A Penalty Function Method for Modelling Frictional Contact in MPM

Hamad, Fursan; Giridharan, Shreyas; Moormann, Christian

doi:10.1016/j.proeng.2017.01.038

Cited by 16 publications

(7 citation statements)

References 21 publications

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“…Subsequently, the usage of Eulerian computational mesh in MPM automatically eliminates the problem of mesh entanglement. It also makes treating fictional contacts between bodies straightforward and efficient (Hamad et al, 2017). Because most MPM algorithms were derived from FEM, transitioning to MPM seems more natural than other meshless methods.…”

Section: Materials Point Methodsmentioning

confidence: 99%

Comparison of Material Point Method and Finite Element Method for Post-Failure Large Deformation Geotechnical Analysis

Sunanhadikusuma

Tjung

Lim

2022

jcef

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Finite Element Method (FEM) has been the state-of-the-art method in geotechnical analysis since it first formulated in the 40s. It capable to handle Multiphysics simulation, soil-structure and soil-water interaction, and time history analysis. Though powerful, the standard Lagrangian FEM suffers mesh distortion when handling large strain deformation problem. This mesh entanglement problem makes post-failure analysis is considerably challenging to model if not impossible to do using FEM. The Material Point Method (MPM) then later introduced to solve these large strain deformation problems. Adapted from the Particle in Cell (PIC) method, MPM is a hybrid method that combines Eularian and Lagrangian approach by utilizing moving material points which are moving over spatially fixed computational mesh. This approach enables MPM to calculate not only fluid mechanics such in PIC but also solid mechanics and its intermediatory states. To demonstrate the capability of MPM and its consistency with FEM in geotechnical analysis, this article presents a comparison of FEM and MPM analysis on a hypothetical slope using Mohr-Coulomb constitutive model. The simulation shows that both FEM and MPM analyses are consistent to each other especially in small strain scheme. However, in large strain deformation, MPM is still able to get convergent result while FEM is not. The MPM simulation is also able to animate post failure behavior clearly, calculate post-failure strains and stresses distribution, and present final geometry of the model.

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Section: Materials Point Methodsmentioning

confidence: 99%

Comparison of Material Point Method and Finite Element Method for Post-Failure Large Deformation Geotechnical Analysis

Sunanhadikusuma

Tjung

Lim

2022

jcef

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“…This is the main motivation behind the choice of implicit boundary imposition by means of penalty method proposed in the current work. The penalty method has been previously used just for contact algorithm in explicit [70,71] and implicit [72] MPM. The method works seamlessly within the nonlinear implicit MPM framework established earlier for Dirichlet boundary enforcement.…”

Section: Nonconforming Boundary Enforcementmentioning

confidence: 99%

Nonconforming Dirichlet boundary conditions in implicit material point method by means of penalty augmentation

et al. 2021

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In many geomechanics applications, material boundaries are subjected to large displacements and deformation. Under these circumstances, the application of boundary conditions using particle methods, such as the material point method (MPM), becomes a challenging task since material boundaries do not coincide with the background mesh. This paper presents a formulation of penalty augmentation to impose nonhomogeneous, nonconforming Dirichlet boundary conditions in implicit MPM. The penalty augmentation is implemented utilizing boundary particles, which can move either according to or independently from the material deformation. Furthermore, releasing contact boundary condition, as well as the capability to accommodate slip boundaries, is introduced in the current work. The accuracy of the proposed method is assessed in both 2D and 3D cases, by convergence analysis reaching the analytical solution and by comparing the results of nonconforming and classical grid-conforming simulations.

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“…Although the imposition of nonhomogeneous boundary conditions can be realized by embedding other media into the continuum body, 24,25 it is difficult to handle more complex problems involving various types of boundary conditions in this way. Since the challenge explained above is widely encountered in mesh‐free methods, 26‐28 several approaches, such as the penalty method, the method of Lagrange multiplier and Nitsche's method, 29 have been studied for imposing Dirichlet boundary conditions, and these approaches have been applied to MPM frameworks 30‐32 . However, even though Dirichlet boundary conditions are properly handled, another problem arises.…”

Section: Introductionmentioning

confidence: 99%

Extended B‐spline‐based implicit material point method enhanced by F‐bar projection method to suppress pressure oscillation

Sugai

Han

Yamaguchi

et al. 2023

Numerical Meth Engineering

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An enhancement of the extended B-spline-based implicit material point method (EBS-MPM) is developed to avoid pressure oscillation and volumetric locking. The EBS-MPM is a stable implicit MPM that enables the imposition of arbitrary boundary conditions thanks to the higher-order EBS basis functions and the help of Nitsche's method. In particular, by means of the higher-order EBS basis functions, the EBS-MPM can suppress the cell-crossing errors caused by material points crossing the background grid boundaries and can avoid both the stress oscillations arising from inaccurate numerical integration and the ill-conditioning of the resulting tangent matrices. Although the higher-order EBS basis functions are known to avoid volumetric locking, the problem of pressure oscillation has not yet been resolved. Therefore, to suppress pressure oscillation due to quasi-incompressibility, we propose the incorporation of the F-bar projection method into the EBS-MPM, which is compatible with the higher-order EBS basis functions. Three representative numerical examples are presented to demonstrate the capability of the proposed method in suppressing both the pressure oscillation and volumetric locking. The results of the proposed method are compared to those of the finite element method with F-bar elements and those of isogeometric analysis with quadratic NURBS elements.

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A Penalty Function Method for Modelling Frictional Contact in MPM

Cited by 16 publications

References 21 publications

Comparison of Material Point Method and Finite Element Method for Post-Failure Large Deformation Geotechnical Analysis

Comparison of Material Point Method and Finite Element Method for Post-Failure Large Deformation Geotechnical Analysis

Nonconforming Dirichlet boundary conditions in implicit material point method by means of penalty augmentation

Extended B‐spline‐based implicit material point method enhanced by F‐bar projection method to suppress pressure oscillation

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