{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T15:36:51Z","timestamp":1778081811636,"version":"3.51.4"},"reference-count":41,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2017,7,11]],"date-time":"2017-07-11T00:00:00Z","timestamp":1499731200000},"content-version":"vor","delay-in-days":365,"URL":"http:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N000141110719, N000141210834"],"award-info":[{"award-number":["N000141110719, N000141210834"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Intel STC-Visual Computing Grant","award":["20112360"],"award-info":[{"award-number":["20112360"]}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-1422795"],"award-info":[{"award-number":["CCF-1422795"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000005","name":"U.S. Department of Defense","doi-asserted-by":"publisher","award":["W81XWH-15-1-0147"],"award-info":[{"award-number":["W81XWH-15-1-0147"]}],"id":[{"id":"10.13039\/100000005","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2016,7,11]]},"abstract":"<jats:p>We simulate sand dynamics using an elastoplastic, continuum assumption. We demonstrate that the Drucker-Prager plastic flow model combined with a Hencky-strain-based hyperelasticity accurately recreates a wide range of visual sand phenomena with moderate computational expense. We use the Material Point Method (MPM) to discretize the governing equations for its natural treatment of contact, topological change and history dependent constitutive relations. The Drucker-Prager model naturally represents the frictional relation between shear and normal stresses through a yield stress criterion. We develop a stress projection algorithm used for enforcing this condition with a non-associative flow rule that works naturally with both implicit and explicit time integration. We demonstrate the efficacy of our approach on examples undergoing large deformation, collisions and topological changes necessary for producing modern visual effects.<\/jats:p>","DOI":"10.1145\/2897824.2925906","type":"journal-article","created":{"date-parts":[[2016,7,11]],"date-time":"2016-07-11T12:04:33Z","timestamp":1468238673000},"page":"1-12","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":155,"title":["Drucker-prager elastoplasticity for sand animation"],"prefix":"10.1145","volume":"35","author":[{"given":"Gergely","family":"Kl\u00e1r","sequence":"first","affiliation":[{"name":"University of California, Los Angeles"}]},{"given":"Theodore","family":"Gast","sequence":"additional","affiliation":[{"name":"University of California, Los Angeles"}]},{"given":"Andre","family":"Pradhana","sequence":"additional","affiliation":[{"name":"University of California, Los Angeles"}]},{"given":"Chuyuan","family":"Fu","sequence":"additional","affiliation":[{"name":"University of California, Los Angeles"}]},{"given":"Craig","family":"Schroeder","sequence":"additional","affiliation":[{"name":"University of California, Los Angeles"}]},{"given":"Chenfanfu","family":"Jiang","sequence":"additional","affiliation":[{"name":"University of California, Los Angeles"}]},{"given":"Joseph","family":"Teran","sequence":"additional","affiliation":[{"name":"University of California, Los Angeles"}]}],"member":"320","published-online":{"date-parts":[[2016,7,11]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/2019406.2019410"},{"key":"e_1_2_2_2_1","volume-title":"Proc Cong Espa\u00f1ol Inf Graf.","author":"Aldu\u00e1n I.","unstructured":"Aldu\u00e1n, I., Tena, A., and Otaduy, M. 2009. Simulation of high-resolution granular media. In Proc Cong Espa\u00f1ol Inf Graf."},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(99)00338-2"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073368.1073379"},{"key":"e_1_2_2_5_1","doi-asserted-by":"crossref","unstructured":"Bonet J. and Wood R. 2008. Nonlinear continuum mechanics for finite element analysis. Cambridge University Press.","DOI":"10.1017\/CBO9780511755446"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","unstructured":"Chanclou B. Luciani A. and Habibi A. 1996. Physical models of loose soils dynamically marked by a moving object. In Comp Anim 27--35.","DOI":"10.5555\/791215.791502"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11432-012-4564-0"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","unstructured":"Chen P. and Wong S. 2013. Real-time auto stylized sand art drawing. In CAD Comp Graph 439--440. 10.1109\/CADGraphics.2013.86","DOI":"10.1109\/CADGraphics.2013.86"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2002.7101"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1090\/qam\/48291"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2015.2459687"},{"key":"e_1_2_2_12_1","unstructured":"Gonzalez O. and Stuart A. 2008. A first course in continuum mechanics. Cambridge University Press."},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cag.2013.04.010"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.68.1259"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/2766996"},{"key":"e_1_2_2_16_1","unstructured":"Jiang C. 2015. The material point method for the physics-based simulation of solids and fluids. PhD thesis University of California Los Angeles."},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","unstructured":"Kl\u00e1r G. Gast T. Pradhana A. Fu C. Schroeder C. Jiang C. and Teran J. 2016. Drucker-prager elastoplasticity for sand animation: Supplementary technical document. ACM Trans Graph. 10.1145\/2897824.2925906","DOI":"10.1145\/2897824.2925906"},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2009.01360.x"},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/166117.166162"},{"key":"e_1_2_2_20_1","volume-title":"Proc Graph Int, 136--146","author":"Luciani A.","unstructured":"Luciani, A., Habibi, A., and Manzotti, E. 1995. A multi-scale physical model of granular materials. In Proc Graph Int, 136--146."},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601152"},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11440-014-0309-0"},{"key":"e_1_2_2_23_1","unstructured":"Mast C. 2013. Modeling landslide-induced flow interactions with structures using the Material Point Method. PhD thesis."},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/2735627"},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/237170.237222"},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.1016\/0097-8493(89)90078-2"},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/1882261.1866195"},{"key":"e_1_2_2_28_1","first-page":"495","article-title":"A real-time sand simulation using a GPU","volume":"1","author":"Nkulikiyimfura D.","year":"2012","unstructured":"Nkulikiyimfura, D., Kim, J., and Kim, H. 2012. A real-time sand simulation using a GPU. In Comp Tech Inf Man, vol. 1, 495--498.","journal-title":"Comp Tech Inf Man"},{"key":"e_1_2_2_29_1","unstructured":"Nocedal J. and Wright S. 2006. Numerical Optimization. Springer series in operations research and financial engineering. Springer."},{"key":"e_1_2_2_30_1","doi-asserted-by":"publisher","DOI":"10.5555\/946250.946949"},{"key":"e_1_2_2_31_1","doi-asserted-by":"publisher","unstructured":"Pla-Castells M. Garcia-Fernandez I. and Martinez R. 2006. Interactive terrain simulation and force distribution models in sand piles. In Cellular Automata vol. 4173 of Lecture Notes Comp Sci. 392--401. 10.1007\/11861201_46","DOI":"10.1007\/11861201_46"},{"key":"e_1_2_2_32_1","doi-asserted-by":"publisher","DOI":"10.1145\/2786784.2786798"},{"key":"e_1_2_2_33_1","doi-asserted-by":"publisher","DOI":"10.1002\/nme.2360"},{"key":"e_1_2_2_34_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2461948"},{"key":"e_1_2_2_35_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601176"},{"key":"e_1_2_2_36_1","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(94)90112-0"},{"key":"e_1_2_2_37_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-8659.00299"},{"key":"e_1_2_2_38_1","doi-asserted-by":"publisher","unstructured":"Yasuda R. Harada T. and Kawaguchi Y. 2008. Realtime simulation of granular materials using graphics hardware. In Comp Graph Imag Vis 28--31. 10.1109\/CGIV.2008.45","DOI":"10.1109\/CGIV.2008.45"},{"key":"e_1_2_2_39_1","doi-asserted-by":"crossref","unstructured":"Yoshioka N. 2003. A sandpile experiment and its implications for self-organized criticality and characteristic earthquake. Earth planets and space 55 6 283--289.","DOI":"10.1186\/BF03351762"},{"key":"e_1_2_2_40_1","doi-asserted-by":"publisher","DOI":"10.1145\/2751541"},{"key":"e_1_2_2_41_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073298"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2897824.2925906","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2897824.2925906","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2897824.2925906","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T09:27:28Z","timestamp":1763458048000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2897824.2925906"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,7,11]]},"references-count":41,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2016,7,11]]}},"alternative-id":["10.1145\/2897824.2925906"],"URL":"https:\/\/doi.org\/10.1145\/2897824.2925906","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,7,11]]},"assertion":[{"value":"2016-07-11","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}