An edge‐based strain smoothing particle finite element method for large deformation problems in geotechnical engineering

Jin, Yulian; Yuan, Wei‐Hai; Yin, Zhen Yu; Cheng, Yung Ming

doi:10.1002/nag.3016

Cited by 46 publications

(33 citation statements)

References 61 publications

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“…References [84,104,106,107] applied their PFEM-solid methods to different types of manufacturing processes, [4,11,12] analyzed tunneling and excavation applications, while bed erosion in river dynamics was tackled in [81,82,86]. Several PFEM-solid formulations have been proposed in the field of soil mechanics and geotechnal engineering, especially for the modelling of frictional materials and granular flows [10,24,56,66,127,128] and for different types of geomechanics problems [75][76][77][78]…”

Section: Pfem For Non-linear Solid and Contact Mechanicsmentioning

confidence: 99%

“…Recently [56,124,126] proposed to use nodal integration rather than the Gaussian one to improve the preservation of historical variables. In nodal integration schemes, all variables (including stresses and strains) are stored at the nodes.…”

Section: Historical Variable Recoverymentioning

confidence: 99%

“…Recently, a PFEM-solid formulation has been validated against several experimental tests of the collapse of granular columns [66], while in [56] a granular flow simulation has been carried out using a nodal integration method.…”

Section: Granular Flowsmentioning

confidence: 99%

“…This feature motivated recent research on the use of nodal integration in a PFEM framework [56,124,126]. The method, called by the authors Smoothed Particle Finite Element Method, took inspiration from the Smoothed Finite Element Method [135] and was successfully applied to 2D geomechanics problems with large deformations.…”

Section: Pfem With Nodal Integrationmentioning

confidence: 99%

“…From a broader perspective, the demonstrated suitability of PFEM with nodal integration for fluid dynamics [31], solid mechanics [56,124,126], and FSI analysis [27] opens the field to a unified treatment of a general multi-physics continuum within a unique PFEM framework.…”

Section: Pfem With Nodal Integrationmentioning

confidence: 99%

See 4 more Smart Citations

A State of the Art Review of the Particle Finite Element Method (PFEM)

Cremonesi

Franci

Idelsohn

et al. 2020

Arch Computat Methods Eng

116

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The particle finite element method (PFEM) is a powerful and robust numerical tool for the simulation of multi-physics problems in evolving domains. The PFEM exploits the Lagrangian framework to automatically identify and follow interfaces between different materials (e.g. fluid–fluid, fluid–solid or free surfaces). The method solves the governing equations with the standard finite element method and overcomes mesh distortion issues using a fast and efficient remeshing procedure. The flexibility and robustness of the method together with its capability for dealing with large topological variations of the computational domains, explain its success for solving a wide range of industrial and engineering problems. This paper provides an extended overview of the theory and applications of the method, giving the tools required to understand the PFEM from its basic ideas to the more advanced applications. Moreover, this work aims to confirm the flexibility and robustness of the PFEM for a broad range of engineering applications. Furthermore, presenting the advantages and disadvantages of the method, this overview can be the starting point for improvements of PFEM technology and for widening its application fields.

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Section: Pfem For Non-linear Solid and Contact Mechanicsmentioning

confidence: 99%

Section: Historical Variable Recoverymentioning

confidence: 99%

Section: Granular Flowsmentioning

confidence: 99%

Section: Pfem With Nodal Integrationmentioning

confidence: 99%

Section: Pfem With Nodal Integrationmentioning

confidence: 99%

See 3 more Smart Citations

A State of the Art Review of the Particle Finite Element Method (PFEM)

Cremonesi

Franci

Idelsohn

et al. 2020

Arch Computat Methods Eng

116

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On the edge‐based smoothed finite element approximation of viscoelastic fluid flows

2022

Numerical Methods in Fluids

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This article discusses the numerical simulation of viscoelastic fluid flows using the edge-based smoothed finite element method (ESFEM). The incompressible Navier-Stokes equations coupled with the Oldroyd-B constitutive relation are decoupled via the characteristic-based split scheme that enables the use of equal-order interpolation for the triple primitive variables. For this reason, the spatial discretization is implemented with linear three-node triangular elements which work very well with the ESFEM. Edge-based smoothing cells (SCs) are constructed on grounds of existing elements, directly underpinning the essential gradient smoothing procedure. New integration points are proposed within local SCs since the ESFEM enjoys the tremendous flexibility of the smoothed Galerkin weak-form integral. The discrete viscoelastic system is entirely formulated in the edge-based notion such that all gradient-related terms are readily smoothed cell-by-cell. Finally, several numerical examples are presented to demonstrate the desirable capability of the ESFEM.

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A novel coupled NS‐PFEM with stable nodal integration and polynomial pressure projection for geotechnical problems

Wang

Jin

Yin

et al. 2022

Num Anal Meth Geomechanics

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The node‐based smoothed particle finite element method (NS‐PFEM) offers high computational efficiency but is numerically unstable due to possible spurious low‐energy mode in direct nodal integration (NI). Moreover, the NS‐PFEM has not been applied to hydromechanical coupled analysis. This study proposes an implicit stabilised T3 element‐based NS‐PFEM (stabilised node‐based smoothed particle finite element method [SNS‐PFEM]) for solving fully hydromechanical coupled geotechnical problems that (1) adopts the stable NI based on multiple stress points over the smooth domain to resolve the NI instability of NS‐PFEM, (2) implements the polynomial pressure projection (PPP) technique in the NI framework to cure possible spurious pore pressure oscillation in the undrained or incompressible limit and (3) expresses the NI for assembling coefficient matrices and calculating internal force in SNS‐PFEM with PPP as closed analytical expressions, guaranteeing computational accuracy and efficiency. Four classical benchmark tests (1D Terzaghi's consolidation, Mandel's problem, 2D strip footing consolidation and foundation on a vertical cut) are simulated and compared with analytical solutions or results from other numerical methods to validate the correctness and efficiency of the proposed approach. Finally, penetration of strip footing into soft soil is investigated, showing the outstanding performance the proposed approach can offer for large deformation problems. All results demonstrate that the proposed SNS‐PFEM with PPP is capable of tracking hydromechanical coupled geotechnical problems under small and large deformation with different drainage capacities.

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An edge‐based strain smoothing particle finite element method for large deformation problems in geotechnical engineering

Cited by 46 publications

References 61 publications

A State of the Art Review of the Particle Finite Element Method (PFEM)

A State of the Art Review of the Particle Finite Element Method (PFEM)

On the edge‐based smoothed finite element approximation of viscoelastic fluid flows

A novel coupled NS‐PFEM with stable nodal integration and polynomial pressure projection for geotechnical problems

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