A new modification to the virtual stress boundary (VSB) method enhances the Material Point Method (MPM), a popular tool for simulating large deformations. The hybrid Eulerian–Lagrangian nature of MPM often leads to challenges in applying nonconforming boundary conditions, such as traction forces. The VSB method addresses this by transforming boundary traction problems into equivalent problems with virtual stress fields. The proposed modification removes the need for cell-wise quadrature, simplifying computations while maintaining accuracy. Tests on 1D, 2D, and 3D benchmark problems demonstrate the method’s reliability and efficient convergence, making it a promising advancement for MPM applications.
Figure 1. Contours of equivalent plastic deviatoric strain for each equilibrium state before specimen collapse
The virtual stress boundary method to impose nonconforming Neumann boundary conditions in the material point method
Joel Given, Yong Liang, Zhixin Zeng, Xiong Zhang & Kenichi Soga