### Abstract

The Material Point Method (MPM) is a quasi Eulerian-Lagrangian approach to solve solid

mechanics problems involving large deformations. The standard MPM [1] discretises the

physical domain using material points which are advected through a standard finite element

background mesh. The method of mapping state variables back and forth between the material

points and background mesh nodes in the MPM significantly influences the results. In the

standard MPM (sMPM), a material point only influences its parent element (i.e. the

background element in which it is located), which can cause spurious stress oscillations when

material points cross between elements. The instability is due to the sudden transfer of

stiffness between elements. It can also result in some elements having very little stiffness or

some internal elements loosing all stiffness. Therefore, several extensions to the sMPM have

been proposed, each of which replaces the material point with a deformable particle domain.

The most notable of these extensions are the Generalised Interpolation Material Point

(GIMP), the Convected Particle Domain Interpolation (CPDI1) and Second-order CPDI

(CPDI2) methods [2]. In this paper, the sMPM, CPDI1 and CPDI2 approaches are unified for

geometrically non-linear elasto-plastic problems using an implicit solver and their

performance investigated for large rotational problems. This type of deformation is common

in applications in the area of soil mechanics, for example the vane shear test and, specifically

of interest here, the installation of screw piles. Screw piles are currently used as an onshore

foundation solution and research being undertaken at Durham, Dundee and Southampton

universities is exploring their use in the area of offshore renewables. The numerical modelling

using the MPM aims to predict the installation torque and vertical force as well as

understanding the “state” of the soil around the screw pile which is critical in understanding

the long term performance of the foundation. In the analysis, the pile is assumed to be a rigid

body and no-slip boundary condition is used at the pile-soil interface. The boundary condition

is imposed using the moving mesh concept within an unstructured mesh fixed to the pile. It

will be shown that the CPDI2 approach produces erroneous torque due to particle domain

distortion, while the CPDI1 approach and sMPM predict physically realistic mechanical

responses.

mechanics problems involving large deformations. The standard MPM [1] discretises the

physical domain using material points which are advected through a standard finite element

background mesh. The method of mapping state variables back and forth between the material

points and background mesh nodes in the MPM significantly influences the results. In the

standard MPM (sMPM), a material point only influences its parent element (i.e. the

background element in which it is located), which can cause spurious stress oscillations when

material points cross between elements. The instability is due to the sudden transfer of

stiffness between elements. It can also result in some elements having very little stiffness or

some internal elements loosing all stiffness. Therefore, several extensions to the sMPM have

been proposed, each of which replaces the material point with a deformable particle domain.

The most notable of these extensions are the Generalised Interpolation Material Point

(GIMP), the Convected Particle Domain Interpolation (CPDI1) and Second-order CPDI

(CPDI2) methods [2]. In this paper, the sMPM, CPDI1 and CPDI2 approaches are unified for

geometrically non-linear elasto-plastic problems using an implicit solver and their

performance investigated for large rotational problems. This type of deformation is common

in applications in the area of soil mechanics, for example the vane shear test and, specifically

of interest here, the installation of screw piles. Screw piles are currently used as an onshore

foundation solution and research being undertaken at Durham, Dundee and Southampton

universities is exploring their use in the area of offshore renewables. The numerical modelling

using the MPM aims to predict the installation torque and vertical force as well as

understanding the “state” of the soil around the screw pile which is critical in understanding

the long term performance of the foundation. In the analysis, the pile is assumed to be a rigid

body and no-slip boundary condition is used at the pile-soil interface. The boundary condition

is imposed using the moving mesh concept within an unstructured mesh fixed to the pile. It

will be shown that the CPDI2 approach produces erroneous torque due to particle domain

distortion, while the CPDI1 approach and sMPM predict physically realistic mechanical

responses.

Original language | English |
---|---|

Title of host publication | 9th NUMGE Conference on Numerical Methods in Geotechnical Engineering |

Publisher | Taylor & Francis |

Pages | 585-592 |

Edition | 1 |

ISBN (Print) | 9780429823190 |

Publication status | Published - Jun 2018 |

Event | 9th European Conference on Numerical Methods in Geotechnical Engineering (NUMGE 2018) - University of Porto, Porto, Portugal Duration: 25 Jun 2018 → 27 Jun 2018 http://www.numge2018.pt/ |

### Conference

Conference | 9th European Conference on Numerical Methods in Geotechnical Engineering (NUMGE 2018) |
---|---|

Country | Portugal |

City | Porto |

Period | 25/06/18 → 27/06/18 |

Internet address |

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### Cite this

Wang, L., Coombs, W. M., Augarde, C. E., Brown, M., Knappett, J., Brennan, A., Davidson, C., Blake, A., & Richards, D. (2018). On the use of the material point method to model problems involving large rotational deformation. In

*9th NUMGE Conference on Numerical Methods in Geotechnical Engineering*(1 ed., pp. 585-592). Taylor & Francis.