A new paper by Yong Liang, Joel Given, Bodhinanda Chandra, Zhixin Zeng, Xiong Zhang, and Kenichi Soga, titled “The Virtual Stress Boundary Method to Impose Nonconforming Neumann Boundary Conditions in the High-Order Material Point Method,” has been published in the International Journal for Numerical Methods in Engineering.
This work extends the virtual stress boundary method to high-order Material Point Method formulations. High-order MPM can improve numerical accuracy, but imposing boundary conditions becomes more challenging because of the wider support domains of high-order shape functions. The paper addresses these challenges and demonstrates how the virtual stress boundary framework can be adapted for high-order MPM.
The study contributes to more accurate and flexible particle-based simulations of complex boundary-value problems, particularly where material boundaries do not align with the computational grid.