Biomimetic Architected Ligaments with Programmable Non-linear Mechanical Behavior via Braiding

Abstract

Natural ligaments achieve joint stability and mobility through hierarchical fibrous architectures encoding non-linear and deformation dependent mechanics, which remain elusive in artificial substitutes. Here, we report a bioinspired braiding strategy for artificial ligaments with programmable mechanical responses. By encoding knot structure, braiding length, and strand count, we achieve ligaments exhibiting tunable non-linear J-shaped force–displacement behavior with independently tunable deformation of the toe region and stiffness of the linear region. This programmability arises from hierarchical deformation, knot reconfiguration governing compliance onset, while structure-mediated strain transmission coordinates global deformation. Integrating mechanical characterization with machine learning enables mapping natural ligament mechanics onto an architected design space for data-driven configuration discovery. The resulting artificial ligaments reproduce non-linear mechanical responses with up to 99% similarity and enable biomimetic joint motions in mechanical validation. By establishing architecture as a programmable mechanical variable, this work provides a new paradigm for inverse design of artificial ligaments across biomedical and robotic applications.

Keywords

Biomimetic design / Architected ligaments / Programmable mechanical behavior / Mechanical metamaterial / Bioinspired joint system

References

[1] Fang J, Wang X, Lai H, Li W, Yao X, Pan Z, Mao R, Yan Y, Xie C, Lin J, Sun W, Li R, Wang J, Dai J, Xu K, Yu X, Xu T, Duan W, Qian J, Ouyang H, Dai X. Decoding the mechanical characteristics of the human anterior cruciate ligament entheses through graduated mineralization interfaces. Nat Commun, 2024, 15: 9253.

[2] Yang G, Lin R, Li H, Chen Y, Liu M, Luo Z, Wang K, Tu J, Xu Y, Fan Z, Zhou Y, Pan Y, Zhao Z, Liu R. Implantable wireless suture sensor for in situ tendon and ligament strain monitoring. Sci Adv, 2025, 11. eadt3811

[3] Shi D, Ji D, Bae J. Hierarchically structuralized hydrogels with ligament-like mechanical performance. Nat Commun, 2025, 16: 11492.

[4] Feng Y, Wang Y, Wang C, Chen X, Shan L, Yan R, Wang Z, Liu S, Liu J. Fatigue resistant hydrogels engineered with twisting hierarchical structures. Adv Mater, 2026, 38: e22623.

[5] Matsuda T, Kawakami R, Namba R, Nakajima T, Gong JP. Mechanoresponsive self-growing hydrogels inspired by muscle training. Science, 2019, 363: 504.

[6] Li M, Chen L, Li Y, Dai X, Jin Z, Zhang Y, Feng W, Yan LT, Cao Y, Wang C. Superstretchable, yet stiff, fatigue-resistant ligament-like elastomers. Nat Commun, 2022, 13: 2279.

[7] Yang H, Yin X, Zhang C, Chen B, Sun P, Xu Y. Weaving liquid crystal elastomer fiber actuators for multifunctional soft robotics. Sci Adv, 2025, 11. eads3058

[8] Surjadi JU, Aymon BFG, Carton M, Portela CM. Double-network-inspired mechanical metamaterials. Nat Mater, 2025, 24: 945.

[9] No YJ, Castillo M, Ramaswamy Y, Zreiqat H. Role of biomaterials and controlled architecture on tendon/ligament repair and regeneration. Adv Mater, 2020, 32: 1904511.

[10] Feng X, Luo Z, Shi H, Chen S, Chen C, Chen P, Zheng S, Wan R, Wang Q, Li Z, Lin C, He Y, Zhao Z, Zhang X, Zhou X, Chen Y, Li Y, Liu Q, Chen S. Advances in artificial ligament biomaterials for anterior cruciate ligament reconstruction. Adv Compos Hybrid Mater, 2025, 8: 282.

[11] Hughes JAF, Maiolino P, Iida E. An anthropomorphic soft skeleton hand exploiting conditional models for piano playing. Sci Robot, 2018, 3. eaau3098

[12] Zhu Y, Wei G, Ren L, Luo Z, Shang J. An anthropomorphic robotic finger with biomechanical advantages. IEEE Trans Robot, 2023, 39: 485.

[13] Yang H, Wei G, Ren L. Enhancing biomimetic robotic elbow performance. IEEE Trans Robot, 2024, 40: 2692.

[14] Choi S, Choi Y, Kim J. Anisotropic hybrid hydrogels with superior mechanical properties. Adv Funct Mater, 2019, 29: 1904342.

[15] Liu L, Zhang D, Bai P, Fang Y, Guo J, Li Q, Ma R. Fatigue-resistant and super-tough thermocells. Nat Commun, 2025, 16: 1963.

[16] Ma P, Chen T, Wu X, Hu Y, Huang K, Wang Y, Dai H. Effects of bioactive hydroxyapatite on artificial ligaments. J Mater Chem B, 2021, 9: 6600.

[17] Heidari BS, Ruan R, Vahabi E, Chen P, De-Juan-Pardo EM, Zheng M, Doyle B. Biopolymers for tendon and ligament regeneration. Bioact Mater, 2023, 19: 179

[18] Li C, Jia R, Yang Y, Liao G. Hierarchical carbon nanotube fiber ligament. Adv Fiber Mater, 2023, 5: 1549.

[19] Wu L, Kang Y, Shi X, Yuezhen B, Qu M, Li J, Wu ZS. Wood-inspired anisotropic hydrogels. ACS Nano, 2023, 17: 13522.

[20] Liu YC, Chen SH, Kuan CH, Chen SH, Huang WY, Chen HX, Wang TW. Interfacial fiber assembly for ligament regeneration. Adv Mater, 2024, 36: 2314294.

[21] Yan C, He X, Yu B, Zhou B, Fang S, Xu J, Liu B, Wang Z. Mechanoluminescence hydrogel for ligament sensing. Adv Funct Mater, 2025, 35: 2420142.

[22] Wang J, Dong X, Qiu H, Liu Z, Kang Y, Du J, Yang X, Li XL, Ding Y. Bioinspired polyurethane for artificial ligaments. Chem Mater, 2025, 37: 1609.

[23] Lu X, Ren L, Wang K, Wei G, Qian Z, Liang W, Ren L. Bioinspired braided fibers for artificial joints. IEEE Trans Neural Syst Rehabil Eng, 2022, 30: 1172.

[24] Lu X, Zhao S, Chen W, Xie H, Teng J, Ren L, Wang K, Qian Z, Ren L. Multilayer braided ligament structures. Mater Des, 2024, 241. 112976

[25] Song G, Jin W, Li G, Sun Y, Wu J, Song H, Wei Y, Wang K, Jiang Z, Qian Z, Ren L. Fabric ligament for lumbar spine kinematics. Small Struct, 2026, 7. e202500797

[26] Li S, Wang S, Shao J, Wang J, Liu W, Chen L, Li Z, Zhang C, Song J. Braided ligament optimization strategy. Adv Healthc Mater, 2024, 13: 2304133.

[27] Kim JW, Allen MJ, Recker EA, Stevens LM, Cater HL, Uddin A, Gao A, Eckstrom W, Arrowood AJ, Sanoja GE, Cullinan MA, Freeman BD, Page ZA. Hybrid resins for multimaterial 3D printing. Nat Mater, 2025, 24: 1116.

[28] Wu Y, Zhang Y, Wu H, Wen J, Zhang S, Xing W, Zhang H, Xue H, Gao J, Mai Y. Wet annealing hydrogels. Adv Mater, 2023, 35: 2210624.

[29] Camarero-Espinosa S, Yuan H, Emans PJ, Moroni L. Mimicking ACL structure. Adv Healthc Mater, 2023, 12: 2370092

[30] Wang L, Jiang H, Wang F, Sun H, Yang Y, Li W, Qian Z, Sun X, Chen P, Chen S, Peng H. High-performance artificial ligament. Adv Healthc Mater, 2023, 12: 2301610.

[31] Chen Y, Sun X, Luo L, Li H, Chen N, Yan C, Liu X, Li J, Qin M, Qin X, Cheng P. Strong PVA hydrogel fibers. Adv Funct Mater, 2025, 35: 2415737.

[32] Kononova O, Krasnikovs A, Dzelzitis K, Harjkova G, Vagele A, Eiduks M. Knitted fabric composites. Est J Eng, 2011, 17: 39.

[33] Maziz A, Concas A, Khaldi A, Stalhand J, Persson NK, Jager EWH. Knitting artificial muscles. Sci Adv, 2017, 3. e1600327

[34] Patil VP, Sandt JD, Kolle M, Dunkel J. Topological mechanics of knots. Science, 2020, 367: 71.

[35] Singal K, Dimitriyev MS, Gonzalez SE, Cachine AP, Quinn S, Matsumoto EA. Programming mechanics in knitted materials. Nat Commun, 2024, 15: 2622.

[36] Xue Y, Cao J, Feng T, Zhang K, Li S, Hu J, Guo H, Zhang J, Song Y, Wang Z, Wang L, Huang Q, Zhou Z, Shen J, Fan W, Wang Z, Li X, Wong JW, Chen Z, Ruan D, Miao Z, Zhang B, Zhou E, Gan L, Wang X, Cao E, Chen T, Zou W, Zhang J, Lu H, Zhang Q, Liu S, Dong H, Xiong S, Peng S, Wong TW, Chen Y, Li T, Chen M, Yang X, Yang W, Cai X. Slipknot mechanical transmission. Nature, 2025, 647: 889.

[37] Dennis DA, Mahfouz MR, Komistek RD, Hoff W. Knee kinematics in vivo. J Biomech, 2005, 38: 241.

[38] Hollister AM, Jatana S, Singh AK, Sullivan WW, Lupichuk AG. Axes of knee rotation. Clin Orthop Relat Res, 1993, 290: 259.

[39] Wilson DR, Feikes JD, O’Connor JJ. Ligament-guided knee motion. J Biomech, 1998, 31: 1127.

[40] Cho HJ, Kwak DS. Mechanical properties of knee ligaments. Appl Sci, 2020, 10: 6266.

[41] Wilson WT, Deakin AH, Payne AP, Picard F, Wearing SC. Structural properties of knee ligaments. J Orthop Sport Phys, 2012, 42: 345.

[42] Criscenti G, De Maria C, Sebastiani E, Tei M, Placella G, Speziali A, Vozzi G, Cerulli G. Patellofemoral ligament properties. J Mech Behav Biomed Mater, 2016, 54: 141.

[43] Jones RS, Nawana NS, Pearcy MJ, Learmonth DJA, Bickerstaff DR, Costi JJ, Paterson RS. ACL mechanical properties. Clin Biomech, 1995, 10: 339.

[44] Bendjaballah MZ, Shirazi-Adl A, Zukor DJ. Knee joint finite element analysis. Clin Biomech, 1997, 12: 139.

[45] Li G, Gil J, Kanamori A, Woo SL. 3D knee model. J Biomech Eng, 1999, 121: 657.

[46] Pintar FA, Yoganandan N, Myers T, Elhagediab A, Sances AJrLumbar ligament properties. J Biomech, 1992, 25: 1351.

[47] Schendel MJ, Wood KB, Buttermann GR, Lewis JL, Ogilvie JW. Lumbar ligament force measurement. J Biomech, 1993, 26: 427.

[48] Kapetanakis S, Chatzivasilidis M, Gkantsinikoudis N. Posterior ligament complex review. Surg Radiol Anat, 2025, 47: 170.

[49] Rohlmann A, Neller S, Claes L, Bergmann G, Wilke HJ. Follower load in spine. Spine, 2001, 26: 557.

[50] Heuer F, Schmidt H, Klezl Z, Claes L, Wilke HJ. Reduction of spinal structures. J Biomech, 2007, 40: 271.

[51] Guan Y, Yoganandan N, Moore J, Pintar FA, Zhang J, Maiman DJ, Laud P. Lumbosacral moment-rotation response. J Biomech, 2007, 40: 1975.

Funding

National Natural Science Foundation of China(No. 52575334)

Rights & permissions

Donghua University, Shanghai, China