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Under our nonlinear magnetization framework, the strength of magnetic forces is effectively saturated to produce stable simulations without requiring any 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.<\/jats:p>","DOI":"10.1145\/3478513.3480541","type":"journal-article","created":{"date-parts":[[2021,12,10]],"date-time":"2021-12-10T18:29:20Z","timestamp":1639160960000},"page":"1-13","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":14,"title":["A material point method for nonlinearly magnetized materials"],"prefix":"10.1145","volume":"40","author":[{"given":"Yuchen","family":"Sun","sequence":"first","affiliation":[{"name":"Peking University, China"}]},{"given":"Xingyu","family":"Ni","sequence":"additional","affiliation":[{"name":"Peking University, China"}]},{"given":"Bo","family":"Zhu","sequence":"additional","affiliation":[{"name":"Dartmouth College"}]},{"given":"Bin","family":"Wang","sequence":"additional","affiliation":[{"name":"Beijing Institute for General Artificial Intelligence, China"}]},{"given":"Baoquan","family":"Chen","sequence":"additional","affiliation":[{"name":"Peking University, China"}]}],"member":"320","published-online":{"date-parts":[[2021,12,10]]},"reference":[{"key":"e_1_2_2_1_1","volume-title":"A short course on fast multipole methods","author":"Beatson Rick","unstructured":"Rick Beatson and Leslie Greengard . 1997. 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