Implicit formulation of material point method for analysis of incompressible materials

Kularathna, Shyamini; Soga, Kenichi

doi:10.1016/j.cma.2016.10.013

Cited by 62 publications

(26 citation statements)

References 30 publications

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“…Furthermore,ṽ denotes an advective velocity field to be specified below, but with the minimal requirement of satisfying the boundary constraints Eqs. (8)(9).…”

Section: Lagrangian Discretization Of Advection Problemmentioning

confidence: 99%

“…To remain consistent with the boundary conditions in Eqs. (8)(9), the momenta of the inserted particles are interpolated from the corresponding values imposed by the boundary conditions.…”

Section: Particle Advectionmentioning

confidence: 99%

“…Their method is currently known as the material point method (MPM) and is especially popular for simulating large deformation problems in solid mechanics. Recently, various attempts have been made to use MPM for the simulation of incompressible fluid flows [8,9]. Despite the attractive features of particle-mesh methods and the wide variety of implementations found in literature, various difficulties remain persistent to these methods.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, non-Gaussian quadrature of this type yields non-optimal accuracy. Attempts have been made to mitigate these problems by using basis functions being at least C 1 -continuous [11,12], or by using a blend between optimal quadrature and quadrature based on moving material points [8]. The implications of the latter approach, in terms of accuracy and physical consistency, remain unknown however.…”

Section: Introductionmentioning

confidence: 99%

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A hybridized discontinuous Galerkin framework for high-order particle–mesh operator splitting of the incompressible Navier–Stokes equations

Maljaars

Labeur

Möller

2018

Journal of Computational Physics

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“…Furthermore,ṽ denotes an advective velocity field to be specified below, but with the minimal requirement of satisfying the boundary constraints Eqs. (8)(9).…”

Section: Lagrangian Discretization Of Advection Problemmentioning

confidence: 99%

“…To remain consistent with the boundary conditions in Eqs. (8)(9), the momenta of the inserted particles are interpolated from the corresponding values imposed by the boundary conditions.…”

Section: Particle Advectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A hybridized discontinuous Galerkin framework for high-order particle–mesh operator splitting of the incompressible Navier–Stokes equations

Maljaars

Labeur

Möller

2018

Journal of Computational Physics

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“…Several methods exist, including finite element (FE) [Demirel, 2015] and boundary element (BE) approaches or coupled BE-FE [Antes and Von-Estorff, 1987;Yazdchi et al, 1999]. The reservoir can be discretized using elastic "solid finite elements" [Wilson, 1975;Zienkiewicz et al, 1986;Wilson, 1995;Dakoulas and Gazetas, 2008;Pelecanos et al, 2013] in which the bulk modulus of the water is assigned to the elements with a very small shear modulus, or "fluid elements", following Eulerian [Kucukarslan et al, 2005;Gogoi and Maity, 2007;Fan and Li, 2008] or Lagrangian [Akkose et al, 2008;Bilici et al, 2009;Kartal and Bayraktar, 2013] or MPM [Kularathna and Soga, 2017a; …”

Section: Introductionmentioning

confidence: 99%

The Effects of Dam–Reservoir Interaction on the Nonlinear Seismic Response of Earth Dams

Pelecanos

Kontoe

Zdravković

2018

Journal of Earthquake Engineering

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The objective of this study is to investigate the effects of damreservoir interaction (DRI) on the nonlinear seismic response of earth dams. Although DRI effects have for long been considered as insignificant for earth dams, that conclusion was mainly based on linear elastic investigations which focused only on the acceleration response of the crest without examining the seismic shear stresses and strains within the dam body. The present study explores further the impact of DRI focusing on the nonlinear behavior of earth dams. The effects of reservoir hydrodynamic pressures are investigated in terms of both seismic dam accelerations and nonlinear dynamic soil behavior (seismic shear stresses and strains). It is shown that although dam crest accelerations are indeed insensitive to DRI, the stress and strain development within the dam body can be significantly underestimated if DRI is ignored. ARTICLE HISTORY

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Variable passing method for combining 3D MPM–FEM hybrid and 2D shallow water simulations of landslide‐induced tsunamis

Pan,

Nomura,

Ling

et al. 2023

Numerical Methods in Fluids

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With a view to simulating the entire process of a landslide‐triggered tsunami, ranging from tsunami generation to offshore wave propagation, with relatively low computational costs, we present a 2D–3D coupling strategy to bridge 3D MPM–FEM hybrid and 2D shallow water (SW) simulations. Specifically, considering the difference in basis functions between the 3D and 2D analysis methods, we devise a novel variable passing scheme in the domain overlapping method, in which a slightly overlapped domain enables the generated wave to pass through the connection boundaries with as little discrepancy as possible. For the tsunami generation stage in the 3D domain, the hybrid method combining the finite element method (FEM) and material point method (MPM) is adopted. In this method, the 3D governing equation of the solid phase is solved with the MPM, whereas the well‐established 3D stabilized FEM is applied to that of the fluid phase in an Eulerian frame. Additionally, the phase‐field method is employed to track the free surface of the 3D fluid domain. On the other hand, the SW equation that represents the offshore wave motion in the 2D domain is solved by the 2D stabilized FEM. Several numerical examples are presented to demonstrate the effectiveness of the developed scheme in properly passing the data from 3D/2D to 2D/3D domains.

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Implicit formulation of material point method for analysis of incompressible materials

Cited by 62 publications

References 30 publications

A hybridized discontinuous Galerkin framework for high-order particle–mesh operator splitting of the incompressible Navier–Stokes equations

A hybridized discontinuous Galerkin framework for high-order particle–mesh operator splitting of the incompressible Navier–Stokes equations

The Effects of Dam–Reservoir Interaction on the Nonlinear Seismic Response of Earth Dams

Variable passing method for combining 3D MPM–FEM hybrid and 2D shallow water simulations of landslide‐induced tsunamis

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