Ghost stabilisation of the Material Point Method for stable quasi-static and dynamic analysis of large deformation problems

@article{Coombs2022GhostSO,
  title={Ghost stabilisation of the Material Point Method for stable quasi-static and dynamic analysis of large deformation problems},
  author={William M. Coombs},
  journal={ArXiv},
  year={2022},
  volume={abs/2209.10955}
}
  • W. Coombs
  • Published 22 September 2022
  • Geology
  • ArXiv
The unstable nature of the material point method is widely documented and is a barrier to the method being used for routine engineering analyses of large deformation problems. The vast majority of papers concerning this issue are focused on the instabilities that manifest when a material point crosses between background grid cells. However, there are other issues related to the stability of material point methods. This paper focuses on the issue of the conditioning of the global system of… 

References

SHOWING 1-10 OF 37 REFERENCES

Imposition of essential boundary conditions in the material point method

There is increasing interest in the material point method (MPM) as a means of modelling solid mechanics problems in which very large deformations occur, e.g. in the study of landslides and metal

On the use of domain-based material point methods for problems involving large distortion

An efficient and locking‐free material point method for three‐dimensional analysis with simplex elements

The Material Point Method is a relative newcomer to the world of solid mechanics modelling. Its key advantage is the ability to model problems having large deformations while being relatively close

Energy Conservation Error in the Material Point Method for Solid Mechanics

The material point method (MPM) for solid mechanics conserves mass and momentum by construction, but energy conservation is not explicitly enforced. Material constitutive response and internal energy

B-spline based boundary conditions in the material point method

High-order cut finite elements for the elastic wave equation

A high-order cut finite element method is formulated for solving the elastic wave equation and Nitsche’s method is used to enforce boundary and interface conditions, resulting in symmetric bilinear forms.

Development and implementation of moving boundary conditions in the Material Point Method

A new technique is developed in this thesis, which applies boundary conditions to moving boundaries in the Material Point Method (MPM). While MPM has been proven to be useful in slope stability,