Ghost stabilisation of the material point method for stable quasi‐static and dynamic analysis of large deformation problems

Coombs, William M.

doi:10.1002/nme.7332

Cited by 7 publications

(4 citation statements)

References 61 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…52 This is especially useful for the MPM due to the fact that it is often the case that MPs around the edge of the physical domain are located in partially filled elements. Coombs 53 implemented the ghost stabilisation method within the MPM where boundary and faces are determined over which the ghost penalty was integrated, resulting in a well-conditioned system and improved stability in analysis.…”

Section: (A) (B) (C) (D) (E) (F)mentioning

confidence: 99%

“…Roller boundary conditions are applied over each edge of the background mesh. The problem is run using the ghost stabilisation technique 53 in order to reduce errors and improve the stability of the simulation due to partially filled background elements. The ghost stabilisation parameter is set to 𝛾 = 10 6 .…”

Section: Hyperelastic Cylinder Under Internal Pressurementioning

confidence: 99%

See 1 more Smart Citation

On the implementation of a material point‐based arc‐length method

Gavin,

Pretti,

Coombs

et al. 2024

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

SummaryThe material point method is a versatile technique which can be used to solve various types of solid mechanics problems, especially those involving large deformations. However, the capability of the material point method to track a load‐displacement response can deteriorate once a limit point, such as snap‐through or snap‐back, in the response is encountered. One way of overcoming this is to use path following techniques, such as an arc‐length method. This technique is well established in finite element analysis but not within any material point method formulation. This paper provides for the first time an arc‐length controlled implicit, quasi‐static material point method. The modifications to the standard arc‐length scheme to allow for the stable execution of an arc‐length solver within the material point method are detailed. The capability of the material point‐based arc‐length method is demonstrated through a number of problems, which include linear elastic, non‐linear elastic, linear elastic‐perfectly plastic and linear elastic‐plastic softening material behaviour under large deformations. The techniques presented in this paper are essential for arc‐length techniques to be applied effectively to the material point method and the combination of these techniques makes the method suitable for new problems that cannot be solved with existing implicit material point approaches.

show abstract

Section: (A) (B) (C) (D) (E) (F)mentioning

confidence: 99%

Section: Hyperelastic Cylinder Under Internal Pressurementioning

confidence: 99%

On the implementation of a material point‐based arc‐length method

Gavin,

Pretti,

Coombs

et al. 2024

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…In addition to volumetric locking, MPM has stress oscillation around the physical body's boundary because of the ill-conditioned mass matrix. Coombs [39] solved this issue using the Ghost stabilisation technique. This method can only be applied to MPM with linear shape functions.…”

Section: Soil Phasementioning

confidence: 99%

“…This method can only be applied to MPM with linear shape functions. Yamaguchi et al [40] developed an extended B-spline MPM to counteract this instability, which however, is usually ignored in explicit MPMs that adopt a lumped mass matrix because the inversion of the mass matrix is trivial in this case [39]. In this research, we also omit this instability due to computational cost reasons.…”

Section: Soil Phasementioning

confidence: 99%

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

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.

show abstract

Thermo‐hydro‐mechanical coupled material point method for modeling freezing and thawing of porous media

Yu,

Zhao,

Zhao

et al. 2024

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

Climate warming accelerates permafrost thawing, causing warming‐driven disasters like ground collapse and retrogressive thaw slump (RTS). These phenomena, involving intricate multiphysics interactions, phase transitions, nonlinear mechanical responses, and fluid‐like deformations, and pose increasing risks to geo‐infrastructures in cold regions. This study develops a thermo‐hydro‐mechanical (THM) coupled single‐point three‐phase material point method (MPM) to simulate the time‐dependent phase transition and large deformation behavior arising from the thawing or freezing of ice/water in porous media. The mathematical framework is established based on the multiphase mixture theory in which the ice phase is treated as a solid constituent playing the role of skeleton together with soil grains. The additional strength due to ice cementation is characterized via an ice saturation‐dependent Mohr–Coulomb model. The coupled formulations are solved using a fractional‐step‐based semi‐implicit integration algorithm, which can offer both satisfactory numerical stability and computational efficiency when dealing with nearly incompressible fluids and extremely low permeability conditions in frozen porous media. Two hydro‐thermal coupling cases, that is, frozen inclusion thaw and Talik closure/opening, are first benchmarked to show the method can correctly simulate both conduction‐ and convection‐dominated thermal regimes in frozen porous systems. The fully THM responses are further validated by simulating a 1D thaw consolidation and a 2D rock freezing example. Good agreements with experimental results are achieved, and the impact of hydro‐thermal variations on the mechanical responses, including thaw settlement and frost heave, are successfully captured. Finally, the predictive capability of the multiphysics MPM framework in simulating thawing‐triggered large deformation and failure is demonstrated by modeling an RTS and the settlement of a strip footing on thawing ground.

show abstract

Ghost stabilisation of the material point method for stable quasi‐static and dynamic analysis of large deformation problems

Cited by 7 publications

References 61 publications

On the implementation of a material point‐based arc‐length method

On the implementation of a material point‐based arc‐length method

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

Thermo‐hydro‐mechanical coupled material point method for modeling freezing and thawing of porous media

Contact Info

Product

Resources

About