{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,31]],"date-time":"2026-08-31T05:17:40Z","timestamp":1788153460834,"version":"build-2803163510"},"reference-count":31,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T00:00:00Z","timestamp":1787702400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Jiangsu Research Center of Intelligent Manufacturing Technology for Carbon Fiber and Advanced Material"},{"name":"High-Level Talent Scientific Research Start-up Fund Project","award":["CZTGI2025644"],"award-info":[{"award-number":["CZTGI2025644"]}]},{"name":"the Fundamental Research Funds for the Central Universities","award":["2232025G-14"],"award-info":[{"award-number":["2232025G-14"]}]},{"name":"Science and Technology Guidance Program Project of China National Textile and Apparel Council","award":["2025043"],"award-info":[{"award-number":["2025043"]}]},{"award":["2025043"],"award-info":[{"award-number":["2025043"]}],"id":[{"id":"https:\/\/ror.org\/02nx9ts82","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Pneumatic soft actuators have been drawing considerable attention in the field of soft robotics, thanks to their inherent flexibility, high power density, and safe interaction. However, the strong, intricate coupling between the material\u2019s hyperelastic behavior and the reinforcement of anisotropic fibers creates significant challenges for both analytical modeling and numerical characterization of these actuators. In this paper, we design and fabricate a fiber-reinforced pneumatic soft actuator using Ecoflex 00-30 silicone rubber as the base material and helically wound fibers as the reinforcing layer. We set up a theoretical framework that combines the Neo-Hookean model for isotropic silicone rubber with a strain energy-based formulation for anisotropic wound fibers. This framework describes how the actuator is stretched, expanded, twisted, and bent. Finite element simulations are then carried out, focusing on three key design parameters: winding fiber density (three levels: high, medium, low), air cavity offset distance from the central axis (1, 2, 3, and 4 mm), and air cavity cross-sectional geometry (cube vs. cylindrical). The simulations reveal that a higher winding fiber density promotes more uniform stress distribution across both the strain and confinement layers. In contrast, a low fiber density can lead to local bulging and large stress variations, which ultimately compromises the bending performance. The offset distance of the air cavity from the neutral axis is directly linked to the bending curvature: a larger offset produces greater air cavity deformation and higher actuation efficiency. Furthermore, the cuboid air cavity yields a larger bending angle (experimentally validated up to 90\u00b0 at 0.045 MPa) and better efficiency, while the cylindrical air cavity distributes stress more evenly across the outer surface of the strain layer and reduces stress concentration at the edges. These findings provide useful quantitative guidance for optimizing the structure of fiber-reinforced soft actuators and establish a framework for hybrid analytical\u2013numerical prediction of their mechanical behavior.<\/jats:p>","DOI":"10.3390\/ma19173631","type":"journal-article","created":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T15:04:32Z","timestamp":1787756672000},"page":"3631","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Finite Element Analysis of Fiber-Reinforced Pneumatic Soft Actuators: A Hybrid Analytical\u2013Numerical Framework"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-7895-9801","authenticated-orcid":false,"given":"Ruibing","family":"Fan","sequence":"first","affiliation":[{"name":"School of Intelligent Manufacturing, Changzhou Vocational Institute of Textile and Garment, Changzhou 213164, China"},{"name":"The Jiangsu Research Center of Intelligent Manufacturing Technology for Carbon Fiber and Advanced Material, Changzhou 213164, China"},{"name":"Engineering Research Center of Artificial Intelligence for Textile Industry Ministry of Education, Institute of Artificial Intelligence, Donghua University, Shanghai 201620, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guowei","family":"Shao","sequence":"additional","affiliation":[{"name":"School of Intelligent Manufacturing, Changzhou Vocational Institute of Textile and Garment, Changzhou 213164, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianhua","family":"Tang","sequence":"additional","affiliation":[{"name":"School of Intelligent Manufacturing, Changzhou Vocational Institute of Textile and Garment, Changzhou 213164, China"},{"name":"The Jiangsu Research Center of Intelligent Manufacturing Technology for Carbon Fiber and Advanced Material, Changzhou 213164, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-2642-4608","authenticated-orcid":false,"given":"Yao","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Intelligent Manufacturing, Changzhou Vocational Institute of Textile and Garment, Changzhou 213164, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4487-5354","authenticated-orcid":false,"given":"Pengyu","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Material Science and Engineering, Zhengzhou University, Zhengzhou 450001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Jung, Y., Kwon, K., Lee, J., and Ko, S.H. (2024). Untethered soft actuators for soft standalone robotics. Nat. Commun., 15.","DOI":"10.1038\/s41467-024-47639-0"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1089\/soro.2016.0008","article-title":"An overview of shape memory alloy-coupled actuators and robots","volume":"4","author":"Rodrigue","year":"2017","journal-title":"Soft Robot."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"836","DOI":"10.1126\/science.287.5454.836","article-title":"High-speed electrically actuated elastomers with strain greater than 100%","volume":"287","author":"Pelrine","year":"2000","journal-title":"Science"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"El-Atab, N., Mishra, R.B., Al-Modaf, F., Joharji, L., Alsharif, A.A., Alamoudi, H., Diaz, M., Qaiser, N., and Hussain, M.M. (2020). Soft Actuators for Soft Robotic Applications: A Review. Adv. Intell. Syst., 2.","DOI":"10.1002\/aisy.202070102"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2835","DOI":"10.1177\/00405175241253867","article-title":"Recent advances of preparing structure-enhanced conductive yarns to control their performance in potential applications","volume":"94","author":"Saty","year":"2024","journal-title":"Text. Res. J."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"237","DOI":"10.2147\/MDER.S476464","article-title":"Design and Driving Performance Study of Soft Actuators for Hand Rehabilitation Training","volume":"17","author":"Zhang","year":"2024","journal-title":"Med. Devices \u00c9vid. Res."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Mohan, P.N., Thirmal, C., Joseph, A., Arun, B., Priya, K.S., Murugavel, P., and Raju, K.J. (2025). Microwave, ferroelectric and electromechanical studies of free standing blended electroactive polymer films. Mater. Res. Bull., 181.","DOI":"10.1016\/j.materresbull.2024.113105"},{"key":"ref_8","first-page":"125","article-title":"Control system of five-axis drived sample weaving machine","volume":"30","author":"Zhou","year":"2009","journal-title":"J. Text. Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"4512","DOI":"10.1177\/0040517519837731","article-title":"Numerical and experimental study on the joint forming mechanism in the pneumatic splicing process","volume":"89","author":"Zhou","year":"2019","journal-title":"Text. Res. J."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"712","DOI":"10.1177\/0040517509342314","article-title":"Studies of flexible fiber trajectory and its pneumatic condensing mechanism in compact spinning with lattice apron","volume":"80","author":"Zou","year":"2010","journal-title":"Text. Res. J."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Wang, Z., Chen, Y., Ma, Y., and Wang, J. (2024). Bioinspired Stimuli-Responsive Materials for Soft Actuators. Biomimetics, 9.","DOI":"10.20944\/preprints202401.2039.v1"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Shabani, M. (2024). Numerical and experimental assessment of tilted-helical fiber orientation effects on deformation of pneumatic soft actuators. Smart Mater. Struct., 33.","DOI":"10.1088\/1361-665X\/ad315d"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Tan, X., McDonald-Bowyer, A., Stoyanov, D., and Stilli, A. (2026, January 7\u201312). Design, Modelling and Characterisation of a Miniature Fibre-Reinforced Soft Bending Actuator for Endoluminal Interventions. Proceedings of the 2026 IEEE 9th International Conference on Soft Robotics (RoboSoft), Kanazawa, Japan.","DOI":"10.1109\/RoboSoft67810.2026.11522843"},{"key":"ref_14","first-page":"211","article-title":"Design, simulation and experimental analysis of fiber-reinforced silicone actuators","volume":"91","author":"Esmalipour","year":"2024","journal-title":"Struct. Eng. Mech."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"9648","DOI":"10.1109\/ACCESS.2023.3346385","article-title":"Multi-Structure Parameter Optimization Analysis of Soft Actuator Based on Numerical Calculation","volume":"12","author":"Wang","year":"2024","journal-title":"IEEE Access"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Dong, C., Yu, C.-P., Wu, Y., Xing, R., Lu, M., and Ding, L. (2024, January 26\u201328). Modeling and Analysis of Eccentric Fiber-Reinforced Flexible Actuators. Proceedings of the 2024 3rd International Conference on Service Robotics (ICoSR), Hangzhou, China.","DOI":"10.1109\/ICoSR63848.2024.00016"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1460","DOI":"10.1177\/0040517511398948","article-title":"Image analysis of the elastane position effect on the appearance of wet pneumatic spliced elastic core-spun yarn","volume":"81","author":"Jaouachi","year":"2011","journal-title":"Text. Res. J."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1974","DOI":"10.1177\/0040517520904374","article-title":"The effects of textile reinforcements on the protective properties of self-healing polymers intended for safety gloves","volume":"90","year":"2020","journal-title":"Text. Res. J."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1038\/nature14543","article-title":"Design, fabrication and control of soft robots","volume":"521","author":"Rus","year":"2015","journal-title":"Nature"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1493","DOI":"10.1016\/0021-9290(92)90062-6","article-title":"On the relationship between the orthotropic Young\u2019s moduli and fabric","volume":"25","author":"Cowin","year":"1992","journal-title":"J. Biomech."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"28682","DOI":"10.1021\/acsami.5c03424","article-title":"Embedded Conductive Fiber for Pumpless Liquid-Gas Phase Transition Soft Actuation","volume":"17","author":"Liu","year":"2025","journal-title":"ACS Appl. Mater. Interfaces"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Zhuang, Y., Xu, K., Liu, Z., Li, J., Shen, L., and Wang, J. (2025). Design and experimental investigation of the grasping system of an agricultural soft manipulator based on FMDS-YOLOv8. Front. Plant Sci., 16.","DOI":"10.3389\/fpls.2025.1683380"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Zhu, Y., Feng, K., Hua, C., Wang, X., Hu, Z., Wang, H., and Su, H. (2022). Model Analysis and Experimental Investigation of Soft Pneumatic Manipulator for Fruit Grasping. Sensors, 22.","DOI":"10.3390\/s22124532"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1177\/0278364920917203","article-title":"A soft manipulator for efficient delicate grasping in shallow water: Modeling, control, and real-world experiments","volume":"40","author":"Gong","year":"2020","journal-title":"Int. J. Robot. Res."},{"key":"ref_25","unstructured":"Tian, D., Lei, H., Jin, L., Zhang, L., Fan, J., and Liu, R. (2025). Design of a modular deployable biomimetic grasping manipulator. Acta Aeronaut. Astronaut. Sin., 46."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Vitucci, G., Trentadue, F., and De Tommasi, D. (2026). Inversion symmetry in separable line, area and volume elastic energies. Contin. Mech. Thermodyn., 38.","DOI":"10.1007\/s00161-026-01473-5"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3719","DOI":"10.1039\/C9SM00409B","article-title":"Damage cross-effect and anisotropy in tough double network hydrogels revealed by biaxial stretching","volume":"15","author":"Mai","year":"2019","journal-title":"Soft Matter"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Fan, R., Xu, P., Wang, Y., Shao, G., and Tang, J. (2026). Piecewise Parameter Optimization of the Neo-Hookean Model for Hyperelastic Silicone Rubber with Large Deformation. Materials, 19.","DOI":"10.3390\/ma19132789"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"3126","DOI":"10.1016\/j.matpr.2022.05.352","article-title":"Stress and bending analysis of a soft pneumatic actuator considering different hyperelastic materials","volume":"65","author":"Gariya","year":"2022","journal-title":"Mater. Today Proc."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1437","DOI":"10.1177\/00405175241228846","article-title":"Study on the water transport performance of the fractal tree-like structure of nonwoven cotton fabrics","volume":"94","author":"Shi","year":"2024","journal-title":"Text. Res. J."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"583","DOI":"10.21741\/9781644903735-68","article-title":"Design optimization and one-shot 3D printing of a bio-inspired soft robot capable of counter-flexural motion at low actuation pressures","volume":"57","author":"Pricci","year":"2025","journal-title":"Mater. Res. Proc."}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/19\/17\/3631\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,31]],"date-time":"2026-08-31T04:25:50Z","timestamp":1788150350000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/19\/17\/3631"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,26]]},"references-count":31,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2026,9]]}},"alternative-id":["ma19173631"],"URL":"https:\/\/doi.org\/10.3390\/ma19173631","relation":{},"ISSN":["1996-1944"],"issn-type":[{"value":"1996-1944","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,26]]}}}