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Nonconforming Dirichlet boundary conditions in implicit material point method by means of penalty augmentation
https://orcid.org/https://orcid.org/0000-0003-2537-8213
https://orcid.org/https://orcid.org/0000-0002-4525-1271
https://orcid.org/https://orcid.org/0000-0002-5411-9715
https://orcid.org/https://orcid.org/0000-0002-7284-3926
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.
Nonconforming Dirichlet boundary conditions in implicit material point method by means of penalty augmentation
https://orcid.org/https://orcid.org/0000-0003-2537-8213
https://orcid.org/https://orcid.org/0000-0002-4525-1271
https://orcid.org/https://orcid.org/0000-0002-5411-9715
https://orcid.org/https://orcid.org/0000-0002-7284-3926
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.
Nonconforming Dirichlet boundary conditions in implicit material point method by means of penalty augmentation
https://orcid.org/https://orcid.org/0000-0003-2537-8213
https://orcid.org/https://orcid.org/0000-0002-4525-1271
https://orcid.org/https://orcid.org/0000-0002-5411-9715
https://orcid.org/https://orcid.org/0000-0002-7284-3926
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.
Nonconforming Dirichlet boundary conditions in implicit material point method by means of penalty augmentation
Acta Geotech.
Chandra, Bodhinanda (author) / Singer, Veronika (author) / Teschemacher, Tobias (author) / Wüchner, Roland (author) / Larese, Antonia (author)
Acta Geotechnica ; 16 ; 2315-2335
2021-08-01
21 pages
Article (Journal)
Electronic Resource
English
Implicit time integration , Material point method , Nonconforming boundary conditions , Penalty method Engineering , Geoengineering, Foundations, Hydraulics , Solid Mechanics , Geotechnical Engineering & Applied Earth Sciences , Soil Science & Conservation , Soft and Granular Matter, Complex Fluids and Microfluidics
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