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The core idea is to decouple material nonlinearity from geometry optimization by introducing the Cauchy stress tensor as an auxiliary variable. We design a three\u2010stage scheme that iteratively optimizes the stress tensors and the rest shape, with each stage being well\u2010posed and efficiently\u2010solvable. To address the lack of a theoretical convergence guarantee arising from the decoupled energy formulation, we incorporate a relaxation method that ensures robust stability in practice. As a result, our method achieves a 3\n                    <jats:italic>\u00d7<\/jats:italic>\n                    speedup over the state\u2010of\u2010the\u2010art asymptotic method [Jia21] on a model with 40k vertices and 112k elements (Fig. 2), and exhibits near\u2010linear scalability to large systems (Fig. 8). We demonstrate applications including rest shape design for various materials (ranging from standard models to complex spline\u2010based materials [XSZB15]), interactive material and force editing, and elastic object reconstruction from images.\n                  <\/jats:p>","DOI":"10.1111\/cgf.70402","type":"journal-article","created":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T12:37:22Z","timestamp":1774874242000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["STAGED: Stress\u2010Tensor Assisted Global\u2013local\u2010global solver for interactive Elastic shape Design"],"prefix":"10.1111","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0803-1429","authenticated-orcid":false,"given":"Liangwang","family":"Ruan","sequence":"first","affiliation":[{"name":"School of Computer Science Peking University  China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9496-772X","authenticated-orcid":false,"given":"Bin","family":"Wang","sequence":"additional","affiliation":[{"name":"Independent Researcher  China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5614-1588","authenticated-orcid":false,"given":"Tiantian","family":"Liu","sequence":"additional","affiliation":[{"name":"Independent Researcher  China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4702-036X","authenticated-orcid":false,"given":"Baoquan","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Intelligent Science and Technology Peking University  China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2026,3,30]]},"reference":[{"key":"e_1_2_7_2_2","doi-asserted-by":"publisher","DOI":"10.1145\/3197517.3201387"},{"key":"e_1_2_7_2_3","doi-asserted-by":"crossref","unstructured":"doi:10.1145\/3197517.3201387. 4","DOI":"10.1145\/3197517.3201387"},{"key":"e_1_2_7_3_2","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601116"},{"key":"e_1_2_7_3_3","doi-asserted-by":"crossref","unstructured":"doi:10.1145\/2601097.2601116. 2 4 7 8","DOI":"10.1145\/2601097.2601116"},{"key":"e_1_2_7_4_2","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459942"},{"key":"e_1_2_7_4_3","doi-asserted-by":"crossref","unstructured":"doi:10.1145\/3450626.3459942. 2 4","DOI":"10.1145\/3450626.3459942"},{"key":"e_1_2_7_5_2","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601189"},{"key":"e_1_2_7_5_3","doi-asserted-by":"crossref","unstructured":"doi:10.1145\/2601097.2601189. 2 3 7","DOI":"10.1145\/2601097.2601189"},{"key":"e_1_2_7_6_2","doi-asserted-by":"publisher","DOI":"10.1145\/2508363.2508398"},{"key":"e_1_2_7_6_3","doi-asserted-by":"crossref","unstructured":"doi:10.1145\/2508363.2508398. 3","DOI":"10.1145\/2508363.2508398"},{"key":"e_1_2_7_7_2","doi-asserted-by":"publisher","DOI":"10.1109\/99.660313"},{"key":"e_1_2_7_8_2","unstructured":"GuennebaudG. 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