An adaptive interpolation material point method and its application on large-deformation geotechnical problems

Peng, Xuefeng; Ji, Enyue; Fu, Zhongzhi; Chen, Shengshui; Zhong, Qiming

doi:10.1016/j.compgeo.2022.104709

Cited by 8 publications

(4 citation statements)

References 31 publications

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“…However, in CPDI, they have a "material point-corner points-grid nodes" topological relationship, which allows the mapping area of a single material point to diffuse through the corner points. 75 The blue grid nodes in Figure 1 are computational nodes determined by the elements occupied by the particle domain corner points. As shown in Figure 1, the CPDI takes two steps to map particle variables to grid nodes.…”

Section: Spatial Discrete Equationsmentioning

confidence: 99%

“…As shown in Figure 1, the CPDI takes two steps to map particle variables to grid nodes. 75 First, the particle variables are mapped to the corner points (the black solid arrows). Then, the corner point variables are mapped to the grid nodes (the blue dotted arrows).…”

Section: Spatial Discrete Equationsmentioning

confidence: 99%

“…In MPM, material points and grid nodes have a one‐to‐one topological relationship. However, in CPDI, they have a “material point‐corner points‐grid nodes” topological relationship, which allows the mapping area of a single material point to diffuse through the corner points 75 . The blue grid nodes in Figure 1 are computational nodes determined by the elements occupied by the particle domain corner points.…”

Section: An Improved Convected Particle Domain Interpolation Material...mentioning

confidence: 99%

“…The blue grid nodes in Figure 1 are computational nodes determined by the elements occupied by the particle domain corner points. As shown in Figure 1, the CPDI takes two steps to map particle variables to grid nodes 75 . First, the particle variables are mapped to the corner points (the black solid arrows).…”

Section: An Improved Convected Particle Domain Interpolation Material...mentioning

confidence: 99%

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An improved convected particle domain interpolation material point method for large deformation geotechnical problems

Wang,

Li,

Zhou

et al. 2023

Numerical Meth Engineering

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A novel material point method called the improved convected particle domain interpolation (ICPDI) is proposed in this paper to simulate large‐deformation problems in geotechnical engineering. The ICPDI framework is based on the existing convected particle domain interpolation (CPDI) and employs an adaptive orthogonal improved interpolating moving least square (AOIIMLS) shape functions. The AOIIMLS shape functions prevent computational instability problems caused by singular or ill‐conditioned matrices through avoiding the direct solving of inverse matrices. Additionally, ICPDI adopts the velocity gradient to calculate the velocity field in particle domains and reduces cell‐crossing errors by using AOIIMLS shape functions. To reconstruct the velocity function in the background grid, the velocities of the material points and four related corner points are employed through AOIIMLS shape functions. The bar axis‐aligned vibration, ring radial expansion, slope elasto‐plastic slumping, and post‐failure tunnel collapse behavior examples are used to verify the accuracy and effectiveness of ICPDI by comparing the results with other numerical methods and experiments. Numerical simulation results show that ICPDI outperforms the material point method (MPM) and CPDI in terms of computational accuracy and convergence while reducing cell‐crossing errors. Consequently, this study demonstrates the capability of ICPDI in simulations of large‐deformation geotechnical problems.

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Section: Spatial Discrete Equationsmentioning

confidence: 99%

Section: Spatial Discrete Equationsmentioning

confidence: 99%

Section: An Improved Convected Particle Domain Interpolation Material...mentioning

confidence: 99%

Section: An Improved Convected Particle Domain Interpolation Material...mentioning

confidence: 99%

See 2 more Smart Citations