{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,23]],"date-time":"2026-07-23T17:36:08Z","timestamp":1784828168591,"version":"3.55.0"},"reference-count":58,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2019,7,12]],"date-time":"2019-07-12T00:00:00Z","timestamp":1562889600000},"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":[[2019,8,31]]},"abstract":"<jats:p>\n            We present an analysis of anisotropic hyperelasticity, specifically transverse isotropy, that obtains closed-form expressions for the eigendecompositions of many common energies. We then use these to build fast and concise Newton implementations. We leverage our analysis in two separate applications. First, we show that existing anisotropic energies are not inversion-safe, and contain spurious stable states under large deformation. We then propose a new anisotropic strain invariant that enables the formulation of a novel, robust, and inversion-safe energy. The new energy fits completely within our analysis, so closed-form expressions are obtained for its eigensystem as well. Secondly, we use our analysis to\n            <jats:italic>rehabilitate<\/jats:italic>\n            badly-conditioned finite elements. Using this method, we can robustly simulate large deformations even when a mesh contains degenerate, zero-volume elements. We accomplish this by swapping the badly-behaved isotropic direction with a well-behaved anisotropic term. We validate our approach on a variety of examples.\n          <\/jats:p>","DOI":"10.1145\/3306346.3323014","type":"journal-article","created":{"date-parts":[[2019,7,12]],"date-time":"2019-07-12T19:04:08Z","timestamp":1562958248000},"page":"1-15","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":35,"title":["Anisotropic elasticity for inversion-safety and element rehabilitation"],"prefix":"10.1145","volume":"38","author":[{"given":"Theodore","family":"Kim","sequence":"first","affiliation":[{"name":"Pixar Animation Studios"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fernando","family":"De Goes","sequence":"additional","affiliation":[{"name":"Pixar Animation Studios"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hayley","family":"Iben","sequence":"additional","affiliation":[{"name":"Pixar Animation Studios"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2019,7,12]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jbiomech.2008.07.008"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/344779.344859"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/280814.280821"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073300"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/1276377.1276397"},{"key":"e_1_2_2_6_1","unstructured":"T. Belytschko W. Liu B. Moran and K. Elkhodary. 2013. Nonlinear finite elements for continua and structures. John Wiley & Sons.  T. Belytschko W. Liu B. Moran and K. Elkhodary. 2013. Nonlinear finite elements for continua and structures. John Wiley & Sons."},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jbiomech.2004.04.009"},{"key":"e_1_2_2_8_1","doi-asserted-by":"crossref","unstructured":"J. Bonet and R. D. Wood. 2008. Nonlinear continuum mechanics for finite element analysis. Cambridge University Press.  J. Bonet and R. D. Wood. 2008. Nonlinear continuum mechanics for finite element analysis. Cambridge University Press.","DOI":"10.1017\/CBO9780511755446"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601116"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10659-014-9508-z"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/3197517.3201386"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmbbm.2011.05.006"},{"key":"e_1_2_2_14_1","volume-title":"Proceedings of Computer Animation. 225--229","author":"Forest C.","unstructured":"C. Forest , H. Delingette , and N. Ayache . 2002. Removing tetrahedra from a manifold mesh . In Proceedings of Computer Animation. 225--229 . C. Forest, H. Delingette, and N. Ayache. 2002. Removing tetrahedra from a manifold mesh. In Proceedings of Computer Animation. 225--229."},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2015.2459687"},{"key":"e_1_2_2_16_1","volume-title":"Matrix computations","author":"Golub G. H.","unstructured":"G. H. Golub and C. F. Van Loan . 2012. Matrix computations . Vol. 3 . JHU Press . G. H. Golub and C. F. Van Loan. 2012. Matrix computations. Vol. 3. JHU Press."},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/1242073.1242187"},{"key":"e_1_2_2_18_1","first-page":"607","article-title":"Similarities between soft biological tissues and rubberlike materials","volume":"4","author":"Holzapfel G.","year":"2005","unstructured":"G. Holzapfel . 2005 . Similarities between soft biological tissues and rubberlike materials . In Constitutive Models for Rubber IV , Vol. 4. 607 . G. Holzapfel. 2005. Similarities between soft biological tissues and rubberlike materials. In Constitutive Models for Rubber IV, Vol. 4. 607.","journal-title":"Constitutive Models for Rubber IV"},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1010835316564"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmps.2005.04.004"},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/3197517.3201353"},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/1401032.1401102"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/1028523.1028541"},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/2659467.2675048"},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-874X(02)00070-7"},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/3072959.3073666"},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1145\/1276377.1276448"},{"key":"e_1_2_2_29_1","doi-asserted-by":"publisher","DOI":"10.1145\/1141911.1142013"},{"key":"e_1_2_2_30_1","doi-asserted-by":"publisher","DOI":"10.1145\/3197517.3201330"},{"key":"e_1_2_2_31_1","doi-asserted-by":"publisher","DOI":"10.1145\/2661229.2661233"},{"key":"e_1_2_2_32_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2015.2448105"},{"key":"e_1_2_2_33_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2016.2620467"},{"key":"e_1_2_2_34_1","doi-asserted-by":"publisher","DOI":"10.1145\/2990496"},{"key":"e_1_2_2_35_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12941"},{"key":"e_1_2_2_36_1","doi-asserted-by":"publisher","DOI":"10.1145\/2010324.1964932"},{"key":"e_1_2_2_37_1","doi-asserted-by":"publisher","DOI":"10.1145\/2897839.2927390"},{"key":"e_1_2_2_38_1","doi-asserted-by":"publisher","DOI":"10.1145\/1015706.1015734"},{"key":"e_1_2_2_39_1","unstructured":"N. Molino R. Bridson J. Teran and R. Fedkiw. 2003. A Crystalline Red Green Strategy for Meshing Highly Deformable Objects with Tetrahedra.. In International Meshing Roundtable. 103--114.  N. Molino R. Bridson J. Teran and R. Fedkiw. 2003. A Crystalline Red Green Strategy for Meshing Highly Deformable Objects with Tetrahedra.. In International Meshing Roundtable. 103--114."},{"key":"e_1_2_2_40_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmbbm.2014.06.016"},{"key":"e_1_2_2_41_1","volume-title":"IEEE International Conference on Robotics and Automation. IEEE, 596--602","author":"Picinbono G.","unstructured":"G. Picinbono , J. Lombardo , H. Delingette , and N. Ayache . 2000. Anisotropic elasticity and force extrapolation to improve realism of surgery simulation . In IEEE International Conference on Robotics and Automation. IEEE, 596--602 . G. Picinbono, J. Lombardo, H. Delingette, and N. Ayache. 2000. Anisotropic elasticity and force extrapolation to improve realism of surgery simulation. In IEEE International Conference on Robotics and Automation. IEEE, 596--602."},{"key":"e_1_2_2_42_1","unstructured":"Y. Qiu. 2018. Spectra a C++ Library For Large Scale Eigenvalue Problems. https:\/\/spectralib.org.  Y. Qiu. 2018. Spectra a C++ Library For Large Scale Eigenvalue Problems. https:\/\/spectralib.org."},{"key":"e_1_2_2_43_1","doi-asserted-by":"publisher","DOI":"10.1137\/15M1026419"},{"key":"e_1_2_2_44_1","doi-asserted-by":"publisher","DOI":"10.1145\/2766987"},{"key":"e_1_2_2_45_1","doi-asserted-by":"publisher","DOI":"10.1145\/2766957"},{"key":"e_1_2_2_46_1","doi-asserted-by":"publisher","DOI":"10.1145\/3272127.3275067"},{"key":"e_1_2_2_47_1","unstructured":"J. Shewchuk. 2002. What is a good linear finite element? interpolation conditioning anisotropy and quality measures. University of California at Berkeley 73 (2002).  J. Shewchuk. 2002. What is a good linear finite element? interpolation conditioning anisotropy and quality measures. University of California at Berkeley 73 (2002)."},{"key":"e_1_2_2_48_1","doi-asserted-by":"publisher","DOI":"10.1145\/3180491"},{"key":"e_1_2_2_49_1","doi-asserted-by":"publisher","DOI":"10.1145\/3241041"},{"key":"e_1_2_2_50_1","volume-title":"Eurog. Symposium on Geometry processing","volume":"4","author":"Sorkine O.","unstructured":"O. Sorkine and M. Alexa . 2007. As-rigid-as-possible surface modeling . In Eurog. Symposium on Geometry processing , Vol. 4 . O. Sorkine and M. Alexa. 2007. As-rigid-as-possible surface modeling. In Eurog. Symposium on Geometry processing, Vol. 4."},{"key":"e_1_2_2_51_1","volume-title":"Energetically Consistent Invertible Elasticity. In ACM SIGGRAPH\/Eurog. Symp. Comp. Anim. 25--32","author":"Stomakhin A.","unstructured":"A. Stomakhin , R. Howes , C. Schroeder , and J. M. Teran . 2012 . Energetically Consistent Invertible Elasticity. In ACM SIGGRAPH\/Eurog. Symp. Comp. Anim. 25--32 . A. Stomakhin, R. Howes, C. Schroeder, and J. M. Teran. 2012. Energetically Consistent Invertible Elasticity. In ACM SIGGRAPH\/Eurog. Symp. Comp. Anim. 25--32."},{"key":"e_1_2_2_52_1","volume-title":"SIGGRAPH\/Eurog. Symp. on Comp. Anim. 68--74","author":"Teran J.","unstructured":"J. Teran , S. Blemker , V. Hing , and R. Fedkiw . 2003. Finite volume methods for the simulation of skeletal muscle . In SIGGRAPH\/Eurog. Symp. on Comp. Anim. 68--74 . J. Teran, S. Blemker, V. Hing, and R. Fedkiw. 2003. Finite volume methods for the simulation of skeletal muscle. In SIGGRAPH\/Eurog. Symp. on Comp. Anim. 68--74."},{"key":"e_1_2_2_53_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073368.1073394"},{"key":"e_1_2_2_54_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882290"},{"key":"e_1_2_2_55_1","doi-asserted-by":"publisher","DOI":"10.1145\/3072959.3073655"},{"key":"e_1_2_2_56_1","doi-asserted-by":"publisher","DOI":"10.1145\/2980179.2980236"},{"key":"e_1_2_2_57_1","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(96)01035-3"},{"key":"e_1_2_2_58_1","doi-asserted-by":"publisher","DOI":"10.1145\/1360612.1360646"},{"key":"e_1_2_2_59_1","doi-asserted-by":"publisher","DOI":"10.1145\/3214745.3214786"},{"key":"e_1_2_2_60_1","doi-asserted-by":"publisher","DOI":"10.1145\/2766917"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3306346.3323014","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3306346.3323014","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T00:25:52Z","timestamp":1750206352000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3306346.3323014"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,12]]},"references-count":58,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,8,31]]}},"alternative-id":["10.1145\/3306346.3323014"],"URL":"https:\/\/doi.org\/10.1145\/3306346.3323014","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,7,12]]},"assertion":[{"value":"2019-07-12","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}