

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“…It will also be assumed that periodic boundary conditions exist, together with appropriate initial conditions. The approach used corresponds to a stress-last [2] or a symplectic Euler A method [3]. Following Bardenhagen [2] it is preferable to increment stress last and to use the GIMP method for spatial discretization.…”

Section: Mpm Model Problemmentioning

confidence: 99%

Error Estimation for the Material Point and Particle in Cell Methods

Berzins¹

2023

XI International Conference on Adaptive Modeling and Simulation

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“…An affine and a polynomial mapping was later added to the B-Splines MPM [22,23] resulting in an angular momentum-conserving model. Other studies explored least squares techniques [24], enabling the recovery of the affine/polynomial splines MPM [25], and the effect of spatial and temporal discretization errors, as well as the application of symplectic integrators [26]. In light of these developments, MPM represents an effective method for the simulation of a wide range of materials and phenomena.…”

Section: Introductionmentioning

confidence: 99%

GPUs Based Material Point Method for Compressible Flows

Baioni,

Benacchio,

Capone

et al. 2023

VIII International Conference on Particle-Based Methods

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Particle-In-Cell (PIC) methods such as the Material Point Method (MPM) can be cast in formulations suitable to the requirements of data locality and fine-grained parallelism of modern hardware accelerators such as Graphics Processing Units (GPUs). While continuum mechanics simulations have already shown the capabilities of MPM on a wide range of phenomena, the use of the method in compressible gas dynamics is less frequent. This contribution aims to show the potential of a GPU-based MPM parallel implementation for compressible fluid dynamics, as well as to assess the reliability of this approach in reproducing supersonic gas flows against solid obstacles. The results in the paper represent a stepping stone towards a highly parallel, Multi-GPU, MPM-base solver for M ach > 1 Fluid-Structure Interaction problems.

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Energy conservation and accuracy of some MPM formulations

Cited by 8 publications

References 14 publications

Ghost stabilisation of the material point method for stable quasi‐static and dynamic analysis of large deformation problems

Ghost stabilisation of the material point method for stable quasi‐static and dynamic analysis of large deformation problems

Error Estimation for the Material Point and Particle in Cell Methods

GPUs Based Material Point Method for Compressible Flows

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