{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T20:26:28Z","timestamp":1792787188592,"version":"4.5.0"},"reference-count":41,"publisher":"American Association for the Advancement of Science (AAAS)","issue":"38","funder":[{"DOI":"10.13039\/501100001348","name":"Agency for Science, Technology and Research","doi-asserted-by":"publisher","award":["M23L8b0049"],"award-info":[{"award-number":["M23L8b0049"]}],"id":[{"id":"10.13039\/501100001348","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Research Foundation Singapore","award":["CREATE - SGSR"],"award-info":[{"award-number":["CREATE - SGSR"]}],"id":[{"id":"https:\/\/ror.org\/03cpyc314","id-type":"ROR","asserted-by":"crossref"}]},{"name":"National Research Foundation Singapore","award":["NRF-NRFI09-0007"],"award-info":[{"award-number":["NRF-NRFI09-0007"]}],"id":[{"id":"https:\/\/ror.org\/03cpyc314","id-type":"ROR","asserted-by":"crossref"}]},{"name":"National Research Foundation Singapore","award":["SHINE"],"award-info":[{"award-number":["SHINE"]}],"id":[{"id":"https:\/\/ror.org\/03cpyc314","id-type":"ROR","asserted-by":"crossref"}]},{"name":"Semiconductor RIE Flagship Programme: Singapore Hybrid-Integrated Next-Generation \u00b5-Electronics (SHINE) Centre 2.0","award":["H26-MSE1554"],"award-info":[{"award-number":["H26-MSE1554"]}]}],"content-domain":{"domain":["www.science.org"],"crossmark-restriction":true},"short-container-title":["Sci. Adv."],"published-print":{"date-parts":[[2026,9,18]]},"abstract":"<jats:p>Accurate shape sensing requires simultaneous quantification of bending angle (\u03c6) and bending direction (\u03b8). Yet existing bending sensors remain confined to uniaxial or discretized modes, relying on tedious, non-generalizable calibration procedures. Here, we present a snowflake-shaped omnidirectional bending sensor that achieves complete and linear decoupling of \u03c6 and \u03b8 through a three-fold rotationally symmetric arrangement of strain-sensitive resistors. By harnessing geometric symmetry as a physical prior, we establish a closed-form analytical model and signal projection framework that transform calibration from an empirical process into a simple, quantitative, universal procedure. The sensor is compatible with standard flexible printed circuit board (FPCB) fabrication on polyimide (PI) and polyethylene terephthalate (PET) substrates, ensuring scalability and integration. We demonstrate real-time reconstruction of multidirectional surface deformation and in situ correction of ultrasound imaging artifacts during bending. This symmetry-guided approach redefines the design principles of deformation sensing, providing a general platform for dynamic shape reconstruction and opening avenues for self-adaptive and self-aware electronic systems.<\/jats:p>","DOI":"10.1126\/sciadv.aeb8359","type":"journal-article","created":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T18:04:04Z","timestamp":1789754644000},"update-policy":"https:\/\/doi.org\/10.34133\/aaas_crossmark","source":"Crossref","is-referenced-by-count":0,"title":["Omnidirectional bending sensor with three-fold structural symmetry enables decoupling of bending angle and direction"],"prefix":"10.1126","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-6892-1644","authenticated-orcid":true,"given":"Yanzhen","family":"Li","sequence":"first","affiliation":[{"name":"Innovative Center for Flexible Devices (iFLEX), Max Planck \u2013 NTU Joint Lab for Artificial Senses, School of Materials Science and Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore."},{"name":"School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0232-8213","authenticated-orcid":true,"given":"Zheren","family":"Cai","sequence":"additional","affiliation":[{"name":"Innovative Center for Flexible Devices (iFLEX), Max Planck \u2013 NTU Joint Lab for Artificial Senses, School of Materials Science and Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5607-4194","authenticated-orcid":true,"given":"Yongli","family":"He","sequence":"additional","affiliation":[{"name":"Innovative Center for Flexible Devices (iFLEX), Max Planck \u2013 NTU Joint Lab for Artificial Senses, School of Materials Science and Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6712-7717","authenticated-orcid":true,"given":"Zhihua","family":"Liu","sequence":"additional","affiliation":[{"name":"Institute of Materials Research and Engineering (IMRE), Agency for Science, Technology and Research (A*STAR), 2 Fusionopolis Way, Innovis #08-03, 138634, Singapore."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9593-7589","authenticated-orcid":true,"given":"Cong","family":"Wang","sequence":"additional","affiliation":[{"name":"Innovative Center for Flexible Devices (iFLEX), Max Planck \u2013 NTU Joint Lab for Artificial Senses, School of Materials Science and Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1779-9448","authenticated-orcid":true,"given":"Jiaofu","family":"Li","sequence":"additional","affiliation":[{"name":"Innovative Center for Flexible Devices (iFLEX), Max Planck \u2013 NTU Joint Lab for Artificial Senses, School of Materials Science and Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0729-0357","authenticated-orcid":true,"given":"Wenlong","family":"Li","sequence":"additional","affiliation":[{"name":"Institute of Materials Research and Engineering (IMRE), Agency for Science, Technology and Research (A*STAR), 2 Fusionopolis Way, Innovis #08-03, 138634, Singapore."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5631-0655","authenticated-orcid":true,"given":"Nuan","family":"Chen","sequence":"additional","affiliation":[{"name":"Innovative Center for Flexible Devices (iFLEX), Max Planck \u2013 NTU Joint Lab for Artificial Senses, School of Materials Science and Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-0977-2991","authenticated-orcid":true,"given":"Dong","family":"Wu","sequence":"additional","affiliation":[{"name":"Innovative Center for Flexible Devices (iFLEX), Max Planck \u2013 NTU Joint Lab for Artificial Senses, School of Materials Science and Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8656-846X","authenticated-orcid":true,"given":"Huajian","family":"Gao","sequence":"additional","affiliation":[{"name":"Mechano-X Institute, Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P. 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China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3312-1664","authenticated-orcid":true,"given":"Xiaodong","family":"Chen","sequence":"additional","affiliation":[{"name":"Innovative Center for Flexible Devices (iFLEX), Max Planck \u2013 NTU Joint Lab for Artificial Senses, School of Materials Science and Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore."},{"name":"School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"221","reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1021\/acsnano.2c12606"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.1182383"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1038\/s44222-024-00194-1"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1038\/nmat3380"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature14002"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1002\/adfm.201504755"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1002\/aisy.202000039"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1002\/adfm.201400379"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1038\/nnano.2011.36"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.3390\/nano11051220"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1109\/JSEN.2022.3156286"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1080\/19475411.2024.2417834"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-020-2892-6"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.aba5504"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1002\/adma.201503558"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1002\/aisy.202200337"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1021\/acs.nanolett.8b02088"},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.carbon.2017.10.034"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1039\/C8TC02505C"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1002\/adfm.201604434"},{"key":"e_1_3_2_22_2","doi-asserted-by":"publisher","DOI":"10.1021\/acsami.9b21816"},{"key":"e_1_3_2_23_2","doi-asserted-by":"publisher","DOI":"10.1021\/acsami.2c14642"},{"key":"e_1_3_2_24_2","doi-asserted-by":"publisher","DOI":"10.1039\/D1TA09252A"},{"key":"e_1_3_2_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.compositesb.2024.111538"},{"key":"e_1_3_2_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.carbon.2024.119201"},{"key":"e_1_3_2_27_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.nanoen.2024.109350"},{"key":"e_1_3_2_28_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cej.2024.149952"},{"key":"e_1_3_2_29_2","doi-asserted-by":"publisher","DOI":"10.1021\/acssensors.4c01097"},{"key":"e_1_3_2_30_2","doi-asserted-by":"publisher","DOI":"10.1002\/admt.201800698"},{"key":"e_1_3_2_31_2","doi-asserted-by":"publisher","DOI":"10.1364\/OL.497509"},{"key":"e_1_3_2_32_2","doi-asserted-by":"publisher","DOI":"10.1063\/5.0158874"},{"key":"e_1_3_2_33_2","doi-asserted-by":"publisher","DOI":"10.1002\/adma.202208184"},{"key":"e_1_3_2_34_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.sna.2020.112275"},{"key":"e_1_3_2_35_2","doi-asserted-by":"publisher","DOI":"10.1109\/JLT.2023.3266341"},{"key":"e_1_3_2_36_2","doi-asserted-by":"publisher","DOI":"10.1021\/acsnano.5c12854"},{"key":"e_1_3_2_37_2","doi-asserted-by":"publisher","DOI":"10.1002\/admt.202401431"},{"key":"e_1_3_2_38_2","doi-asserted-by":"publisher","DOI":"10.1364\/OL.480907"},{"key":"e_1_3_2_39_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.nanoen.2022.107173"},{"key":"e_1_3_2_40_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41528-021-00102-2"},{"key":"e_1_3_2_41_2","doi-asserted-by":"publisher","DOI":"10.1021\/acssensors.4c02734"},{"key":"e_1_3_2_42_2","doi-asserted-by":"crossref","unstructured":"D. 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