Mechanical modeling of plantar pressure during human walking in different terrains: Experiments and analysis
Accurate plantar pressure models play a pivotal in predicting human gait dynamics and have broad applications, including the development of exoskeletons, prosthetics, and legged robots. However, existing models often overlook the influence of varying terrains on plantar pressures. In this study, we...
Saved in:
| Published in: | European journal of mechanics, A, Solids Vol. 111; p. 105566 |
|---|---|
| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier Masson SAS
01.05.2025
|
| Subjects: | |
| ISSN: | 0997-7538 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | Accurate plantar pressure models play a pivotal in predicting human gait dynamics and have broad applications, including the development of exoskeletons, prosthetics, and legged robots. However, existing models often overlook the influence of varying terrains on plantar pressures. In this study, we conducted a comprehensive modeling analysis of plantar pressure using experimental walking data collected from 12 subjects (6 males and 6 females). Statistical analysis reveals significant variations in vertical ground reaction forces across different plantar regions and terrains. In response to these findings, we develop a novel viscoelastic ellipsoid model capable of describing the complex mechanical behavior of foot-ground contact. The plantar tissue is divided into five distinct regions, each represented by an ellipsoid with viscoelastic material properties. Our model also expresses the plantar deformation by the contact area, which can be measured by in-shoe pressure sensors, thus addressing the challenge of measuring plantar tissue deformation in walking experiments. Additionally, we employ a quasi-static contact model to estimate the equivalent contact area, overcoming the challenge of contact area saturation during walking and improving the model's accuracy. Based on this foundation, we apply an intelligent optimization algorithm to identify the optimal geometric and material parameters of the ellipsoid models. Comparison of model outputs and experimental results demonstrate that the ellipsoid model can accurately render the vertical ground reaction forces of different plantar regions under various terrains, providing valuable insights into foot-ground interaction. Moreover, by comparing the results of parameter optimization in different terrain contexts, we unveil the critical relationships between terrain factors and model parameters, thereby deepening our understanding of foot-ground contact mechanics.
•Experiments reveal significant variations in VGRF in different plantar regions and terrains.•A viscoelastic ellipsoid model incorporating five distinct plantar regions is developed.•Equivalent contact area is estimated to solve contact area saturation and improve accuracy.•Comparison of predictions and test results indicate high accuracy and robustness of model.•Critical relationships between terrain factors and model parameters are unveiled. |
|---|---|
| AbstractList | Accurate plantar pressure models play a pivotal in predicting human gait dynamics and have broad applications, including the development of exoskeletons, prosthetics, and legged robots. However, existing models often overlook the influence of varying terrains on plantar pressures. In this study, we conducted a comprehensive modeling analysis of plantar pressure using experimental walking data collected from 12 subjects (6 males and 6 females). Statistical analysis reveals significant variations in vertical ground reaction forces across different plantar regions and terrains. In response to these findings, we develop a novel viscoelastic ellipsoid model capable of describing the complex mechanical behavior of foot-ground contact. The plantar tissue is divided into five distinct regions, each represented by an ellipsoid with viscoelastic material properties. Our model also expresses the plantar deformation by the contact area, which can be measured by in-shoe pressure sensors, thus addressing the challenge of measuring plantar tissue deformation in walking experiments. Additionally, we employ a quasi-static contact model to estimate the equivalent contact area, overcoming the challenge of contact area saturation during walking and improving the model's accuracy. Based on this foundation, we apply an intelligent optimization algorithm to identify the optimal geometric and material parameters of the ellipsoid models. Comparison of model outputs and experimental results demonstrate that the ellipsoid model can accurately render the vertical ground reaction forces of different plantar regions under various terrains, providing valuable insights into foot-ground interaction. Moreover, by comparing the results of parameter optimization in different terrain contexts, we unveil the critical relationships between terrain factors and model parameters, thereby deepening our understanding of foot-ground contact mechanics.
•Experiments reveal significant variations in VGRF in different plantar regions and terrains.•A viscoelastic ellipsoid model incorporating five distinct plantar regions is developed.•Equivalent contact area is estimated to solve contact area saturation and improve accuracy.•Comparison of predictions and test results indicate high accuracy and robustness of model.•Critical relationships between terrain factors and model parameters are unveiled. |
| ArticleNumber | 105566 |
| Author | Fang, Hongbin Feng, Mingfei Zhang, Qiwei Xu, Jian Liu, Jiaqi |
| Author_xml | – sequence: 1 givenname: Jiaqi surname: Liu fullname: Liu, Jiaqi organization: School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, China – sequence: 2 givenname: Hongbin orcidid: 0000-0001-6691-0531 surname: Fang fullname: Fang, Hongbin organization: Institute of AI and Robotics, MOE Engineering Research Center of AI and Robotics, Shanghai Engineering Research Center of AI and Robotics, Fudan University, Shanghai, 200433, China – sequence: 3 givenname: Mingfei surname: Feng fullname: Feng, Mingfei organization: Institute of AI and Robotics, MOE Engineering Research Center of AI and Robotics, Shanghai Engineering Research Center of AI and Robotics, Fudan University, Shanghai, 200433, China – sequence: 4 givenname: Qiwei surname: Zhang fullname: Zhang, Qiwei organization: Yiwu Research Institute, Fudan University, Yiwu, Zhejiang, 322000, China – sequence: 5 givenname: Jian orcidid: 0000-0002-3521-6843 surname: Xu fullname: Xu, Jian email: xujian@tongji.edu.cn organization: School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, China |
| BookMark | eNqNUMtOwzAQ9KFItIV_MB-QYsdJTLggVJWHBOICZ8uxN9TFsSM7Afr3OCoHxKmH1Wp3dkY7s0Az5x0gdEHJihJaXe5WMAbfgdpGb1c5yYu0L8uqmqE5qWue8ZJdnaJFjDtCSMLpHNnndC6dUdLizmuwxr1j3-LeSjfIgPsAMY4BsB7DBG3HTjr8Je3HNBmHtWlbCOAGPEAI0rh4jTffPQTTpWXE0ulU0u6jiWfopJU2wvlvX6K3u83r-iF7erl_XN8-ZYrldMgkq3IKVFNWA29aWUtGFSUNz3lJCw5A21px1nDNdEFUUxHNG8aUKqCUpKzZEtUHXRV8jAFa0ad3ZNgLSsQUldiJP1GJKSpxiCpxb_5xlRnkYLwbkjt7lML6oADJ4qeBIKIy4BRoE0ANQntzhMoPT7OVGw |
| CitedBy_id | crossref_primary_10_1016_j_triboint_2025_111202 |
| Cites_doi | 10.3390/app10072342 10.1016/S0020-7683(96)00172-2 10.1299/jbse.23-00130 10.1016/j.proeng.2016.06.240 10.1080/10255842.2015.1081181 10.1016/j.mechmachtheory.2021.104501 10.1016/j.mechmachtheory.2022.105046 10.1115/1.2389230 10.1007/978-3-319-10723-3 10.1016/j.apm.2024.06.034 10.1016/j.jbiomech.2005.08.021 10.1007/s11044-010-9237-4 10.3390/app14156541 10.1007/s11044-010-9220-0 10.1053/apmr.2002.35661 10.3390/sports11060117 10.1007/s10439-015-1538-6 10.1016/0021-9290(95)00141-7 10.1016/j.jbiomech.2019.05.041 10.1109/LSENS.2023.3279392 10.1016/j.jbiomech.2017.04.038 10.1016/j.ijmecsci.2022.107214 10.1016/j.fas.2022.07.007 10.1115/1.2897737 10.1109/TRO.2018.2862902 10.1136/bjsports-2022-106588 10.1016/j.robot.2014.10.001 10.1016/j.mechmachtheory.2021.104327 10.1081/SME-120022855 10.1007/s11044-017-9605-4 10.1016/j.gaitpost.2013.07.118 10.1007/s10439-018-2026-6 10.1016/S0268-0033(03)00080-9 10.1109/TAC.1981.1102780 10.1155/2018/8610458 10.1007/s11044-013-9363-x 10.3389/fbioe.2016.00077 10.3390/s22062203 10.1016/S0021-9290(98)00085-2 10.1016/j.arcontrol.2022.12.002 10.1115/1.4038739 10.1016/j.mechmachtheory.2023.105305 |
| ContentType | Journal Article |
| Copyright | 2025 Elsevier Masson SAS |
| Copyright_xml | – notice: 2025 Elsevier Masson SAS |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.euromechsol.2024.105566 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences |
| ExternalDocumentID | 10_1016_j_euromechsol_2024_105566 S0997753824003462 |
| GroupedDBID | --K --M -~X .~1 0R~ 1B1 1~. 1~5 29G 4.4 457 4G. 5GY 5VS 7-5 71M 8P~ AACTN AAEDT AAEDW AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXKI AAXUO ABMAC ABWVN ABXDB ACDAQ ACGFS ACIWK ACKIV ACNNM ACRLP ACRPL ADEZE ADMUD ADNMO ADTZH AEBSH AECPX AEIPS AEKER AFJKZ AFTJW AGHFR AGUBO AGYEJ AHJVU AI. AIEXJ AIKHN AITUG ALMA_UNASSIGNED_HOLDINGS AMRAJ ANKPU AXJTR BJAXD BKOJK BLXMC CS3 EBS EFJIC EJD EO8 EO9 EP2 EP3 FDB FEDTE FGOYB FIRID FNPLU FYGXN G-Q GBLVA HVGLF HZ~ IHE J1W JJJVA KOM M41 MO0 N9A O-L O9- OAUVE OZT P-8 P-9 PC. Q38 R2- RIG ROL RPZ SDF SDG SDP SES SEW SPC SPCBC SPD SST SSZ T5K VH1 XPP ZMT ~02 ~G- 9DU AATTM AAYWO AAYXX ACLOT AGQPQ AIIUN APXCP CITATION EFKBS EFLBG ~HD |
| ID | FETCH-LOGICAL-c321t-a3621e1d139e7bfa9a31c10b7275147ee1f9c73b7d3d40cb60d7b33cc4e5a0593 |
| ISICitedReferencesCount | 1 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001423286300001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0997-7538 |
| IngestDate | Sat Nov 29 08:10:32 EST 2025 Tue Nov 18 22:23:54 EST 2025 Sat Mar 08 15:49:42 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Viscoelastic ellipsoid Human biomechanics Biomechanical modeling Parameter identification Foot-ground contact |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c321t-a3621e1d139e7bfa9a31c10b7275147ee1f9c73b7d3d40cb60d7b33cc4e5a0593 |
| ORCID | 0000-0001-6691-0531 0000-0002-3521-6843 |
| ParticipantIDs | crossref_primary_10_1016_j_euromechsol_2024_105566 crossref_citationtrail_10_1016_j_euromechsol_2024_105566 elsevier_sciencedirect_doi_10_1016_j_euromechsol_2024_105566 |
| PublicationCentury | 2000 |
| PublicationDate | May-June 2025 2025-05-00 |
| PublicationDateYYYYMMDD | 2025-05-01 |
| PublicationDate_xml | – month: 05 year: 2025 text: May-June 2025 |
| PublicationDecade | 2020 |
| PublicationTitle | European journal of mechanics, A, Solids |
| PublicationYear | 2025 |
| Publisher | Elsevier Masson SAS |
| Publisher_xml | – name: Elsevier Masson SAS |
| References | Lin, Pandy (bib27) 2017; 59 Trindade, Ono, Lemaire, Almohimeed (bib47) 2014; IUS Chen, Ju, Tang (bib10) 2003; 18 Cenk Güler, Berme, Simon (bib9) 1998; 31 Antunes, Dias, Coelho, Rebelo, Pereira (bib1) 2008; 1 Wojtyra (bib50) 2003; 31 Flores, Ambrósio, Lankarani (bib16) 2023; 184 Yarnitzky, Yizhar, Gefen (bib51) 2006; 39 Febrer-Nafría, Nasr, Ezati, Brown, Font-Llagunes, McPhee (bib15) 2023; B.V Peasgood, Kubica, McPhee (bib38) 2007; 2 Wang, Liu, Liu (bib49) 2022; 221 Flores, MacHado, Silva, Martins (bib17) 2011; 25 Sun, Wu, Voglewede (bib43) 2018; 140 Carpentier, Mansard (bib8) 2018; 34 Corral, García, Castejon, Meneses, Gismeros (bib11) 2020; 10 Gardner, Porbanderwala, Haider (bib18) 2023; 7 Azad, Mistry (bib3) 2015 DeBerardinis, Dufek, Trabia (bib13) 2019; 92 Gilchrist, Winter (bib20) 1996; 29 Lugrís, Carlín, Pàmies-Vilà, Font-Llagunes, Cuadrado (bib58) 2013; 30 Rodrigues da Silva, Marques, Tavares da Silva, Flores (bib41) 2022; 167 Meyer, Eskinazi, Jackson, Rao, Patten, Fregly (bib33) 2016; 4 Liu, Fang, Xu (bib29) 2022; 10 Cramer, Wimmer, Malloy, O’keefe, Knowlton, Ferrigno (bib12) 2022; 22 Wang, Jia, Cheng, Flores (bib48) 2024; 135 Gonthier, Lange, McPhee, Piedbœuf (bib21) 2005; 6 A Millard, McPhee, Kubica (bib57) 2009 Mills, Nguyen (bib34) 1992; 114 Lopes, Silva, Ambrósio, Flores (bib32) 2010; 24 Oh, Baek, Song, Mohammed, Jeon, Kong (bib37) 2015; 73 Tallis, Morris, Duncan, Eyre, Guimaraes-Ferreira (bib45) 2023; 11 Lopes, Neptune, Ambrósio, Silva (bib54) 2015; 19 Brown, McPhee (bib55) 2018; 42 Taha, Norman, Omar, Suwarganda (bib44) 2016; 147 Moreira, Silva, Flores (bib35) 2009 Kotsifaki, Sideris, King, Bahr, Whiteley (bib26) 2023; 57 Giannakopoulos, Suresh (bib19) 1997; 34 Yue, Lin, Zhang, Qiu, Cheng (bib52) 2018; 2018 Lin, Walter, Pandy (bib28) 2018; 46 Phillips, Kokotovic (bib39) 1981; 26 Haraguchi, Hase (bib22) 2024; 19 Ayari, Knani (bib2) 2017 Porsa, Lin, Pandy (bib40) 2016; 44 Saraiva, Rodrigues da Silva, Marques, Tavares da Silva, Flores (bib42) 2022; 177 Mouzo, Lugris, Pamies-Vila, Font-Llagunes, Cuadrado (bib36) 2015 Klaesner, Hastings, Zou, Lewis, Mueller (bib25) 2002; 83 Telfer, Woodburn, Turner (bib46) 2014; 39 Boos, McPhee (bib4) 2013; 8 Brogliato (bib5) 2023; 55 Hu, Guo (bib23) 2021; 162 Zhuang, Wang, Wang, Li, Li, Li, Dong (bib53) 2024; 14 Eidmann, Vinke, Jakuscheit, Rudert, Stratos (bib14) 2022; 28 Kecskeméthy, Flores (bib24) 2015; 26 Lopes (10.1016/j.euromechsol.2024.105566_bib32) 2010; 24 Trindade (10.1016/j.euromechsol.2024.105566_bib47) 2014; IUS Cramer (10.1016/j.euromechsol.2024.105566_bib12) 2022; 22 Liu (10.1016/j.euromechsol.2024.105566_bib29) 2022; 10 Millard (10.1016/j.euromechsol.2024.105566_bib57) 2009 Wojtyra (10.1016/j.euromechsol.2024.105566_bib50) 2003; 31 Kotsifaki (10.1016/j.euromechsol.2024.105566_bib26) 2023; 57 Peasgood (10.1016/j.euromechsol.2024.105566_bib38) 2007; 2 Brogliato (10.1016/j.euromechsol.2024.105566_bib5) 2023; 55 Moreira (10.1016/j.euromechsol.2024.105566_bib35) 2009 Mouzo (10.1016/j.euromechsol.2024.105566_bib36) 2015 Gonthier (10.1016/j.euromechsol.2024.105566_bib21) 2005; 6 A Wang (10.1016/j.euromechsol.2024.105566_bib49) 2022; 221 Sun (10.1016/j.euromechsol.2024.105566_bib43) 2018; 140 Oh (10.1016/j.euromechsol.2024.105566_bib37) 2015; 73 Eidmann (10.1016/j.euromechsol.2024.105566_bib14) 2022; 28 Wang (10.1016/j.euromechsol.2024.105566_bib48) 2024; 135 Lin (10.1016/j.euromechsol.2024.105566_bib28) 2018; 46 Rodrigues da Silva (10.1016/j.euromechsol.2024.105566_bib41) 2022; 167 Carpentier (10.1016/j.euromechsol.2024.105566_bib8) 2018; 34 Klaesner (10.1016/j.euromechsol.2024.105566_bib25) 2002; 83 Mills (10.1016/j.euromechsol.2024.105566_bib34) 1992; 114 Boos (10.1016/j.euromechsol.2024.105566_bib4) 2013; 8 Lin (10.1016/j.euromechsol.2024.105566_bib27) 2017; 59 Taha (10.1016/j.euromechsol.2024.105566_bib44) 2016; 147 Flores (10.1016/j.euromechsol.2024.105566_bib17) 2011; 25 Porsa (10.1016/j.euromechsol.2024.105566_bib40) 2016; 44 Zhuang (10.1016/j.euromechsol.2024.105566_bib53) 2024; 14 Flores (10.1016/j.euromechsol.2024.105566_bib16) 2023; 184 Gardner (10.1016/j.euromechsol.2024.105566_bib18) 2023; 7 Corral (10.1016/j.euromechsol.2024.105566_bib11) 2020; 10 DeBerardinis (10.1016/j.euromechsol.2024.105566_bib13) 2019; 92 Gilchrist (10.1016/j.euromechsol.2024.105566_bib20) 1996; 29 Phillips (10.1016/j.euromechsol.2024.105566_bib39) 1981; 26 Brown (10.1016/j.euromechsol.2024.105566_bib55) 2018; 42 Tallis (10.1016/j.euromechsol.2024.105566_bib45) 2023; 11 Chen (10.1016/j.euromechsol.2024.105566_bib10) 2003; 18 Lopes (10.1016/j.euromechsol.2024.105566_bib54) 2015; 19 Saraiva (10.1016/j.euromechsol.2024.105566_bib42) 2022; 177 Lugrís (10.1016/j.euromechsol.2024.105566_bib58) 2013; 30 Antunes (10.1016/j.euromechsol.2024.105566_bib1) 2008; 1 Cenk Güler (10.1016/j.euromechsol.2024.105566_bib9) 1998; 31 Kecskeméthy (10.1016/j.euromechsol.2024.105566_bib24) 2015; 26 Meyer (10.1016/j.euromechsol.2024.105566_bib33) 2016; 4 Hu (10.1016/j.euromechsol.2024.105566_bib23) 2021; 162 Telfer (10.1016/j.euromechsol.2024.105566_bib46) 2014; 39 Febrer-Nafría (10.1016/j.euromechsol.2024.105566_bib15) 2023; B.V Yarnitzky (10.1016/j.euromechsol.2024.105566_bib51) 2006; 39 Ayari (10.1016/j.euromechsol.2024.105566_bib2) 2017 Haraguchi (10.1016/j.euromechsol.2024.105566_bib22) 2024; 19 Giannakopoulos (10.1016/j.euromechsol.2024.105566_bib19) 1997; 34 Azad (10.1016/j.euromechsol.2024.105566_bib3) 2015 Yue (10.1016/j.euromechsol.2024.105566_bib52) 2018; 2018 |
| References_xml | – volume: 10 start-page: 2342 year: 2020 ident: bib11 article-title: Dynamic modeling of the dissipative contact and friction forces of a passive biped-walking robot publication-title: Appl. Sci. – volume: 19 start-page: 1 year: 2024 end-page: 14 ident: bib22 article-title: Prediction of ground reaction forces and moments and joint kinematics and kinetics by inertial measurement units using 3D forward dynamics model publication-title: J. Biomech. Sci. Eng. – volume: 11 start-page: 117 year: 2023 ident: bib45 article-title: Agreement between force platform and smartphone application-derived measures of vertical jump height in youth grassroots soccer players publication-title: Sports – volume: 6 A start-page: 477 year: 2005 end-page: 486 ident: bib21 article-title: A contact modeling method based on volumetric properties publication-title: Proc. ASME Int. Des. Eng. Tech. Conf. Comput. Inf. Eng. Conf. - DETC2005 – volume: 18 start-page: 17 year: 2003 end-page: 24 ident: bib10 article-title: Effects of total contact insoles on the plantar stress redistribution: a finite element analysis publication-title: Clin. Biomech. – volume: 28 start-page: 1384 year: 2022 end-page: 1388 ident: bib14 article-title: The influence of partial weight bearing on plantar peak forces using three different types of postoperative shoes publication-title: Foot Ankle Surg. – volume: 25 start-page: 357 year: 2011 end-page: 375 ident: bib17 article-title: On the continuous contact force models for soft materials in multibody dynamics publication-title: Multibody Syst. Dyn. – volume: IUS start-page: 2112 year: 2014 end-page: 2115 ident: bib47 article-title: Development of a wearable ultrasonic sensor and method for continuous monitoring of mechanical properties of plantar soft tissue for diabetic patients publication-title: IEEE Int. Ultrason. Symp. – volume: 162 year: 2021 ident: bib23 article-title: A new concept of contact joint to model the geometric foot-environment contacts for efficiently determining possible stances for legged robots publication-title: Mech. Mach. Theory – volume: 39 start-page: 328 year: 2014 end-page: 332 ident: bib46 article-title: Measurement of functional heel pad behaviour in-shoe during gait using orthotic embedded ultrasonography publication-title: Gait Posture – volume: 135 start-page: 51 year: 2024 end-page: 72 ident: bib48 article-title: An enhanced contact force model with accurate evaluation of the energy dissipation during contact-impact events in dynamical systems publication-title: Appl. Math. Model. – volume: 147 start-page: 240 year: 2016 end-page: 245 ident: bib44 article-title: A finite element analysis of a human foot model to simulate neutral standing on ground publication-title: Procedia Eng. – volume: 34 start-page: 1441 year: 2018 end-page: 1460 ident: bib8 article-title: Multicontact locomotion of legged robots publication-title: IEEE Trans. Robot. – start-page: 849 year: 2017 end-page: 854 ident: bib2 article-title: Kinematics velocity and dynamic modeling of biped robot publication-title: 2017 4th Int. Conf. Control. Decis. Inf. Technol. CoDIT 2017 2017-Janua – volume: 184 year: 2023 ident: bib16 article-title: Contact-impact events with friction in multibody dynamics: back to basics publication-title: Mech. Mach. Theory – volume: 26 start-page: 1087 year: 1981 end-page: 1094 ident: bib39 article-title: A singular perturbation approach to modeling and control of Markov chains publication-title: IEEE Trans. Automat. Contr. – volume: 8 year: 2013 ident: bib4 article-title: Volumetric modeling and experimental validation of normal contact dynamic forces publication-title: J. Comput. Nonlinear Dyn. – volume: 140 year: 2018 ident: bib43 article-title: Dynamic simulation of human gait model with predictive capability publication-title: J. Biomech. Eng. – volume: 4 start-page: 77 year: 2016 ident: bib33 article-title: Muscle synergies facilitate computational prediction of subject-specific walking motions publication-title: Front. Bioeng. Biotechnol. – volume: 177 year: 2022 ident: bib42 article-title: A review on foot-ground contact modeling strategies for human motion analysis publication-title: Mech. Mach. Theory – volume: 55 start-page: 297 year: 2023 end-page: 337 ident: bib5 article-title: Modeling, analysis and control of robot–object nonsmooth underactuated Lagrangian systems: a tutorial overview and perspectives publication-title: Annu. Rev. Control – volume: 39 start-page: 2673 year: 2006 end-page: 2689 ident: bib51 article-title: Real-time subject-specific monitoring of internal deformations and stresses in the soft tissues of the foot: a new approach in gait analysis publication-title: J. Biomech. – volume: B.V year: 2023 ident: bib15 article-title: Predictive multibody dynamic simulation of human neuromusculoskeletal systems: a review, Multibody System Dynamics publication-title: The Author(s), under exclusive licence to Springer Nature – volume: 34 start-page: 2393 year: 1997 end-page: 2428 ident: bib19 article-title: Indentation of solids with gradients in elastic properties: Part II. Axisymmetric indentors publication-title: Int. J. Solids Struct. – volume: 42 start-page: 447 year: 2018 end-page: 467 ident: bib55 article-title: A 3D ellipsoidal volumetric foot–ground contact model for forward dynamics publication-title: Multibody Syst. Dyn. – volume: 57 start-page: 1304 year: 2023 end-page: 1310 ident: bib26 article-title: Performance and symmetry measures during vertical jump testing at return to sport after ACL reconstruction publication-title: Br. J. Sports Med. – start-page: 1 year: 2009 end-page: 13 ident: bib35 article-title: Ground foot interaction in human gait: modelling and simulation publication-title: 7th EUROMECH Solid Mech. Conf. – volume: 22 start-page: 2203 year: 2022 ident: bib12 article-title: Validity and reliability of the Insole3 instrumented shoe insole for ground reaction force measurement during walking and running publication-title: Sensors – volume: 31 start-page: 357 year: 2003 end-page: 379 ident: bib50 article-title: Multibody simulation model of human walking publication-title: Mech. Based Des. Struct. Mach. – volume: 24 start-page: 255 year: 2010 end-page: 280 ident: bib32 article-title: A mathematical framework for rigid contact detection between quadric and superquadric surfaces publication-title: Multibody Syst. Dyn. – volume: 2 start-page: 65 year: 2007 end-page: 72 ident: bib38 article-title: Stabilization of a dynamic walking gait simulation publication-title: J. Comput. Nonlinear Dyn. – volume: 1 start-page: 1 year: 2008 end-page: 11 ident: bib1 article-title: Non-linear finite element modelling of anatomically detailed 3D foot model publication-title: Rep. Pap. – volume: 221 year: 2022 ident: bib49 article-title: Energy dissipation analysis for elastoplastic contact and dynamic dashpot models publication-title: Int. J. Mech. Sci. – volume: 59 start-page: 1 year: 2017 end-page: 8 ident: bib27 article-title: Three-dimensional data-tracking dynamic optimization simulations of human locomotion generated by direct collocation publication-title: J. Biomech. – volume: 73 start-page: 68 year: 2015 end-page: 77 ident: bib37 article-title: A generalized control framework of assistive controllers and its application to lower limb exoskeletons publication-title: Rob. Auton. Syst. – volume: 83 start-page: 1796 year: 2002 end-page: 1801 ident: bib25 article-title: Plantar tissue stiffness in patients with diabetes mellitus and peripheral neuropathy publication-title: Arch. Phys. Med. Rehabil. – start-page: 25 year: 2009 end-page: 43 ident: bib57 article-title: Multi-Step Forward Dynamic Gait Simulation publication-title: Multibody Dyn. Comput. methods Appl. – volume: 30 start-page: 247 year: 2013 end-page: 263 ident: bib58 publication-title: Multibody Syst. Dyn. – volume: 46 start-page: 1216 year: 2018 end-page: 1227 ident: bib28 article-title: Predictive simulations of neuromuscular coordination and joint-contact loading in human gait publication-title: Ann. Biomed. Eng. – volume: 14 year: 2024 ident: bib53 article-title: A review of foot–terrain interaction mechanics for heavy-duty legged robots publication-title: Appl. Sci. – start-page: 4391 year: 2015 end-page: 4396 ident: bib3 article-title: Balance control strategy for legged robots with compliant contacts publication-title: Proc. - IEEE Int. Conf. Robot. Autom. 2015-June – volume: 29 start-page: 795 year: 1996 end-page: 798 ident: bib20 article-title: A two-part, viscoelastic foot model for use in gait simulations publication-title: J. Biomech. – volume: 92 start-page: 137 year: 2019 end-page: 145 ident: bib13 article-title: A viscoelastic ellipsoidal model of the mechanics of plantar tissues publication-title: J. Biomech. – volume: 19 start-page: 954 year: 2015 end-page: 963 ident: bib54 article-title: A superellipsoid-plane model for simulating foot-ground contact during human gait publication-title: Comput. Methods Biomech. Biomed. Engin. – volume: 44 start-page: 2542 year: 2016 end-page: 2557 ident: bib40 article-title: Direct methods for predicting movement biomechanics based upon optimal control theory with implementation in OpenSim publication-title: Ann. Biomed. Eng. – start-page: 1092 year: 2015 end-page: 1100 ident: bib36 article-title: Underactuated approach for the control-based forward dynamic analysis of acquired gait motions publication-title: Multibody Dyn. 2015. Proc. ECCOMAS Themat. Conf. Multibody Dyn. 2015. Cent. Int. Mètodes Numèrics en Eng. (CIMNE) – volume: 26 year: 2015 ident: bib24 article-title: Interdisciplinary applications of kinematics: proceedings of the international conference, Lima, Peru, september 9-11, 2013 publication-title: Mech. Mach. Sci. – volume: 10 start-page: 1 year: 2022 end-page: 25 ident: bib29 article-title: Online adaptive pid control for a multi-joint lower extremity exoskeleton system using improved particle swarm optimization publication-title: Machines – volume: 114 start-page: 650 year: 1992 end-page: 659 ident: bib34 article-title: Robotic manipulator collisions: modeling and simulation publication-title: J. Dyn. Syst. Meas. Control. Trans. ASME – volume: 167 year: 2022 ident: bib41 article-title: A compendium of contact force models inspired by Hunt and Crossley's cornerstone work publication-title: Mech. Mach. Theory – volume: 31 start-page: 847 year: 1998 end-page: 853 ident: bib9 article-title: A viscoelastic sphere model for the representation of plantar soft tissue during simulations publication-title: J. Biomech. – volume: 2018 year: 2018 ident: bib52 article-title: Design and performance evaluation of a wearable sensing system for lower-limb exoskeleton publication-title: Appl. Bionics Biomech. – volume: 7 start-page: 1 year: 2023 end-page: 4 ident: bib18 article-title: An affordable inkjet-printed foot sole sensor and machine learning for telehealth devices publication-title: IEEE Sensors Lett – volume: 10 start-page: 2342 year: 2020 ident: 10.1016/j.euromechsol.2024.105566_bib11 article-title: Dynamic modeling of the dissipative contact and friction forces of a passive biped-walking robot publication-title: Appl. Sci. doi: 10.3390/app10072342 – volume: 34 start-page: 2393 year: 1997 ident: 10.1016/j.euromechsol.2024.105566_bib19 article-title: Indentation of solids with gradients in elastic properties: Part II. Axisymmetric indentors publication-title: Int. J. Solids Struct. doi: 10.1016/S0020-7683(96)00172-2 – volume: 19 start-page: 1 year: 2024 ident: 10.1016/j.euromechsol.2024.105566_bib22 article-title: Prediction of ground reaction forces and moments and joint kinematics and kinetics by inertial measurement units using 3D forward dynamics model publication-title: J. Biomech. Sci. Eng. doi: 10.1299/jbse.23-00130 – volume: 147 start-page: 240 year: 2016 ident: 10.1016/j.euromechsol.2024.105566_bib44 article-title: A finite element analysis of a human foot model to simulate neutral standing on ground publication-title: Procedia Eng. doi: 10.1016/j.proeng.2016.06.240 – volume: B.V year: 2023 ident: 10.1016/j.euromechsol.2024.105566_bib15 article-title: Predictive multibody dynamic simulation of human neuromusculoskeletal systems: a review, Multibody System Dynamics publication-title: The Author(s), under exclusive licence to Springer Nature – volume: 8 year: 2013 ident: 10.1016/j.euromechsol.2024.105566_bib4 article-title: Volumetric modeling and experimental validation of normal contact dynamic forces publication-title: J. Comput. Nonlinear Dyn. – volume: 19 start-page: 954 year: 2015 ident: 10.1016/j.euromechsol.2024.105566_bib54 article-title: A superellipsoid-plane model for simulating foot-ground contact during human gait publication-title: Comput. Methods Biomech. Biomed. Engin. doi: 10.1080/10255842.2015.1081181 – volume: 167 year: 2022 ident: 10.1016/j.euromechsol.2024.105566_bib41 article-title: A compendium of contact force models inspired by Hunt and Crossley's cornerstone work publication-title: Mech. Mach. Theory doi: 10.1016/j.mechmachtheory.2021.104501 – volume: 6 A start-page: 477 year: 2005 ident: 10.1016/j.euromechsol.2024.105566_bib21 article-title: A contact modeling method based on volumetric properties publication-title: Proc. ASME Int. Des. Eng. Tech. Conf. Comput. Inf. Eng. Conf. - DETC2005 – volume: 177 year: 2022 ident: 10.1016/j.euromechsol.2024.105566_bib42 article-title: A review on foot-ground contact modeling strategies for human motion analysis publication-title: Mech. Mach. Theory doi: 10.1016/j.mechmachtheory.2022.105046 – volume: 2 start-page: 65 year: 2007 ident: 10.1016/j.euromechsol.2024.105566_bib38 article-title: Stabilization of a dynamic walking gait simulation publication-title: J. Comput. Nonlinear Dyn. doi: 10.1115/1.2389230 – volume: 26 year: 2015 ident: 10.1016/j.euromechsol.2024.105566_bib24 article-title: Interdisciplinary applications of kinematics: proceedings of the international conference, Lima, Peru, september 9-11, 2013 publication-title: Mech. Mach. Sci. doi: 10.1007/978-3-319-10723-3 – volume: 135 start-page: 51 year: 2024 ident: 10.1016/j.euromechsol.2024.105566_bib48 article-title: An enhanced contact force model with accurate evaluation of the energy dissipation during contact-impact events in dynamical systems publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2024.06.034 – volume: 39 start-page: 2673 year: 2006 ident: 10.1016/j.euromechsol.2024.105566_bib51 article-title: Real-time subject-specific monitoring of internal deformations and stresses in the soft tissues of the foot: a new approach in gait analysis publication-title: J. Biomech. doi: 10.1016/j.jbiomech.2005.08.021 – volume: 25 start-page: 357 year: 2011 ident: 10.1016/j.euromechsol.2024.105566_bib17 article-title: On the continuous contact force models for soft materials in multibody dynamics publication-title: Multibody Syst. Dyn. doi: 10.1007/s11044-010-9237-4 – volume: 14 year: 2024 ident: 10.1016/j.euromechsol.2024.105566_bib53 article-title: A review of foot–terrain interaction mechanics for heavy-duty legged robots publication-title: Appl. Sci. doi: 10.3390/app14156541 – volume: 24 start-page: 255 year: 2010 ident: 10.1016/j.euromechsol.2024.105566_bib32 article-title: A mathematical framework for rigid contact detection between quadric and superquadric surfaces publication-title: Multibody Syst. Dyn. doi: 10.1007/s11044-010-9220-0 – start-page: 1 year: 2009 ident: 10.1016/j.euromechsol.2024.105566_bib35 article-title: Ground foot interaction in human gait: modelling and simulation publication-title: 7th EUROMECH Solid Mech. Conf. – volume: 83 start-page: 1796 year: 2002 ident: 10.1016/j.euromechsol.2024.105566_bib25 article-title: Plantar tissue stiffness in patients with diabetes mellitus and peripheral neuropathy publication-title: Arch. Phys. Med. Rehabil. doi: 10.1053/apmr.2002.35661 – volume: 11 start-page: 117 year: 2023 ident: 10.1016/j.euromechsol.2024.105566_bib45 article-title: Agreement between force platform and smartphone application-derived measures of vertical jump height in youth grassroots soccer players publication-title: Sports doi: 10.3390/sports11060117 – volume: 44 start-page: 2542 year: 2016 ident: 10.1016/j.euromechsol.2024.105566_bib40 article-title: Direct methods for predicting movement biomechanics based upon optimal control theory with implementation in OpenSim publication-title: Ann. Biomed. Eng. doi: 10.1007/s10439-015-1538-6 – volume: 29 start-page: 795 year: 1996 ident: 10.1016/j.euromechsol.2024.105566_bib20 article-title: A two-part, viscoelastic foot model for use in gait simulations publication-title: J. Biomech. doi: 10.1016/0021-9290(95)00141-7 – start-page: 1092 year: 2015 ident: 10.1016/j.euromechsol.2024.105566_bib36 article-title: Underactuated approach for the control-based forward dynamic analysis of acquired gait motions – volume: 92 start-page: 137 year: 2019 ident: 10.1016/j.euromechsol.2024.105566_bib13 article-title: A viscoelastic ellipsoidal model of the mechanics of plantar tissues publication-title: J. Biomech. doi: 10.1016/j.jbiomech.2019.05.041 – volume: 7 start-page: 1 year: 2023 ident: 10.1016/j.euromechsol.2024.105566_bib18 article-title: An affordable inkjet-printed foot sole sensor and machine learning for telehealth devices publication-title: IEEE Sensors Lett doi: 10.1109/LSENS.2023.3279392 – volume: 59 start-page: 1 year: 2017 ident: 10.1016/j.euromechsol.2024.105566_bib27 article-title: Three-dimensional data-tracking dynamic optimization simulations of human locomotion generated by direct collocation publication-title: J. Biomech. doi: 10.1016/j.jbiomech.2017.04.038 – volume: 221 year: 2022 ident: 10.1016/j.euromechsol.2024.105566_bib49 article-title: Energy dissipation analysis for elastoplastic contact and dynamic dashpot models publication-title: Int. J. Mech. Sci. doi: 10.1016/j.ijmecsci.2022.107214 – volume: 28 start-page: 1384 year: 2022 ident: 10.1016/j.euromechsol.2024.105566_bib14 article-title: The influence of partial weight bearing on plantar peak forces using three different types of postoperative shoes publication-title: Foot Ankle Surg. doi: 10.1016/j.fas.2022.07.007 – volume: 114 start-page: 650 year: 1992 ident: 10.1016/j.euromechsol.2024.105566_bib34 article-title: Robotic manipulator collisions: modeling and simulation publication-title: J. Dyn. Syst. Meas. Control. Trans. ASME doi: 10.1115/1.2897737 – volume: 34 start-page: 1441 year: 2018 ident: 10.1016/j.euromechsol.2024.105566_bib8 article-title: Multicontact locomotion of legged robots publication-title: IEEE Trans. Robot. doi: 10.1109/TRO.2018.2862902 – start-page: 849 year: 2017 ident: 10.1016/j.euromechsol.2024.105566_bib2 article-title: Kinematics velocity and dynamic modeling of biped robot – volume: 57 start-page: 1304 year: 2023 ident: 10.1016/j.euromechsol.2024.105566_bib26 article-title: Performance and symmetry measures during vertical jump testing at return to sport after ACL reconstruction publication-title: Br. J. Sports Med. doi: 10.1136/bjsports-2022-106588 – start-page: 4391 year: 2015 ident: 10.1016/j.euromechsol.2024.105566_bib3 article-title: Balance control strategy for legged robots with compliant contacts publication-title: Proc. - IEEE Int. Conf. Robot. Autom. 2015-June – volume: 73 start-page: 68 year: 2015 ident: 10.1016/j.euromechsol.2024.105566_bib37 article-title: A generalized control framework of assistive controllers and its application to lower limb exoskeletons publication-title: Rob. Auton. Syst. doi: 10.1016/j.robot.2014.10.001 – volume: 162 year: 2021 ident: 10.1016/j.euromechsol.2024.105566_bib23 article-title: A new concept of contact joint to model the geometric foot-environment contacts for efficiently determining possible stances for legged robots publication-title: Mech. Mach. Theory doi: 10.1016/j.mechmachtheory.2021.104327 – volume: 31 start-page: 357 year: 2003 ident: 10.1016/j.euromechsol.2024.105566_bib50 article-title: Multibody simulation model of human walking publication-title: Mech. Based Des. Struct. Mach. doi: 10.1081/SME-120022855 – volume: 42 start-page: 447 year: 2018 ident: 10.1016/j.euromechsol.2024.105566_bib55 article-title: A 3D ellipsoidal volumetric foot–ground contact model for forward dynamics publication-title: Multibody Syst. Dyn. doi: 10.1007/s11044-017-9605-4 – volume: 39 start-page: 328 year: 2014 ident: 10.1016/j.euromechsol.2024.105566_bib46 article-title: Measurement of functional heel pad behaviour in-shoe during gait using orthotic embedded ultrasonography publication-title: Gait Posture doi: 10.1016/j.gaitpost.2013.07.118 – start-page: 25 year: 2009 ident: 10.1016/j.euromechsol.2024.105566_bib57 article-title: Multi-Step Forward Dynamic Gait Simulation publication-title: Multibody Dyn. Comput. methods Appl. – volume: 46 start-page: 1216 year: 2018 ident: 10.1016/j.euromechsol.2024.105566_bib28 article-title: Predictive simulations of neuromuscular coordination and joint-contact loading in human gait publication-title: Ann. Biomed. Eng. doi: 10.1007/s10439-018-2026-6 – volume: 18 start-page: 17 year: 2003 ident: 10.1016/j.euromechsol.2024.105566_bib10 article-title: Effects of total contact insoles on the plantar stress redistribution: a finite element analysis publication-title: Clin. Biomech. doi: 10.1016/S0268-0033(03)00080-9 – volume: 26 start-page: 1087 year: 1981 ident: 10.1016/j.euromechsol.2024.105566_bib39 article-title: A singular perturbation approach to modeling and control of Markov chains publication-title: IEEE Trans. Automat. Contr. doi: 10.1109/TAC.1981.1102780 – volume: IUS start-page: 2112 year: 2014 ident: 10.1016/j.euromechsol.2024.105566_bib47 article-title: Development of a wearable ultrasonic sensor and method for continuous monitoring of mechanical properties of plantar soft tissue for diabetic patients publication-title: IEEE Int. Ultrason. Symp. – volume: 2018 year: 2018 ident: 10.1016/j.euromechsol.2024.105566_bib52 article-title: Design and performance evaluation of a wearable sensing system for lower-limb exoskeleton publication-title: Appl. Bionics Biomech. doi: 10.1155/2018/8610458 – volume: 30 start-page: 247 year: 2013 ident: 10.1016/j.euromechsol.2024.105566_bib58 article-title: Solution methods for the double-support indeterminacy in human gait publication-title: Multibody Syst. Dyn. doi: 10.1007/s11044-013-9363-x – volume: 4 start-page: 77 year: 2016 ident: 10.1016/j.euromechsol.2024.105566_bib33 article-title: Muscle synergies facilitate computational prediction of subject-specific walking motions publication-title: Front. Bioeng. Biotechnol. doi: 10.3389/fbioe.2016.00077 – volume: 10 start-page: 1 year: 2022 ident: 10.1016/j.euromechsol.2024.105566_bib29 article-title: Online adaptive pid control for a multi-joint lower extremity exoskeleton system using improved particle swarm optimization publication-title: Machines – volume: 22 start-page: 2203 year: 2022 ident: 10.1016/j.euromechsol.2024.105566_bib12 article-title: Validity and reliability of the Insole3 instrumented shoe insole for ground reaction force measurement during walking and running publication-title: Sensors doi: 10.3390/s22062203 – volume: 31 start-page: 847 year: 1998 ident: 10.1016/j.euromechsol.2024.105566_bib9 article-title: A viscoelastic sphere model for the representation of plantar soft tissue during simulations publication-title: J. Biomech. doi: 10.1016/S0021-9290(98)00085-2 – volume: 55 start-page: 297 year: 2023 ident: 10.1016/j.euromechsol.2024.105566_bib5 article-title: Modeling, analysis and control of robot–object nonsmooth underactuated Lagrangian systems: a tutorial overview and perspectives publication-title: Annu. Rev. Control doi: 10.1016/j.arcontrol.2022.12.002 – volume: 1 start-page: 1 year: 2008 ident: 10.1016/j.euromechsol.2024.105566_bib1 article-title: Non-linear finite element modelling of anatomically detailed 3D foot model publication-title: Rep. Pap. – volume: 140 year: 2018 ident: 10.1016/j.euromechsol.2024.105566_bib43 article-title: Dynamic simulation of human gait model with predictive capability publication-title: J. Biomech. Eng. doi: 10.1115/1.4038739 – volume: 184 year: 2023 ident: 10.1016/j.euromechsol.2024.105566_bib16 article-title: Contact-impact events with friction in multibody dynamics: back to basics publication-title: Mech. Mach. Theory doi: 10.1016/j.mechmachtheory.2023.105305 |
| SSID | ssj0002021 |
| Score | 2.422902 |
| Snippet | Accurate plantar pressure models play a pivotal in predicting human gait dynamics and have broad applications, including the development of exoskeletons,... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 105566 |
| SubjectTerms | Biomechanical modeling Foot-ground contact Human biomechanics Parameter identification Viscoelastic ellipsoid |
| Title | Mechanical modeling of plantar pressure during human walking in different terrains: Experiments and analysis |
| URI | https://dx.doi.org/10.1016/j.euromechsol.2024.105566 |
| Volume | 111 |
| WOSCitedRecordID | wos001423286300001&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: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 issn: 0997-7538 databaseCode: AIEXJ dateStart: 19980101 customDbUrl: isFulltext: true dateEnd: 99991231 titleUrlDefault: https://www.sciencedirect.com omitProxy: false ssIdentifier: ssj0002021 providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1ta9RAEF7Oq4hffBdrVVbwm0Rus7nb3eKXUk6qaFGocN9CdrM5UmNS764vP6k_09nXXKWlVRBCCEt2k8w82Z0dZuZB6I3myqzzpgKAzJKMS51IVZVJyUtCtZgQxSpLNsH29_lsJr4OBuchF-akYW3Lz87E0X9VNbSBsk3q7F-oOw4KDXANSoczqB3ON1L8F22Sea3sLc1NCGtuQIamrrXdXy90SFB0JH2nRfPDZ7cEypTVWxC5IZCwQXPTyASw9PVdXTGTKz373sr96d_GkR5bX2vX1GW05D_XxxZIdfGrjljyPuy9rp3LOqIXpDx3kf7tvNLx7ujy_laf-lbvxUjHfcxgcEcKlsDWiV-Ymf087OZWS-U5uXTadx6IQ1MrszPfBXqErX-avev7XCy1_ccSGAMTQ8zbYb42VG6Gyt1Qt9BGysaCD9HGzsfp7FNc9eEey84YvuMOet3HEl7xXpfbQmv2zcEDdM9vTPCOA9RDNNDtI3Tfb1KwXwKWj1HT4wsHfOGuwh5fOOALO3xhiy_s8YXrFkd84YCvbbyGLgzowgFdT9D3D9OD3b3EU3YkiqZklRRgDxFN4D8XmsmqEAUliowkWMlgmTOtSSUUo5KVtMxGSk5GJZOUKpXpcWHYJZ-iYdu1-hnCTCnKSp6RytQwpFKMKBySMVMobEL1JuJBeLny9ewNrUqTX6vETZTGrkeuqMtNOr0PGsq9deqszhxQeH335__yzC10t_9ZXqDhanGsX6Lb6mRVLxevPAR_A0d_vGU |
| linkProvider | Elsevier |
| 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=Mechanical+modeling+of+plantar+pressure+during+human+walking+in+different+terrains%3A+Experiments+and+analysis&rft.jtitle=European+journal+of+mechanics%2C+A%2C+Solids&rft.au=Liu%2C+Jiaqi&rft.au=Fang%2C+Hongbin&rft.au=Feng%2C+Mingfei&rft.au=Zhang%2C+Qiwei&rft.date=2025-05-01&rft.issn=0997-7538&rft.volume=111&rft.spage=105566&rft_id=info:doi/10.1016%2Fj.euromechsol.2024.105566&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_euromechsol_2024_105566 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0997-7538&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0997-7538&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0997-7538&client=summon |