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This difficulty becomes more pronounced for multiple two-way-coupled bodies. This paper introduces a novel framework that leverages the linear kinematic mapping of Affine Body Dynamics (ABD). As ABD targets near-rigid objects, the constitutive variations of different materials become negligible, which justifies a co-rotational approach to isolate geometric nonlinearities of the system. This insight enables the use of constant system matrices that can be pre-factorized throughout the simulation, even with fully implicit integration schemes. To manage the high DOF counts of large-scale systems, we map primal body coordinates onto a compact dual space defined by minimal joint degrees of freedom. By solving the resulting KKT systems, our method ensures exact constraint enforcement and physically accurate motion propagation. We provide a suite of specialized solvers tailored for diverse joint topologies, including chains, trees, closed loops, and irregular networks. Experimental results show that our approach achieves interactive rates for systems with hundreds of thousands of bodies on a single CPU core, while maintaining excellent stability at large time steps.<\/jats:p>","DOI":"10.1145\/3811276","type":"journal-article","created":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T07:05:51Z","timestamp":1783062351000},"page":"1-19","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["M-ABD: Scalable, Efficient, and Robust Multi-Affine-Body Dynamics"],"prefix":"10.1145","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-7198-0443","authenticated-orcid":false,"given":"Zhiyong","family":"He","sequence":"first","affiliation":[{"name":"University of Utah, Salt Lake City, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7393-5486","authenticated-orcid":false,"given":"Dewen","family":"Guo","sequence":"additional","affiliation":[{"name":"University of Utah, Salt Lake City, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3408-4997","authenticated-orcid":false,"given":"Minghao","family":"Guo","sequence":"additional","affiliation":[{"name":"Computer Science and Artificial Intelligence Laboratory (CSAIL), Massachusetts Institute of Technology (MIT), Cambridge, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-9768-0795","authenticated-orcid":false,"given":"Yili","family":"Zhao","sequence":"additional","affiliation":[{"name":"USC, Los Angeles, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0212-5643","authenticated-orcid":false,"given":"Wojciech","family":"Matusik","sequence":"additional","affiliation":[{"name":"Computer Science and Artificial Intelligence Laboratory (CSAIL), Massachusetts Institute of Technology (MIT), Cambridge, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1796-2682","authenticated-orcid":false,"given":"Hao","family":"Su","sequence":"additional","affiliation":[{"name":"University of California San Diego, San Diego, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3506-0583","authenticated-orcid":false,"given":"Chenfanfu","family":"Jiang","sequence":"additional","affiliation":[{"name":"University of California Los Angeles, Los Angeles, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1919-5437","authenticated-orcid":false,"given":"Peter Yichen","family":"Chen","sequence":"additional","affiliation":[{"name":"The University of British Columbia, Vancouver, Canada"},{"name":"New York University, Vancouver, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7645-5931","authenticated-orcid":false,"given":"Yin","family":"Yang","sequence":"additional","affiliation":[{"name":"University of Utah, Salt Lake City, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2026,7,3]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.13122"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/2668064.2668066"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/74334.74356"},{"key":"e_1_2_2_4_1","volume-title":"An introduction to physically based modeling: rigid body simulation I\u2014unconstrained rigid body dynamics. 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