{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T15:53:28Z","timestamp":1778860408374,"version":"3.51.4"},"reference-count":58,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2015,7,27]],"date-time":"2015-07-27T00:00:00Z","timestamp":1437955200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2015,7,27]]},"abstract":"<jats:p>We present a new brittle fracture simulation method based on a boundary integral formulation of elasticity and recent explicit surface mesh evolution algorithms. Unlike prior physically-based simulations in graphics, this avoids the need for volumetric sampling and calculations, which aren't reflected in the rendered output. We represent each quasi-rigid body by a closed triangle mesh of its boundary, on which we solve quasi-static linear elasticity via boundary integrals in response to boundary conditions and loads such as impact forces and gravity. A fracture condition based on maximum tensile stress is subsequently evaluated at mesh vertices, while crack initiation and propagation are formulated as an interface tracking procedure in material space. Existing explicit mesh tracking methods are modified to support evolving cracks directly in the triangle mesh representation, giving highly detailed fractures with sharp features, independent of any volumetric sampling (unlike tetrahedral mesh or level set approaches); the triangle mesh representation also allows simple integration into rigid body engines. We also give details on our well-conditioned integral equation treatment solved with a kernel-independent Fast Multipole Method for linear time summation. Various brittle fracture scenarios demonstrate the efficacy and robustness of our new method.<\/jats:p>","DOI":"10.1145\/2766942","type":"journal-article","created":{"date-parts":[[2015,7,28]],"date-time":"2015-07-28T12:26:38Z","timestamp":1438086398000},"page":"1-11","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":24,"title":["Simulating rigid body fracture with surface meshes"],"prefix":"10.1145","volume":"34","author":[{"given":"Yufeng","family":"Zhu","sequence":"first","affiliation":[{"name":"University of British Columbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert","family":"Bridson","sequence":"additional","affiliation":[{"name":"University of British Columbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chen","family":"Greif","sequence":"additional","affiliation":[{"name":"University of British Columbia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2015,7,27]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1137\/0914010"},{"key":"e_1_2_2_2_1","volume-title":"Hypersingular integral equations in fracture analysis","author":"Ang W.-T.","unstructured":"Ang , W.-T. 2014. Hypersingular integral equations in fracture analysis . Elsevier . Ang, W.-T. 2014. Hypersingular integral equations in fracture analysis. Elsevier."},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2007.39"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1038\/324446a0"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12272"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1620170308"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1137\/080737617"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/1778765.1778784"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.5555\/2421731.2421746"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2461920"},{"key":"e_1_2_2_11_1","doi-asserted-by":"crossref","unstructured":"Chen Z. Yao M. Feng R. and Wang H. 2014. Physics-inspired adaptive fracture refinement. 113:1--113:7.  Chen Z. Yao M. Feng R. and Wang H. 2014. Physics-inspired adaptive fracture refinement. 113:1--113:7.","DOI":"10.1145\/2601097.2601115"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601146"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/1243980.1243986"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1020770506931"},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2012.121"},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/2366145.2366167"},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(87)90140-9"},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01396324"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/122718.122740"},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/2485895.2485908"},{"key":"e_1_2_2_22_1","doi-asserted-by":"crossref","unstructured":"Hockney R. W. and Eastwood J. W. 1988. Computer Simulation Using Particles. Taylor & Francis Inc. Bristol PA USA.   Hockney R. W. and Eastwood J. W. 1988. Computer Simulation Using Particles. Taylor & Francis Inc. Bristol PA USA.","DOI":"10.1201\/9781439822050"},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/1028523.1028541"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/311535.311542"},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/588272.588278"},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.1145\/1141911.1141983"},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531356"},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2013.06.027"},{"key":"e_1_2_2_29_1","doi-asserted-by":"publisher","DOI":"10.1145\/2614217.2614245"},{"key":"e_1_2_2_30_1","first-page":"46","article-title":"A gentle introduction to the Boundary Element Method in Matlab\/Freemat. In Proc. 10th WSEAS International Conference on Mathematical Methods, Computational Techniques and Intelligent Systems","volume":"08","author":"Kirkup S.","year":"2008","unstructured":"Kirkup , S. , and Yazdani , J. 2008 . A gentle introduction to the Boundary Element Method in Matlab\/Freemat. In Proc. 10th WSEAS International Conference on Mathematical Methods, Computational Techniques and Intelligent Systems , MAMECTIS' 08 , 46 -- 52 . Kirkup, S., and Yazdani, J. 2008. A gentle introduction to the Boundary Element Method in Matlab\/Freemat. In Proc. 10th WSEAS International Conference on Mathematical Methods, Computational Techniques and Intelligent Systems, MAMECTIS' 08, 46--52.","journal-title":"MAMECTIS'"},{"key":"e_1_2_2_31_1","volume-title":"Proc. ACM SIGGRAPH\/Eurographics Symp. Comp. Anim.","author":"Koschier D.","unstructured":"Koschier , D. , Lipponer , S. , and Bender , J . 2014. Adaptive tetrahedral meshes for brittle fracture simulation . In Proc. ACM SIGGRAPH\/Eurographics Symp. Comp. Anim. Koschier, D., Lipponer, S., and Bender, J. 2014. Adaptive tetrahedral meshes for brittle fracture simulation. In Proc. ACM SIGGRAPH\/Eurographics Symp. Comp. Anim."},{"key":"e_1_2_2_32_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.enganabound.2010.06.007"},{"key":"e_1_2_2_34_1","doi-asserted-by":"publisher","DOI":"10.1145\/1015706.1015734"},{"key":"e_1_2_2_35_1","first-page":"239","article-title":"Interactive virtual materials","volume":"2004","author":"M\u00fcller M.","year":"2004","unstructured":"M\u00fcller , M. , and Gross , M. 2004 . Interactive virtual materials . In Graphics Interface 2004 , 239 -- 246 . M\u00fcller, M., and Gross, M. 2004. Interactive virtual materials. In Graphics Interface 2004, 239--246.","journal-title":"Graphics Interface"},{"key":"e_1_2_2_36_1","volume-title":"Proc. Eurographics Workshop on Computer Animation and Simulation, 113--124","author":"M\u00fcller M.","unstructured":"M\u00fcller , M. , McMillan , L. , Dorsey , J. , and Jagnow , R . 2001. Real-time simulation of deformation and fracture of stiff materials . In Proc. Eurographics Workshop on Computer Animation and Simulation, 113--124 . M\u00fcller, M., McMillan, L., Dorsey, J., and Jagnow, R. 2001. Real-time simulation of deformation and fracture of stiff materials. In Proc. Eurographics Workshop on Computer Animation and Simulation, 113--124."},{"key":"e_1_2_2_37_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2461934"},{"key":"e_1_2_2_38_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01900837"},{"key":"e_1_2_2_39_1","doi-asserted-by":"publisher","DOI":"10.1145\/311535.311550"},{"key":"e_1_2_2_40_1","doi-asserted-by":"publisher","DOI":"10.1145\/566570.566579"},{"key":"e_1_2_2_41_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073368.1073406"},{"key":"e_1_2_2_42_1","doi-asserted-by":"publisher","DOI":"10.1145\/1599470.1599492"},{"key":"e_1_2_2_43_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073296"},{"key":"e_1_2_2_44_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601132"},{"key":"e_1_2_2_45_1","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1620330611"},{"key":"e_1_2_2_46_1","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(86)90060-5"},{"key":"e_1_2_2_47_1","volume-title":"Proc. ACM SIGGRAPH\/Eurographics Symp. Comp. Anim., 73--80","author":"Sifakis E.","unstructured":"Sifakis , E. , Der , K. G. , and Fedkiw , R . 2007. Arbitrary cutting of deformable tetrahedralized objects . In Proc. ACM SIGGRAPH\/Eurographics Symp. Comp. Anim., 73--80 . Sifakis, E., Der, K. G., and Fedkiw, R. 2007. Arbitrary cutting of deformable tetrahedralized objects. In Proc. ACM SIGGRAPH\/Eurographics Symp. Comp. Anim., 73--80."},{"key":"e_1_2_2_48_1","first-page":"477","article-title":"Meshless local petrov-galerkin method in anisotropic elasticity","volume":"6","author":"Sladek J.","year":"2004","unstructured":"Sladek , J. , Sladek , V. , and Atluri , S. 2004 . Meshless local petrov-galerkin method in anisotropic elasticity . Comput Model Eng Sci 6 , 477 -- 489 . Sladek, J., Sladek, V., and Atluri, S. 2004. Meshless local petrov-galerkin method in anisotropic elasticity. Comput Model Eng Sci 6, 477--489.","journal-title":"Comput Model Eng Sci"},{"key":"e_1_2_2_49_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-8659.t01-1-00202"},{"key":"e_1_2_2_50_1","volume-title":"Proc. ACM SIGGRAPH\/Eurographics Symp. Comp. Anim., 63--72","author":"Steinemann D.","unstructured":"Steinemann , D. , Otaduy , M. A. , and Gross , M . 2006. Fast arbitrary splitting of deforming objects . In Proc. ACM SIGGRAPH\/Eurographics Symp. Comp. Anim., 63--72 . Steinemann, D., Otaduy, M. A., and Gross, M. 2006. Fast arbitrary splitting of deforming objects. In Proc. ACM SIGGRAPH\/Eurographics Symp. Comp. Anim., 63--72."},{"key":"e_1_2_2_51_1","doi-asserted-by":"publisher","DOI":"10.1145\/1599470.1599491"},{"key":"e_1_2_2_52_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601187"},{"key":"e_1_2_2_53_1","doi-asserted-by":"publisher","DOI":"10.1145\/54852.378522"},{"key":"e_1_2_2_54_1","doi-asserted-by":"publisher","DOI":"10.1137\/0913035"},{"key":"e_1_2_2_55_1","doi-asserted-by":"publisher","DOI":"10.1145\/1778765.1778852"},{"key":"e_1_2_2_56_1","doi-asserted-by":"publisher","DOI":"10.1145\/1778765.1778786"},{"key":"e_1_2_2_57_1","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531382"},{"key":"e_1_2_2_58_1","unstructured":"Wu J. Westermann R. and Dick C. 2014. Physically-based simulation of cuts in deformable bodies: A survey. In Eurographics 2014 State-of-the-Art Report 1--19.  Wu J. Westermann R. and Dick C. 2014. Physically-based simulation of cuts in deformable bodies: A survey. In Eurographics 2014 State-of-the-Art Report 1--19."},{"key":"e_1_2_2_59_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2003.11.021"},{"key":"e_1_2_2_60_1","doi-asserted-by":"publisher","DOI":"10.1145\/1778765.1778806"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2766942","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2766942","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T05:43:01Z","timestamp":1750225381000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2766942"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,7,27]]},"references-count":58,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2015,7,27]]}},"alternative-id":["10.1145\/2766942"],"URL":"https:\/\/doi.org\/10.1145\/2766942","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,7,27]]},"assertion":[{"value":"2015-07-27","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}