A Material Point Method for Nonlinearly Magnetized Materials

Published in ACM Transactions on Graphics (TOG), 2021

Yuchen Sun*, Xingyu Ni* (joint 1st authors), Bo Zhu, Bin Wang, and Baoquan Chen. 2021. A material point method for nonlinearly magnetized materials. ACM Trans. Graph. 40, 6, Article 1 (December 2021), 13 pages. https://doi.org/10.1145/3478513.3480541

Abstract

We propose a novel numerical scheme to simulate interactions between a magnetic field and nonlinearly magnetized objects immersed in it. Under our nonlinear magnetization framework, the strength of magnetic forces is effectively saturated to produce stable simulations without requiring any hyper-parameter tuning. The mathematical model of our approach is based upon Langevin’s nonlinear theory of paramagnetism, which bridges microscopic structures and macroscopic equations after a statistical derivation. We devise a hybrid Eulerian-Lagrangian numerical approach to simulating this strongly nonlinear process by leveraging the discrete material points to transfer both material properties and the number density of magnetic micro-particles in the simulation domain. The magnetic equations can then be built and solved efficiently on a background Cartesian grid, followed by a finite difference method to incorporate magnetic forces. The multi-scale coupling can be processed naturally by employing the established particle-grid interpolation schemes in a conventional MLS-MPM framework. We demonstrate the efficacy of our approach with a host of simulation examples governed by magnetic-mechanical coupling effects, ranging from magnetic deformable bodies to magnetic viscous fluids with nonlinear elastic constitutive laws.

[Paper]