Material point method after 25 years: Theory, implementation, and applications

Vaucorbeil, Alban de; Nguyen, Vinh Phu; Sinaie, Sina; Wu, Jian

doi:10.1016/bs.aams.2019.11.001

Cited by 123 publications

(50 citation statements)

References 250 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…One of the simplest approaches toward such a problem is the so‐called “cutoff method,” in which the degenerated basis functions as well as the associated degrees of freedom (DOFs) are omitted. The cutoff method has been employed for both the embedded domain‐based FEM 38 and MPM, 24,37 the latter of which is referred to as “cutoff‐MPM " hereafter. However, the choice of the parameter for determining a degenerated basis is not an easy task and the resulting numerical solution involves severe pollution in many cases as pointed out in Reference 38.…”

Section: Extended B‐spline‐based Materials Point Methodsmentioning

confidence: 99%

“…where are coordinates in the parameter space, and is the degree of polynomials. Also, n+ are called knots constituting the knot vector 23and (24). An open knot vector, in which the first and last knots appear + 1 times, enables us to define a bounded domain, called "patch," and is endowed with the Kronecker delta property at the nodes located on the boundaries; see Figure 2.…”

Section: B-spline Basis Functionsmentioning

confidence: 99%

“…in which are the parameter coordinates in the -directions. Note that i in Equations (23) and (24) corresponds to i 1 in this expression with d = 1. In this study, a background grid in the physical space is identified with a B-spline regular mesh in the parameter space, in which the uniform B-spline basis functions are used, as shown in Figure 1.…”

Section: B-spline Basis Functionsmentioning

confidence: 99%

“…However, each of these processes is needed mainly for the bases associated with boundary cells and therefore does not cause severe loss in the whole computation time. Check convergence for equilibrium 13 bases in the literature, 24,37 the cutoff-MPM degenerated from EBS-MPM will be employed for comparison purpose in the numerical example in Section 4.…”

Section: Ebs-mpm Algorithmmentioning

confidence: 99%

“…With the above‐mentioned beneficial characteristics, MPM has been applied successfully to various problems in geotechnical and other engineering fields, and extended with the intention to analyze more complex phenomena such as crack propagation, 17 frictional‐contact, 18 impact behavior, 19 fluid–solid interaction, 20 porous‐interaction, 21‐23 and so on. Comprehensive reviews for the recent advancements of MPM can be found in the review paper; see, for example, Reference 24. Also, although the explicit time‐integration scheme is most commonly employed for MPM calculations, it is quite natural to develop the “implicit MPM” as it has close analogy with FEM as mentioned above.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Extended B‐spline‐based implicit material point method

Yamaguchi

Moriguchi

Terada

2020

Numerical Meth Engineering

View full text Add to dashboard Cite

An implicit material point method (MPM) is enhanced by extended B-splines with the aim of achieving numerical stability and properly imposing boundary conditions. The standard B-spline basis functions capable of suppressing the cell-crossing error are used for the approximation over the domain, whereas extended B-splines (EBS) are active for boundary cells, each of which is occupied by a small physical domain. The basis consisting of EBS plays a central role to avoid both stress oscillation arising from inaccurate numerical integration and ill-conditioning of their resulting tangent matrices, both of which are caused by the boundary cells containing smaller number of material points than interior ones. Besides the standard material points for the interior region, boundary points are introduced to explicitly represent the boundary geometries and their movements, and to weakly impose an arbitrary boundary condition with the Nitsche's method. The Nitsche's terms in the linearized weak form are decomposed into normal and tangential directions to deal with both slip and nonslip boundary conditions. Four case studies are made to demonstrate the performance and capability of the proposed method, named EBS-MPM, in stably solving the quasi-static equilibrium problems for hyperelastic bodies and properly applying arbitrary boundary conditions.

show abstract

Section: Extended B‐spline‐based Materials Point Methodsmentioning

confidence: 99%

Section: B-spline Basis Functionsmentioning

confidence: 99%

Section: B-spline Basis Functionsmentioning

confidence: 99%

Section: Ebs-mpm Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Extended B‐spline‐based implicit material point method

Yamaguchi

Moriguchi

Terada

2020

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

Two‐phase model for the excavation analysis in partially saturated soft soils using the particle finite element method

Bal

Meschke

2022

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

A two-phase velocity-pressure stabilized formulation is proposed for the numerical analysis of mechanized excavations in partially saturated soft soils using the Particle Finite Element Method (PFEM). The fully coupled formulation is based on the theory of porous media in association with the Soil Water Characteristic Curve and the porosity-dependent Kozeni-Carman model for the realistic estimation of the soil permeability. The combination of the PFEM methodology, characterized by a global re-meshing strategy equipped with a new adaptive mesh refinement scheme for the resolution of strain localization zones in the ground, with a hypoplastic constitutive model for the description of the nonlinear behavior of the deformable soil skeleton, allows for the modeling of very large deformations, as required for excavation simulations. The PFEM model is validated based on selected geotechnical benchmark problems concerned with fully and partially saturated soil specimens. The model is further applied to computational re-analyses of excavation tests involving a single cutting tool moving in a sandbox. The reaction force-tool displacement curve for the excavation tool as well as the evolution of the deformed topology of the sand including the formation of shear zones obtained from the computational model are compared with respective experimental observations. Parametric investigations aimed at elucidating the influence of selected geotechnical parameters on the excavation process are also carried out. Finally, the suitability of the proposed PFEM-based numerical strategy for the modeling of 3D excavation problems is demonstrated by means of 3D PFEM simulations in fully saturated sand.

show abstract

Lagrangian–Eulerian multidensity topology optimization with the material point method

et al. 2021

Numerical Meth Engineering

View full text Add to dashboard Cite

In this paper, a hybrid Lagrangian-Eulerian topology optimization (LETO) method is proposed to solve the elastic force equilibrium with the Material Point Method (MPM). LETO transfers density information from freely movable Lagrangian carrier particles to a fixed set of Eulerian quadrature points. This transfer is based on a smooth radial kernel involved in the compliance objective to avoid the artificial checkerboard pattern. The quadrature points act as MPM particles embedded in a lower-resolution grid and enable a subcell multidensity resolution of intricate structures with a reduced computational cost.A quadrature-level connectivity graph-based method is adopted to avoid the artificial checkerboard issues commonly existing in multiresolution topology optimization methods. Numerical experiments are provided to demonstrate the efficacy of the proposed approach.

show abstract

Material point method after 25 years: Theory, implementation, and applications

Cited by 123 publications

References 250 publications

Extended B‐spline‐based implicit material point method

Extended B‐spline‐based implicit material point method

Two‐phase model for the excavation analysis in partially saturated soft soils using the particle finite element method

Lagrangian–Eulerian multidensity topology optimization with the material point method

Contact Info

Product

Resources

About