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

Chandra, Bodhinanda; Singer, Veronika; Teschemacher, Tobias; Wüchner, Roland; Larese, Antonia

doi:10.1007/s11440-020-01123-3

Cited by 24 publications

(27 citation statements)

References 63 publications

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“…Three-dimensional granular column collapse has been frequently investigated in both experiments [46][47][48] and numerical simulations, [48][49][50][51] which can be used as another benchmark test for the proposed framework. During the collapse process, the soil may simultaneously exhibit solid-like and fluid-like characteristics, making it challenging to predict by a single constitutive model.…”

Section: Granular Column Collapsementioning

confidence: 99%

Scalable three‐dimensional hybrid continuum‐discrete multiscale modeling of granular media

Liang

Zhao

et al. 2022

Numerical Meth Engineering

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This study presents a scalable three‐dimensional (3D) multiscale framework for continuum‐discrete modeling of granular materials. The proposed framework features rigorous coupling of a continuum‐based material point method (MPM) and a discrete approach discrete element method (DEM) to enable cross‐scale modeling of boundary value problems pertaining to granular media. It employs MPM to solve the governing equations of a macroscopic continuum domain for a boundary value problem that may undergo large deformation. The required loading‐path‐dependent constitutive responses at each material point of the MPM are provided by a DEM solution based on grain‐scale contact‐based discrete simulations that receive macroscopic information at the specific material point as boundary conditions. This hierarchical coupling enables direct dialogs between the macro and micro scales of granular media while fully harnessing the predictive advantages of both MPM and DEM at the two scales. An effective, scalable parallel scheme is further developed, based on the flat message passing interface (MPI) model, to address the computational cost of the proposed framework for 3D large‐scale simulations. We demonstrate that the proposed parallel scheme may offer up to 32X and 40X speedup in strong and weak scaling tests, respectively, significantly empowering the numerical performance and predictive capability of the proposed framework. The 3D parallelized multiscale framework is validated by an element test and a column collapse problem, before being applied to simulate the intrusion of a solid object. The multiscale simulation successfully captures the characteristic response of intrusion as postulated by the modified Archimedes' law theory. The progressive development of the stagnant zone during the intrusion is further examined from a cross‐scale perspective.

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Section: Granular Column Collapsementioning

confidence: 99%

Scalable three‐dimensional hybrid continuum‐discrete multiscale modeling of granular media

Liang

Zhao

et al. 2022

Numerical Meth Engineering

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“…However, as the material points move independently of the grid, the boundaries do not necessarily coincide with the nodes of the background grid leading to the necessity of imposing in-homogeneous or non-conforming boundary conditions for the general case. Several attempts have been made to address this issue, just mentioning among them the Penalty Method [49] for the weak imposition of Dirichlet conditions, and [50] to impose moving Neumann boundary conditions.…”

Section: Boundary Conditions In Mpmmentioning

confidence: 99%

A partitioned material point method and discrete element method coupling scheme

Singer

Sautter

Larese

et al. 2022

Adv. Model. and Simul. in Eng. Sci.

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Mass-movement hazards involving fast and large soil deformation often include huge rocks or other significant obstacles increasing tremendously the risks for humans and infrastructures. Therefore, numerical investigations of such disasters are in high economic demand for prediction as well as for the design of countermeasures. Unfortunately, classical numerical approaches are not suitable for such challenging multiphysics problems. For this reason, in this work we explore the combination of the Material Point Method, able to simulate elasto-plastic continuum materials and the Discrete Element Method to accurately calculate the contact forces, in a coupled formulation. We propose a partitioned MPM-DEM coupling scheme, thus the solvers involved are treated as black-box solvers, whereas the communication of the involved sub-systems is shifted to the shared interface. This approach allows to freely choose the best suited solver for each model and to combine the advantages of both physics in a generalized manner. The examples validate the novel coupling scheme and show its applicability for the simulation of large strain flow events interacting with obstacles.

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“…For the imposition of Dirichlet Boundary conditions a penalty augmentation is a suitable method and its accuracy has been proven in [10]. Using those introduced boundary particles, moving boundaries, slip boundaries as well as releasing-contact conditions can be realized, by penalty augmentation.…”

Section: Boundary Conditions In Mpmmentioning

confidence: 99%

A Staggered Coupling Scheme of the Material Point Method and the Finite Element Method using Gauss Seidel Communication Pattern

Singer¹,

Chandra²,

Wüchner³

et al. 2021

9th Edition of the International Conference on Computational Methods for Coupled Problems in Science and Engineering

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The goal of the present work is the simulation mass movement hazards, involving fast and large soil deformation, interacting with flexible protection structures. For the simulation of those large deformation phenomena, involving complex history dependent material laws, the Material Point Method (MPM) is a powerful method, as the particles move trough a fixed background mesh. This allows to overcome the classical limitation of the Finite Element Method (FEM) related to mesh distortion in large strain problems. Therefore, a staggered or partitioned coupling scheme is proposed, combining the advantages of FEM and MPM by solving both models separately using their respective established environment, whereas the communication between the two fields is achieved by mapping boundary conditions on the shared interface. In this work a Gauss-Seidel communication pattern is considered, leading to the necessity of imposing Dirichlet Boundary Conditions on one interface (in this study: FEM) and Neumann Boundary Conditions on the corresponding counterpart (in this study: MPM). For validation purposes, a structural example with analytical solution is chosen.

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

Cited by 24 publications

References 63 publications

Scalable three‐dimensional hybrid continuum‐discrete multiscale modeling of granular media

Scalable three‐dimensional hybrid continuum‐discrete multiscale modeling of granular media

A partitioned material point method and discrete element method coupling scheme

A Staggered Coupling Scheme of the Material Point Method and the Finite Element Method using Gauss Seidel Communication Pattern

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