An implicit locking-free B-spline Material Point Method for large strain geotechnical modelling
Abstract
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.
Versions
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BibTeX
@misc{xie2026implicit,
title = {{An implicit locking-free B-spline Material Point Method for large strain geotechnical modelling}},
author = {Mian Xie and Pedro Navas and Susana López-Querol},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26104},
eprint = {2609.26104},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26104},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An implicit locking-free B-spline Material Point Method for large strain geotechnical modelling
AU - Mian Xie
AU - Pedro Navas
AU - Susana López-Querol
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.26104
UR - https://arxiv.org/abs/2609.26104
AB - 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.
ER -