A mechanics‐informed artificial neural network approach in data‐driven constitutive modeling
A mechanics‐informed artificial neural network approach for learning constitutive laws governing complex, nonlinear, elastic materials from strain–stress data is proposed. The approach features a robust and accurate method for training a regression‐based model capable of capturing highly nonlinear s...
Gespeichert in:
| Veröffentlicht in: | International journal for numerical methods in engineering Jg. 123; H. 12; S. 2738 - 2759 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Hoboken, USA
John Wiley & Sons, Inc
30.06.2022
Wiley Subscription Services, Inc |
| Schlagworte: | |
| ISSN: | 0029-5981, 1097-0207 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | A mechanics‐informed artificial neural network approach for learning constitutive laws governing complex, nonlinear, elastic materials from strain–stress data is proposed. The approach features a robust and accurate method for training a regression‐based model capable of capturing highly nonlinear strain–stress mappings, while preserving some fundamental principles of solid mechanics. In this sense, it is a structure‐preserving approach for constructing a data‐driven model featuring both the form‐agnostic advantage of purely phenomenological data‐driven regressions and the physical soundness of mechanistic models. The proposed methodology enforces desirable mathematical properties on the network architecture to guarantee the satisfaction of physical constraints such as objectivity, consistency (preservation of rigid body modes), dynamic stability, and material stability, which are important for successfully exploiting the resulting model in numerical simulations. Indeed, embedding such notions in a learning approach reduces a model's sensitivity to noise and promotes its robustness to inputs outside the training domain. The merits of the proposed learning approach are highlighted using several finite element analysis examples. Its potential for ensuring the computational tractability of multi‐scale applications is demonstrated with the acceleration of the nonlinear, dynamic, multi‐scale, fluid‐structure simulation of the supersonic inflation dynamics of a parachute system with a canopy made of a woven fabric. |
|---|---|
| AbstractList | A mechanics‐informed artificial neural network approach for learning constitutive laws governing complex, nonlinear, elastic materials from strain–stress data is proposed. The approach features a robust and accurate method for training a regression‐based model capable of capturing highly nonlinear strain–stress mappings, while preserving some fundamental principles of solid mechanics. In this sense, it is a structure‐preserving approach for constructing a data‐driven model featuring both the form‐agnostic advantage of purely phenomenological data‐driven regressions and the physical soundness of mechanistic models. The proposed methodology enforces desirable mathematical properties on the network architecture to guarantee the satisfaction of physical constraints such as objectivity, consistency (preservation of rigid body modes), dynamic stability, and material stability, which are important for successfully exploiting the resulting model in numerical simulations. Indeed, embedding such notions in a learning approach reduces a model's sensitivity to noise and promotes its robustness to inputs outside the training domain. The merits of the proposed learning approach are highlighted using several finite element analysis examples. Its potential for ensuring the computational tractability of multi‐scale applications is demonstrated with the acceleration of the nonlinear, dynamic, multi‐scale, fluid‐structure simulation of the supersonic inflation dynamics of a parachute system with a canopy made of a woven fabric. |
| Author | Farhat, Charbel Avery, Philip As'ad, Faisal |
| Author_xml | – sequence: 1 givenname: Faisal orcidid: 0000-0002-8538-9283 surname: As'ad fullname: As'ad, Faisal email: faisal3@stanford.edu organization: Stanford University – sequence: 2 givenname: Philip orcidid: 0000-0002-1310-6790 surname: Avery fullname: Avery, Philip organization: Stanford University – sequence: 3 givenname: Charbel orcidid: 0000-0003-2563-8820 surname: Farhat fullname: Farhat, Charbel organization: Stanford University |
| BookMark | eNp1kM9OAyEQxompibWa-AgkXrxshWWXLcemqX-Sqhc9I8uCpe5CBWrTm4_gM_ok0taT0dNkMr_vm5nvGPSsswqAM4yGGKH80nZqSFlZHYA-RqzKUI6qHuinEctKNsJH4DiEBUIYl4j0wfMYdkrOhTUyfH18Gqud71QDhY9GG2lEC61a-V2Ja-dfoVguvRNyDo2FjYgiqRpv3pWF0tkQTVzF1MHONao19uUEHGrRBnX6Uwfg6Wr6OLnJZg_Xt5PxLJOkTGfKHDV0VEmiirqkIq9rycoSadwwLVBBKGZIU0JJRQqa_iskZlrVRAjFROLIAJzvfdN1bysVIl-4lbdpJc9pciI5ZlWiLvaU9C4ErzRfetMJv-EY8W1-POXHt_kldPgLlSaKaJyNXpj2L0G2F6xNqzb_GvP7u-mO_wbsKIX5 |
| CitedBy_id | crossref_primary_10_1007_s00466_024_02481_5 crossref_primary_10_1016_j_cma_2025_117743 crossref_primary_10_1016_j_cma_2023_116131 crossref_primary_10_1016_j_eml_2024_102274 crossref_primary_10_1016_j_cma_2023_116534 crossref_primary_10_1007_s00466_023_02316_9 crossref_primary_10_1016_j_compgeo_2024_106907 crossref_primary_10_1016_j_cma_2024_117063 crossref_primary_10_1145_3618310 crossref_primary_10_1007_s00366_023_01906_8 crossref_primary_10_1016_j_cma_2025_118273 crossref_primary_10_1016_j_compgeo_2023_105254 crossref_primary_10_1002_nme_7481 crossref_primary_10_1016_j_mechmat_2024_105141 crossref_primary_10_1016_j_cma_2023_116007 crossref_primary_10_1016_j_matdes_2023_111697 crossref_primary_10_1002_nme_7509 crossref_primary_10_1007_s00466_024_02477_1 crossref_primary_10_1016_j_probengmech_2025_103763 crossref_primary_10_1002_cav_2262 crossref_primary_10_1002_nme_7502 crossref_primary_10_1016_j_mechmat_2023_104726 crossref_primary_10_3390_app15073697 crossref_primary_10_1016_j_cma_2025_118289 crossref_primary_10_3390_polym16223222 crossref_primary_10_1016_j_ijmecsci_2023_108709 crossref_primary_10_1016_j_cma_2025_118040 crossref_primary_10_2514_1_J064350 crossref_primary_10_1016_j_mechmat_2023_104682 crossref_primary_10_1088_2632_2153_ad95da crossref_primary_10_1098_rsos_231606 crossref_primary_10_5802_crmeca_303 crossref_primary_10_1002_nme_7473 crossref_primary_10_1016_j_cma_2024_116910 crossref_primary_10_1016_j_cma_2024_117725 crossref_primary_10_1073_pnas_2508732122 crossref_primary_10_1016_j_tafmec_2024_104717 crossref_primary_10_1016_j_cma_2025_118258 crossref_primary_10_1016_j_cma_2023_116432 crossref_primary_10_1016_j_cma_2024_117289 crossref_primary_10_1016_j_cma_2024_117286 crossref_primary_10_1137_24M1631092 crossref_primary_10_1007_s00466_023_02276_0 crossref_primary_10_1016_j_jmps_2023_105424 crossref_primary_10_1016_j_mechmat_2025_105443 crossref_primary_10_1002_msd2_70005 crossref_primary_10_1007_s11831_024_10196_2 crossref_primary_10_1007_s11340_024_01106_5 crossref_primary_10_3390_polym15214254 crossref_primary_10_1016_j_cma_2022_115731 crossref_primary_10_1186_s40323_024_00279_x crossref_primary_10_1016_j_mechrescom_2022_103993 crossref_primary_10_1016_j_cma_2023_116046 crossref_primary_10_1016_j_eml_2024_102260 crossref_primary_10_1007_s40747_025_02071_9 crossref_primary_10_1016_j_euromechsol_2023_105195 crossref_primary_10_1016_j_cma_2025_118145 crossref_primary_10_1016_j_jmps_2025_106212 crossref_primary_10_1007_s00466_023_02435_3 crossref_primary_10_1016_j_jmps_2025_106337 crossref_primary_10_1137_23M1585015 crossref_primary_10_1016_j_jmps_2025_106209 crossref_primary_10_1007_s00466_023_02278_y crossref_primary_10_1016_j_mechmat_2025_105316 crossref_primary_10_1016_j_compbiomed_2025_109691 crossref_primary_10_1002_nme_7319 crossref_primary_10_1016_j_ijnonlinmec_2024_104793 crossref_primary_10_1007_s11831_024_10063_0 crossref_primary_10_3390_ma15248878 crossref_primary_10_1002_nme_7439 crossref_primary_10_1002_nme_70083 crossref_primary_10_1016_j_cma_2023_116333 crossref_primary_10_1016_j_jmps_2024_105570 crossref_primary_10_1007_s44379_025_00022_2 crossref_primary_10_1016_j_cma_2025_117937 crossref_primary_10_1016_j_cma_2024_116967 crossref_primary_10_1038_s41467_024_45323_x crossref_primary_10_1016_j_cma_2023_116463 crossref_primary_10_1016_j_cma_2024_117532 crossref_primary_10_1016_j_engstruct_2024_118038 crossref_primary_10_1080_10589759_2025_2522299 crossref_primary_10_1016_j_actbio_2023_01_055 crossref_primary_10_1016_j_cma_2025_118089 crossref_primary_10_1016_j_jmps_2024_106015 crossref_primary_10_1016_j_eml_2024_102243 crossref_primary_10_1016_j_eml_2023_102103 crossref_primary_10_2514_1_J064791 crossref_primary_10_1016_j_jmps_2024_105837 crossref_primary_10_1016_j_actbio_2024_09_005 crossref_primary_10_1016_j_cma_2022_115501 crossref_primary_10_1016_j_ijsolstr_2023_112261 crossref_primary_10_1016_j_brain_2023_100066 crossref_primary_10_1016_j_jmbbm_2025_106934 crossref_primary_10_1016_j_cma_2023_116739 crossref_primary_10_1007_s00466_023_02355_2 crossref_primary_10_3390_axioms14050385 crossref_primary_10_1002_nme_7616 crossref_primary_10_1016_j_cma_2024_117525 crossref_primary_10_1007_s00466_025_02670_w crossref_primary_10_1016_j_cma_2023_116236 crossref_primary_10_1016_j_eml_2024_102170 crossref_primary_10_1016_j_jmps_2025_106122 crossref_primary_10_1016_j_jmbbm_2023_106021 crossref_primary_10_1016_j_ijsolstr_2025_113469 crossref_primary_10_1186_s42162_024_00322_6 crossref_primary_10_1016_j_jmps_2023_105231 crossref_primary_10_1016_j_jmps_2022_105076 crossref_primary_10_1007_s00466_024_02497_x crossref_primary_10_1016_j_cma_2023_115930 crossref_primary_10_1002_gamm_70005 crossref_primary_10_1177_14644207251330497 crossref_primary_10_1016_j_cma_2024_117359 crossref_primary_10_1016_j_prostr_2025_08_134 crossref_primary_10_1016_j_eml_2024_102181 crossref_primary_10_1007_s00466_023_02324_9 crossref_primary_10_1016_j_cma_2025_118188 crossref_primary_10_1016_j_cma_2025_118186 crossref_primary_10_1016_j_eml_2024_102220 crossref_primary_10_1016_j_eml_2024_102188 crossref_primary_10_1016_j_finel_2025_104431 crossref_primary_10_1016_j_jmps_2023_105363 crossref_primary_10_3934_nhm_2025012 crossref_primary_10_1016_j_ijmecsci_2025_110757 crossref_primary_10_1002_nme_7178 |
| Cites_doi | 10.1109/AERO.2019.8741611 10.2514/6.2021-1963 10.1007/s00466-021-02064-8 10.1007/BF00126996 10.1016/S0045-7825(99)00224-8 10.1007/978-3-642-65817-4_1 10.1016/j.cma.2021.113852 10.1007/BF01212634 10.1177/1081286508099385 10.1016/S0045-7825(97)00139-4 10.1016/j.jcp.2014.01.018 10.1016/S0045-7825(98)00218-7 10.1108/02644400210423918 10.1088/1742-6596/1168/2/022022 10.1016/j.crme.2019.08.001 10.2514/1.J059945 10.1002/(SICI)1097-0207(19980515)42:1<105::AID-NME356>3.0.CO;2-V 10.1016/j.jmps.2021.104703 10.1002/nme.2883 10.1007/s004660000212 10.2514/6.2022-0100 10.1016/j.jtbi.2018.01.014 10.1007/s10659-016-9601-6 10.1016/j.jcp.2020.110072 10.1109/TRPMS.2021.3066428 10.1002/nme.4953 10.2514/2.1975 10.1002/(SICI)1097-0207(19980930)43:2<195::AID-NME418>3.0.CO;2-6 10.1002/fld.4728 10.1016/S0749-6419(02)00091-8 10.1002/nme.6634 10.5220/0005635804810486 10.2514/6.2020-1863 10.1016/j.cma.2020.113299 10.1007/BF00040848 10.1061/(ASCE)0733-9399(1991)117:1(132) 10.1002/nme.6455 10.1007/BF00281381 10.1016/j.jcp.2020.109491 |
| ContentType | Journal Article |
| Copyright | 2022 John Wiley & Sons Ltd. 2022 John Wiley & Sons, Ltd. |
| Copyright_xml | – notice: 2022 John Wiley & Sons Ltd. – notice: 2022 John Wiley & Sons, Ltd. |
| DBID | AAYXX CITATION 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D |
| DOI | 10.1002/nme.6957 |
| DatabaseName | CrossRef Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database ProQuest Computer Science Collection Civil Engineering Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Civil Engineering Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Mechanical & Transportation Engineering Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Engineering Research Database Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Civil Engineering Abstracts CrossRef |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Engineering Mathematics |
| EISSN | 1097-0207 |
| EndPage | 2759 |
| ExternalDocumentID | 10_1002_nme_6957 NME6957 |
| Genre | article |
| GrantInformation_xml | – fundername: National Aeronautics and Space Administration funderid: 80NSSC21K0228 – fundername: National Science Foundation funderid: 1937129 – fundername: Air Force Office of Scientific Research funderid: FA9550‐20‐1‐0358 |
| GroupedDBID | -~X .3N .4S .DC .GA 05W 0R~ 10A 1L6 1OB 1OC 1ZS 33P 3SF 3WU 4.4 4ZD 50Y 50Z 51W 51X 52M 52N 52O 52P 52S 52T 52U 52W 52X 5GY 5VS 66C 702 7PT 8-0 8-1 8-3 8-4 8-5 8UM 930 A03 AAESR AAEVG AAHHS AAHQN AAMNL AANLZ AAONW AAXRX AAYCA AAZKR ABCQN ABCUV ABIJN ABJNI ACAHQ ACCFJ ACCZN ACGFS ACIWK ACPOU ACXBN ACXQS ADBBV ADEOM ADIZJ ADKYN ADMGS ADOZA ADXAS ADZMN ADZOD AEEZP AEIGN AEIMD AENEX AEQDE AEUQT AEUYR AFBPY AFFPM AFGKR AFPWT AFWVQ AFZJQ AHBTC AITYG AIURR AIWBW AJBDE AJXKR ALAGY ALMA_UNASSIGNED_HOLDINGS ALUQN ALVPJ AMBMR AMYDB ARCSS ATUGU AUFTA AZBYB AZVAB BAFTC BFHJK BHBCM BMNLL BMXJE BNHUX BROTX BRXPI BY8 CS3 D-E D-F DCZOG DPXWK DR2 DRFUL DRSTM DU5 EBS F00 F01 F04 F5P G-S G.N GNP GODZA H.T H.X HBH HGLYW HHY HZ~ IX1 J0M JPC KQQ LATKE LAW LC2 LC3 LEEKS LH4 LITHE LOXES LP6 LP7 LUTES LW6 LYRES MEWTI MK4 MRFUL MRSTM MSFUL MSSTM MXFUL MXSTM N04 N05 NF~ O66 O9- OIG P2P P2W P2X P4D Q.N Q11 QB0 QRW R.K ROL RWI RWS RX1 RYL SUPJJ TN5 TUS UB1 V2E W8V W99 WBKPD WIB WIH WIK WLBEL WOHZO WQJ WRC WXSBR WYISQ XG1 XPP XV2 ZZTAW ~02 ~IA ~WT AAMMB AAYXX AEFGJ AEYWJ AGHNM AGXDD AGYGG AIDQK AIDYY CITATION O8X 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D |
| ID | FETCH-LOGICAL-c3597-c20d687c3e4b56a2bbc9550f1d9fa0436190f636373466954c19feb3aae9a50f3 |
| IEDL.DBID | DRFUL |
| ISICitedReferencesCount | 140 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000765500200001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0029-5981 |
| IngestDate | Fri Jul 25 12:20:15 EDT 2025 Sat Nov 29 06:44:01 EST 2025 Tue Nov 18 22:31:44 EST 2025 Wed Jan 22 16:25:07 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 12 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c3597-c20d687c3e4b56a2bbc9550f1d9fa0436190f636373466954c19feb3aae9a50f3 |
| Notes | Funding information Air Force Office of Scientific Research, FA9550‐20‐1‐0358; National Aeronautics and Space Administration, 80NSSC21K0228; National Science Foundation, 1937129 ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0003-2563-8820 0000-0002-1310-6790 0000-0002-8538-9283 |
| PQID | 2655032197 |
| PQPubID | 996376 |
| PageCount | 22 |
| ParticipantIDs | proquest_journals_2655032197 crossref_primary_10_1002_nme_6957 crossref_citationtrail_10_1002_nme_6957 wiley_primary_10_1002_nme_6957_NME6957 |
| PublicationCentury | 2000 |
| PublicationDate | 30 June 2022 |
| PublicationDateYYYYMMDD | 2022-06-30 |
| PublicationDate_xml | – month: 06 year: 2022 text: 30 June 2022 day: 30 |
| PublicationDecade | 2020 |
| PublicationPlace | Hoboken, USA |
| PublicationPlace_xml | – name: Hoboken, USA – name: Bognor Regis |
| PublicationTitle | International journal for numerical methods in engineering |
| PublicationYear | 2022 |
| Publisher | John Wiley & Sons, Inc Wiley Subscription Services, Inc |
| Publisher_xml | – name: John Wiley & Sons, Inc – name: Wiley Subscription Services, Inc |
| References | 2021; 428 2021; 68 2019; 90 2021; 5 2002; 19 2015; 104 1999; 171 2018; 444 2019; 347 1974 2021; 381 1995; 113 1994 2001; 27 2003; 19 2021; 122 1959; 4 1998; 155 1991; 117 1998; 43 1998; 42 2022; 159 2019; 1168 2010; 84 2009; 14 2021; 59 2020; 371 2000; 183 1994; 36 2003; 41 2014; 263 2020; 416 2017; 127 1975; 5 e_1_2_7_6_1 e_1_2_7_5_1 e_1_2_7_4_1 e_1_2_7_3_1 e_1_2_7_9_1 e_1_2_7_8_1 e_1_2_7_7_1 e_1_2_7_19_1 e_1_2_7_18_1 e_1_2_7_17_1 e_1_2_7_16_1 e_1_2_7_40_1 e_1_2_7_2_1 e_1_2_7_15_1 e_1_2_7_41_1 e_1_2_7_14_1 e_1_2_7_42_1 e_1_2_7_13_1 e_1_2_7_43_1 e_1_2_7_12_1 e_1_2_7_44_1 e_1_2_7_11_1 e_1_2_7_10_1 e_1_2_7_27_1 e_1_2_7_28_1 e_1_2_7_29_1 e_1_2_7_30_1 e_1_2_7_25_1 e_1_2_7_31_1 e_1_2_7_24_1 e_1_2_7_32_1 e_1_2_7_23_1 e_1_2_7_33_1 e_1_2_7_22_1 e_1_2_7_34_1 e_1_2_7_21_1 e_1_2_7_35_1 e_1_2_7_20_1 e_1_2_7_36_1 e_1_2_7_37_1 e_1_2_7_38_1 e_1_2_7_39_1 Marsden JE (e_1_2_7_26_1) 1994 |
| References_xml | – volume: 159 year: 2022 article-title: Polyconvex anisotropic hyperelasticity with neural networks publication-title: J Mech Phys Solids – volume: 36 start-page: 201 issue: 3 year: 1994 end-page: 226 article-title: Positive definiteness of the elasticity tensor of a residually stressed material publication-title: J Elast – volume: 14 start-page: 369 issue: 4 year: 2009 end-page: 376 article-title: Must elastic materials be hyperelastic? publication-title: Math Mec Solids – volume: 90 start-page: 389 issue: 8 year: 2019 end-page: 424 article-title: Mesh adaptation framework for embedded boundary methods for computational fluid dynamics and fluid‐structure interaction publication-title: Int J Numer Methods Fluids – volume: 59 start-page: 2045 issue: 6 year: 2021 end-page: 2059 article-title: Homogenized flux‐body force treatment of compressible viscous porous wall boundary conditions publication-title: AIAA J – volume: 113 start-page: 63 issue: 1 year: 1995 end-page: 75 article-title: Plasticity including the Bauschinger effect, studied by a neural network approach publication-title: Acta Mech – volume: 381 year: 2021 article-title: Unsupervised discovery of interpretable hyperelastic constitutive laws publication-title: Comput Methods Appl Mech Eng – volume: 27 start-page: 37 issue: 1 year: 2001 end-page: 48 article-title: An approach to micro‐macro modeling of heterogeneous materials publication-title: Comput Mech – volume: 84 start-page: 73 issue: 1 year: 2010 end-page: 107 article-title: Robust and provably second‐order explicit–explicit and implicit–explicit staggered time‐integrators for highly non‐linear compressible fluid–structure interaction problems publication-title: Int J Numer Methods Eng – volume: 444 start-page: 108 year: 2018 end-page: 123 article-title: Microstructurally‐based constitutive modelling of the skin–linking intrinsic ageing to microstructural parameters publication-title: J Theor Biol – volume: 5 start-page: 341 issue: 3 year: 1975 end-page: 361 article-title: On the ellipticity of the equations of nonlinear elastostatics for a special material publication-title: J Elast – volume: 155 start-page: 181 issue: 192 year: 1998 article-title: Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi‐level finite element modeling publication-title: Comput Methods Appl Mech Eng – volume: 19 start-page: 254 issue: 3 year: 2002 end-page: 271 article-title: Using finite strain 3D‐material models in beam and shell elements publication-title: Eng Comput – volume: 171 start-page: 387 issue: 3‐4 year: 1999 end-page: 418 article-title: Computational homogenization analysis in finite plasticity simulation of texture development in polycrystalline materials publication-title: Comput Methods Appl Mech Eng – volume: 117 start-page: 132 issue: 1 year: 1991 end-page: 153 article-title: Knowledge‐based modeling of material behavior with neural networks publication-title: J Eng Mech – volume: 122 start-page: 5353 issue: 19 year: 2021 end-page: 5383 article-title: Discrete embedded boundary method with smooth dependence on the evolution of a fluid‐structure interface publication-title: Int J Numer Methods Eng – start-page: 1 year: 1974 end-page: 30 – year: 1994 – volume: 347 start-page: 561 issue: 8 year: 2019 end-page: 575 article-title: An empirical statistical constitutive relationship for rock joint shearing considering scale effect publication-title: C R Méc – volume: 42 start-page: 105 issue: 1 year: 1998 end-page: 126 article-title: Autoprogressive training of neural network constitutive models publication-title: Int J Numer Methods Eng – volume: 428 year: 2021 article-title: Learning constitutive relations using symmetric positive definite neural networks publication-title: J Comput Phys – volume: 371 year: 2020 article-title: Geometric deep learning for computational mechanics Part I: anisotropic hyperelasticity publication-title: Comput Methods Appl Mech Eng – volume: 263 start-page: 53 year: 2014 end-page: 70 article-title: An ALE formulation of embedded boundary methods for tracking boundary layers in turbulent fluid–structure interaction problems publication-title: J Comput Phys – volume: 43 start-page: 195 issue: 2 year: 1998 end-page: 219 article-title: Implicit constitutive modelling for viscoplasticity using neural networks publication-title: Int J Numer Methods Eng – volume: 4 start-page: 97 issue: 1 year: 1959 end-page: 128 article-title: On the thermostatics of continuous media publication-title: Arch Ration Mech Anal – volume: 104 start-page: 1061 issue: 12 year: 2015 end-page: 1084 article-title: Computational homogenization of nonlinear elastic materials using neural networks publication-title: Int J Numer Methods Eng – volume: 19 start-page: 1019 issue: 7 year: 2003 end-page: 1036 article-title: A phenomenological constitutive model for rubberlike materials and its numerical applications publication-title: Int J Plast – volume: 183 start-page: 309 issue: 3‐4 year: 2000 end-page: 330 article-title: FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials publication-title: Comput Methods Appl Mech Eng – volume: 68 start-page: 1179 issue: 5 year: 2021 end-page: 1204 article-title: Constrained neural network training and its application to hyperelastic material modeling publication-title: Comput Mech – volume: 416 year: 2020 article-title: Learning constitutive relations from indirect observations using deep neural networks publication-title: J Comput Phys – volume: 122 start-page: 2598 issue: 10 year: 2021 end-page: 2625 article-title: A computationally tractable framework for nonlinear dynamic multiscale modeling of membrane woven fabrics publication-title: Int J Numer Methods Eng – volume: 41 start-page: 363 issue: 3 year: 2003 end-page: 371 article-title: Aeroelastic dynamic analysis of a full F‐16 configuration for various flight conditions publication-title: AIAA J – volume: 1168 year: 2019 article-title: An overview of overfitting and its solutions publication-title: J Phys Conf Ser – volume: 127 start-page: 303 issue: 2 year: 2017 end-page: 308 article-title: On the convexity of nonlinear elastic energies in the right Cauchy‐Green tensor publication-title: J Elast – volume: 5 start-page: 741 issue: 6 year: 2021 end-page: 760 article-title: On interpretability of artificial neural networks: a survey publication-title: IEEE Trans Radiat Plasma Med Sci – ident: e_1_2_7_39_1 doi: 10.1109/AERO.2019.8741611 – ident: e_1_2_7_13_1 doi: 10.2514/6.2021-1963 – ident: e_1_2_7_23_1 doi: 10.1007/s00466-021-02064-8 – ident: e_1_2_7_25_1 doi: 10.1007/BF00126996 – ident: e_1_2_7_34_1 doi: 10.1016/S0045-7825(99)00224-8 – volume-title: Mathematical Foundations of Elasticity year: 1994 ident: e_1_2_7_26_1 – ident: e_1_2_7_24_1 doi: 10.1007/978-3-642-65817-4_1 – ident: e_1_2_7_16_1 doi: 10.1016/j.cma.2021.113852 – ident: e_1_2_7_8_1 doi: 10.1007/BF01212634 – ident: e_1_2_7_20_1 doi: 10.1177/1081286508099385 – ident: e_1_2_7_32_1 doi: 10.1016/S0045-7825(97)00139-4 – ident: e_1_2_7_41_1 doi: 10.1016/j.jcp.2014.01.018 – ident: e_1_2_7_33_1 doi: 10.1016/S0045-7825(98)00218-7 – ident: e_1_2_7_37_1 doi: 10.1108/02644400210423918 – ident: e_1_2_7_38_1 doi: 10.1088/1742-6596/1168/2/022022 – ident: e_1_2_7_2_1 doi: 10.1016/j.crme.2019.08.001 – ident: e_1_2_7_43_1 doi: 10.2514/1.J059945 – ident: e_1_2_7_7_1 doi: 10.1002/(SICI)1097-0207(19980515)42:1<105::AID-NME356>3.0.CO;2-V – ident: e_1_2_7_18_1 doi: 10.1016/j.jmps.2021.104703 – ident: e_1_2_7_44_1 doi: 10.1002/nme.2883 – ident: e_1_2_7_35_1 doi: 10.1007/s004660000212 – ident: e_1_2_7_5_1 doi: 10.2514/6.2022-0100 – ident: e_1_2_7_4_1 doi: 10.1016/j.jtbi.2018.01.014 – ident: e_1_2_7_29_1 doi: 10.1007/s10659-016-9601-6 – ident: e_1_2_7_17_1 doi: 10.1016/j.jcp.2020.110072 – ident: e_1_2_7_19_1 doi: 10.1109/TRPMS.2021.3066428 – ident: e_1_2_7_11_1 doi: 10.1002/nme.4953 – ident: e_1_2_7_36_1 doi: 10.2514/2.1975 – ident: e_1_2_7_9_1 doi: 10.1002/(SICI)1097-0207(19980930)43:2<195::AID-NME418>3.0.CO;2-6 – ident: e_1_2_7_21_1 – ident: e_1_2_7_42_1 doi: 10.1002/fld.4728 – ident: e_1_2_7_30_1 – ident: e_1_2_7_3_1 doi: 10.1016/S0749-6419(02)00091-8 – ident: e_1_2_7_14_1 doi: 10.1002/nme.6634 – ident: e_1_2_7_31_1 doi: 10.5220/0005635804810486 – ident: e_1_2_7_12_1 doi: 10.2514/6.2020-1863 – ident: e_1_2_7_22_1 doi: 10.1016/j.cma.2020.113299 – ident: e_1_2_7_28_1 doi: 10.1007/BF00040848 – ident: e_1_2_7_6_1 doi: 10.1061/(ASCE)0733-9399(1991)117:1(132) – ident: e_1_2_7_40_1 doi: 10.1002/nme.6455 – ident: e_1_2_7_27_1 doi: 10.1007/BF00281381 – ident: e_1_2_7_10_1 doi: 10.1016/j.jcp.2020.109491 – ident: e_1_2_7_15_1 |
| SSID | ssj0011503 |
| Score | 2.6912992 |
| Snippet | A mechanics‐informed artificial neural network approach for learning constitutive laws governing complex, nonlinear, elastic materials from strain–stress data... |
| SourceID | proquest crossref wiley |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 2738 |
| SubjectTerms | artificial neural network Artificial neural networks Computer architecture Computer simulation constitutive modeling convexity Dynamic stability Finite element method hyperelasticity Learning machine learning Mechanics Neural networks Noise sensitivity Parachute canopies Regression models Rigid structures Robustness (mathematics) Solid mechanics stability Strain supersonic parachute inflation dynamics Training Woven fabrics |
| Title | A mechanics‐informed artificial neural network approach in data‐driven constitutive modeling |
| URI | https://onlinelibrary.wiley.com/doi/abs/10.1002%2Fnme.6957 https://www.proquest.com/docview/2655032197 |
| Volume | 123 |
| WOSCitedRecordID | wos000765500200001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVWIB databaseName: Wiley Online Library Full Collection 2020 customDbUrl: eissn: 1097-0207 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0011503 issn: 0029-5981 databaseCode: DRFUL dateStart: 19960101 isFulltext: true titleUrlDefault: https://onlinelibrary.wiley.com providerName: Wiley-Blackwell |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1BS8MwFH7o5kEPTqfidEoE0VN1bdq0OQ7d8LANESe71STNYOA2Wadnf4K_0V_iS5vOCQqCpxD6XpvmvZd8aV--AJwGOKn4ipssca4dP9C-EwlNHV8KV0nBeJDRLj50wl4vGgz4rc2qNHthcn6IxQc3ExnZeG0CXMj0cok0dKwv8FbhKpQ9dNugBOXru3a_s_iHgFCHFgkeAY_cgnq24V0Wut8noy-EuYxTs4mmXflPE7dg08JL0sz9YRtW9KQKFQs1iQ3ktAobSzyEWOsuyFvTHXhskrE2G4Kx9vH2nlOrorZxspxvghgWzKzIcshJQUxORhNiUk5RK5mZYZSoqU1GwBrJTt3BB-5Cv926v7px7EEMjkITho7yGgmLQkW1LwMmPCkVx5XN0E34UBgOe0QVQ0YZDanP8IV95fIhrtKF0FygHN2D0mQ60ftAlI9TJmMyUIIiUktk4kpFDc5UkZCNoAbnhUViZVnKzWEZT3HOr-zF2Kmx6dQanCwkn3Nmjh9k6oVRYxubaewxbDvFkRovn2Xm-1U_7nVbpjz4q-AhrHtmf0SWUFiH0nz2oo9gTb3OR-ns2HroJ1Uv7MA |
| linkProvider | Wiley-Blackwell |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1fS8MwED_mFNQH_4vTqRFEn-rWJk0bfBrqmLgNERXfapJmMHCbbNNnP4Kf0U_ipX_mBAXBpxJ616a5u-SX9PILwKGPgwrTwmaJC-Mw3zAnlIY6TElXK8mFn9Au3jeDdjt8eBDXBTjN98Kk_BCTBTcbGUl_bQPcLkhXplhDe-YEnxXMwCxDL0L3nj2_qd81Jz8REOvQPMPDF6Gbc89WvUqu-300-oKY00A1GWnqy_-q4wosZQCT1FKPWIWC6a_BcgY2SRbKozVYnGIixFJrQt86WofHGukZuyUYSx9v7ym5KmpbN0sZJ4jlwUwuSRY5yanJSbdPbNIpasVD25ESPcjSEbBEknN38IUbcFe_uD1rONlRDI5GIwaO9qoxDwNNDVM-l55SWuDcpuPGoiMtiz3iig6nnAaUcfxgpl3RwXm6lEZIlKObUOwP-mYLiGY4aHKufC0pYrVYxa7S1CJNHUpV9UtwnJsk0hlPuT0u4ylKGZa9CBs1so1agoOJ5HPKzfGDTDm3apRF5yjyONadYl-Nt48S-_2qH7VbF_a6_VfBfZhv3LaaUfOyfbUDC57dLZGkF5ahOB6-mF2Y06_j7mi4l7nrJ3j_8LA |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1bS8MwFD7oFNEH7-JlagTRp7q1SdMGn4Y6FLcxRMW3mqQpCLqNVX32J_gb_SWe9DInKAg-hdBz2jQnJ_nSnnwHYN_HRYVpYaPEhXGYb5gTSkMdpqSrleTCz2gXb1tBpxPe3YnuBByXZ2FyfojRBzfrGdl8bR3cDOKkNsYa-mSO8F7BJEwxm0OmAlOnV82b1ugnAmIdWkZ4-CJ0S-7Zulcrdb-vRl8QcxyoZitNc-FfbVyE-QJgkkY-IpZgwvSWYaEAm6Rw5XQZ5saYCLHWHtG3pitw3yBPxh4JxtrH23tOroradpjljBPE8mBmRRZFTkpqcvLQIzboFLXioZ1Iie4X4QhYI1neHXzgKtw0z65Pzp0iFYOj0YiBo716zMNAU8OUz6WnlBa4t0ncWCTSstgjrkg45TSgjOMLM-2KBPfpUhohUY6uQaXX75l1IJrhosm58rWkiNViFbtKU4s0dShV3d-Aw9IkkS54ym26jMcoZ1j2IuzUyHbqBuyNJAc5N8cPMtXSqlHhnWnkcWw7xbkaLx9k9vtVP-q0z2y5-VfBXZjpnjaj1kXncgtmPXtYIosurELlefhitmFavz4_pMOdYrR-AhwU8Cs |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+mechanics%E2%80%90informed+artificial+neural+network+approach+in+data%E2%80%90driven+constitutive+modeling&rft.jtitle=International+journal+for+numerical+methods+in+engineering&rft.au=As%27ad%2C+Faisal&rft.au=Avery%2C+Philip&rft.au=Farhat%2C+Charbel&rft.date=2022-06-30&rft.pub=John+Wiley+%26+Sons%2C+Inc&rft.issn=0029-5981&rft.eissn=1097-0207&rft.volume=123&rft.issue=12&rft.spage=2738&rft.epage=2759&rft_id=info:doi/10.1002%2Fnme.6957&rft.externalDBID=10.1002%252Fnme.6957&rft.externalDocID=NME6957 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0029-5981&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0029-5981&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0029-5981&client=summon |