Coupled material point and level set methods for simulating soils interacting with rigid objects with complex geometry

Zhao, Yidong; Choo, Jinhyun; Jiang, Yupeng; Li, Liuchi

doi:10.1016/j.compgeo.2023.105708

Cited by 12 publications

(14 citation statements)

References 44 publications

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“…From the above illustration, the key to the F‐bar approach is to determine the averaged Jacobian

\Delta \bar{J}

in Equation (15). Departing from the research conducted by Zhao et al., 28 we calculate the averaged Jacobian

\Delta \bar{J}

by mapping the original one

\Delta {J}

to the related grid nodes and then mapping back to the material points. The mathematical formulation of this mapping and remapping procedure is stated as follows: The nodal mass‐weighted Jacobian can be calculated by mapping the product of mass and

\Delta {J}

from material points as

\begin{equation} (m\Delta {J})_I = \sum _{p=1}^{{n}_{p}} {N}_{Ip} {m}_{p} \Delta {J}, \end{equation}

where

{m}_{p}

is the mass of material point p ;

(m\Delta {J})_I

is the nodal mass‐weighted Jacobian. Then, the nodal Jacobian can be obtained by

\begin{equation} \Delta {J}_I = \frac{(m\Delta {J})_I}{m_I}, \end{equation}

where

{m_I} = \sum _{p=1}^{{n}_{p}} {N}_{Ip} {m_p}

is the nodal mass. Finally, the nodal Jacobian is mapped back to the ...…”

Section: Description Of the Numerical Modelmentioning

confidence: 99%

“…The BSMPM shows less volumetric locking than the MPMs with linear shape functions. However, fully overcoming the volumetric locking for BSMPM is challenging since its shape functions are associated with adjacent cells 28 . Navas et al 29 .…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

“…This approach relies on the triangular mesh, however, the rectangular mesh is a more popular choice in the MPM literature. To the best of our knowledge, there are currently only three available pieces of research 28,30,31 related to the mitigation of volumetric locking for a higher‐order MPM. Two of them 30,31 are based on the F‐bar projection method proposed by Elguedj et al., 32 which was originally developed for B‐spline FEM.…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

“…Two of them 30,31 are based on the F‐bar projection method proposed by Elguedj et al., 32 which was originally developed for B‐spline FEM. However, the application of this method is not straightforward due to the introduction of an additional background grid with low‐order shape functions 28 . Also, it is hard to apply to other types of MPM (i.e.…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

“…GIMPM) because of this feature. The method proposed by Zhao et al 28 . is simple enough, but its performance has not been well tested by a wide range of large deformation geotechnical problems.…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

See 4 more Smart Citations

An implicit locking‐free B‐spline Material Point Method for large strain geotechnical modelling

Xie

Navas

López‐Querol

2023

Num Anal Meth Geomechanics

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The Material Point Method (MPM) has drawn great attention in the numerical modelling of large deformation, geotechnical problems. The popularity of MPM is mainly because its formulation shares significant similarities with the Finite Element Method. In MPM, the iteration points can move independently from the mesh, allowing for the resolution of large deformation problems. However, because of this, the original MPM formulation suffers from the well‐known cell‐crossing noise and volumetric‐locking instabilities, resulting in a strongly oscillated stress field. A novel implicit locking‐free B‐spline MPM that controls stress oscillations to a negligible level is proposed in this paper. A novel, but very straightforward B‐spline shape function implementation procedure, avoids the need for a complex material point searching algorithm, providing seamless transformation from the original MPM to this robust B‐spline MPM, aiming at modelling large‐strain geotechnical problems. The newly proposed volumetric locking mitigation strategy is also very easy to implement, which facilitates the reproducibility of this research. The proposed method is validated against three numerical studies: granular column collapse experiment, slope failure and footing with large penetration. The proposed numerical method agrees well with experiments reported in the literature and previous numerical studies. Also, these numerical examples show that the proposed method provides a more prominent stress field than other available methodologies.

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“…From the above illustration, the key to the F‐bar approach is to determine the averaged Jacobian

\Delta \bar{J}

in Equation (15). Departing from the research conducted by Zhao et al., 28 we calculate the averaged Jacobian

\Delta \bar{J}

by mapping the original one

\Delta {J}

\Delta {J}

from material points as

\begin{equation} (m\Delta {J})_I = \sum _{p=1}^{{n}_{p}} {N}_{Ip} {m}_{p} \Delta {J}, \end{equation}

where

{m}_{p}

is the mass of material point p ;

(m\Delta {J})_I

is the nodal mass‐weighted Jacobian. Then, the nodal Jacobian can be obtained by

\begin{equation} \Delta {J}_I = \frac{(m\Delta {J})_I}{m_I}, \end{equation}

where

{m_I} = \sum _{p=1}^{{n}_{p}} {N}_{Ip} {m_p}

is the nodal mass. Finally, the nodal Jacobian is mapped back to the ...…”

Section: Description Of the Numerical Modelmentioning

confidence: 99%

Section: Introduction and Literature Reviewmentioning

confidence: 99%

Section: Introduction and Literature Reviewmentioning

confidence: 99%

Section: Introduction and Literature Reviewmentioning

confidence: 99%

Section: Introduction and Literature Reviewmentioning

confidence: 99%

See 3 more Smart Citations

An implicit locking‐free B‐spline Material Point Method for large strain geotechnical modelling

Xie

Navas

López‐Querol

2023

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

show abstract

Mapped material point method for large deformation problems with sharp gradients and its application to soil‐structure interactions

Zhao,

Li,

Jiang

et al. 2024

Num Anal Meth Geomechanics

Self Cite

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The material point method (MPM) is often applied to large deformation problems that involve sharp gradients in the solution field. Representative examples in geomechanics are interactions between soils and various “structures” such as foundations, penetrometers, and machines, where the displacement fields exhibit sharp gradients around the soil‐structure interfaces. Such sharp gradients should be captured properly in the MPM discretization to ensure that the numerical solution is sufficiently accurate. In the MPM literature, several types of locally refined discretizations have been developed and used for this purpose. However, these local refinement schemes are not only quite complicated but also restricted to certain types of basis functions or update schemes. In this work, we propose a new MPM formulation, called the mapped MPM, that can efficiently capture sharp gradients with a uniform background grid compatible with every standard MPM basis function and scheme. The mapped MPM is built on the method of auxiliary mapping that reparameterizes the given problem in a different domain whereby sharp gradients become much smoother. Because the reparameterized problem is free of undesirably sharp gradients, it can be well solved with the standard MPM ingredients including a uniform background grid. We verify and demonstrate the mapped MPM through several numerical examples, with particular attention to soil‐structure interaction problems.

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Unstructured moving least squares material point methods: a stable kernel approach with continuous gradient reconstruction on general unstructured tessellations

Cao,

Zhao,

et al. 2024

Comput Mech

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Coupled material point and level set methods for simulating soils interacting with rigid objects with complex geometry

Cited by 12 publications

References 44 publications

An implicit locking‐free B‐spline Material Point Method for large strain geotechnical modelling

An implicit locking‐free B‐spline Material Point Method for large strain geotechnical modelling

Mapped material point method for large deformation problems with sharp gradients and its application to soil‐structure interactions

Unstructured moving least squares material point methods: a stable kernel approach with continuous gradient reconstruction on general unstructured tessellations

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