A consistent boundary method for the material point method - using imge particles to reduce boundary artefacts

The material point method (MPM) is a continuum-based numerical method hich discretises the object as material points. It is particulary ell suited for and has shon great success in the community for large deformations. Even though it has been idely adopted, ther are still fundamental questions to be addressed. In MPM the material properties are carried on the material points and the dynamics is calculated on an overlaid grid. Afterwards the material points are integrated according to are applied on the grid values, such as setting the grid momentum to zero for grid nodes inside a fixed wall. These disort the stress multiple grid lengths into the object. Inthis papr e propose a novel consistent boundary method to reduce these artefacts. The method is based on image particles, an approach originally developed for electrotatic problems. This concept allos a consistent formulation for the momentum field on both the grid and particles. We demonstrate a way of optimization that makes the explicit construction of mirror particles unnecessary. The explicit boundary method and image particle method are then compared using numerical examples featuring stress induced by simple shear and body forces. These numerical examples sho a significant reduction of boundary artefacts using the image particle method