  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 equations caused by the arbitrary nature
of the position of the physical domain relative to the background computational
grid. The issue is remedied here via the use of a Ghost stabilisation technique
that penalises variations in the gradient of the solution field near the
boundaries of the physical domain. This technique transforms the stability of
the material point method, providing a robust computational framework for large
deformation dynamic and quasi-static analysis.
