Strain amplification from within: Harnessing programmable intrinsic resonance in dielectric elastomers driven by space charge mechanism

Abstract

The flight of insects exemplifies nature’s use of resonance to achieve large-amplitude, high-frequency motion with exceptional energy efficiency. Emulating this resonant amplification effect (RAE) in artificial systems remains a key challenge in soft robotics. Conventional dielectric elastomers (DEs) can be tuned electrically but rely on in-plane deformation. This generates insufficient inertial forces for resonance and thus requires rigid external frames, which consequently add fabrication complexity and reduces energy density. Here, we present a material-level approach to achieve intrinsic resonance amplification using space charge-driven dielectric elastomers (SC-DEs), which generate asymmetric electric fields and self-induced bending without external support. The optimized materials exhibited efficient actuation at low driving fields (~1 V μm^-1), with bending angles amplified from 20° to 150° through resonance without increasing field strength. This work establishes a framework for realizing resonance-amplified electromechanical actuation intrinsically within soft materials, offering new design routes toward lightweight, energy-efficient, and high-performance soft robotic systems.

Keywords

Resonant effect / amplitude amplification / dielectric elastomer / space charge

Acknowledgements

We thank Mrs. Hui Li for assistance in using the broadband dielectric spectrometer at the State Key Laboratory of Chemical Engineering (Zhejiang University). We also thank Mr. Ben He for assisting in performing the 1H-NMR spectrum.

Authors contribution

Zhang CK: Writing-original draft, data curation, formal analysis, methodology. Zhang CC: Methodology, investigation. Jin BJ: Conceptualization writing-review & editing. Xie T: Funding acquisition, resources, supervision.

Conflicts of interest

The authors declare no conflicts of interest.

Ethical approval

Not applicable.

Consent to participate

Not applicable.

Consent for publication

Not applicable.

Availability of data and materials

Data and materials supporting the findings of this study are available from the supplementary materials and the corresponding authors upon reasonable request.

Funding

This work was supported by the National Natural Science Foundation of China (Grant No. U23A2098 and 52473111) and TCL Science and Technology Innovation Fund (Grant No. 20242061).

References

[1] Weis-Fogh T . Energetics of hovering flight in hummingbirds and in drosophila. J Exp Biol. 1972; 56(1): 79-104.

[2] Liu H . Integrated modeling of insect flight: From morphology, kinematics to aerodynamics. J Comput Phys. 2009; 228(2): 439-459.

[3] Floreano D, Wood RJ . Science, technology and the future of small autonomous drones. Nature. 2015; 521(7553): 460-466.

[4] Sunada S, Wang H, Zeng L, Kawachi K . Analysis of maneuvering flight of an insect. J Bionic Eng. 2004; 1(2): 88-101.

[5] Aracheloff C, Garrouste R, Nel A, Godoy-Diana R, Thiria B . Subtle frequency matching reveals resonant phenomenon in the flight of Odonata. J R Soc Interface. 2024; 21(219): 20240401.

[6] Masoud H, Alexeev A . Resonance of flexible flapping wings at low Reynolds number. Phys Rev E Stat Nonlin Soft Matter Phys. 2010; 81(5 Pt 2): 056304.

[7] Pons A, Beatus T . Distinct forms of resonant optimality within insect indirect flight motors. J R Soc Interface. 2022; 19(190): 20220080.

[8] Zhang C, Rossi C . A review of compliant transmission mechanisms for bio-inspired flapping-wing micro air vehicles. Bioinspir Biomim. 2017; 12(2): 025005.

[9] Helbling EF, Wood RJ . A review of propulsion, power, and control architectures for insect-scale flapping-wing vehicles. Appl Mech Rev. 2018; 70(1): 010801.

[10] Zhang J, Deng X . Resonance principle for the design of flapping wing micro air vehicles. IEEE Trans Robot. 2017; 33(1): 183-197.

[11] Shi Y, Askounis E, Plamthottam R, Libby T, Peng Z, Youssef K, et al. A processable, high-performance dielectric elastomer and multilayering process. Science. 2022; 377(6602): 228-232.

[12] Yin LJ, Du B, Hu HY, Dong WZ, Zhao Y, Zhang Z, et al. A high-response-frequency bimodal network polyacrylate elastomer with ultrahigh power density under low electric field. Nat Commun. 2024; 15(1): 9819.

[13] Suo Z. Theory of dielectric elastomers. Acta Mech Solida Sin. 2010; 23(6): 549-578.

[14] Zhang J, Zhao J, Chen H, Li D . Dynamic analyses of viscoelastic dielectric elastomers incorporating viscous damping effect. Smart Mater Struct. 2017; 26(1): 015010.

[15] Li T, Li G, Liang Y, Cheng T, Dai J, Yang X, et al. Fast-moving soft electronic fish. Sci Adv. 2017; 3(4): e1602045.

[16] Feng W, Sun L, Jin Z, Chen L, Liu Y, Xu H, et al. A large-strain and ultrahigh energy density dielectric elastomer for fast moving soft robot. Nat Commun. 2024; 15(1): 4222.

[17] Ren Z, Kim S, Ji X, Zhu W, Niroui F, Kong J, et al. A high-lift micro-aerial-robot powered by low-voltage and long-endurance dielectric elastomer actuators. Adv Mater. 2022; 34(7): 2106757.

[18] Xiao Y, Mao J, Shan Y, Yang T, Chen Z, Zhou F, et al. Anisotropic electroactive elastomer for highly maneuverable soft robotics. Nanoscale. 2020; 12(14): 7514-7521.

[19] Chen Y, Zhao H, Mao J, Chirarattananon P, Helbling EF, Hyun NP, et al. Controlled flight of a microrobot powered by soft artificial muscles. Nature. 2019; 575(7782): 324-329.

[20] Watanabe M, Wakimoto N, Shirai H, Hirai T . Bending electrostriction and space-charge distribution in polyurethane films. J Appl Phys. 2003; 94(4): 2494-2497.

[21] Watanabe M, Hirai T . Bending-electrostrictive response of polyurethane films subjected to a reversed electric field. J Appl Polym Sci. 2004; 92(6): 3644-3650.

[22] Zhang C, Jin B, Cao X, Chen Z, Miao W, Yang X, et al. Dielectric polymer with designable large motion under low electric field. Adv Mater. 2022; 34(50): e2206393.

[23] Hirai T, Sadatoh H, Ueda T, Kasazaki T, Kurita Y, Hirai M, et al. Polyurethane-elastomer-actuator. Angew Makromol Chem. 1996; 240(1): 221-229.

[24] Zhang C, Chen G, Zhang K, Jin B, Zhao Q, Xie T . Repeatedly programmable liquid crystal dielectric elastomer with multimodal actuation. Adv Mater. 2024; 36(16): e2313078.

[25] Kakizaki S, Shintake J, Iwatake Y, Baba K, Takeuchi H, Yamamoto A . Large, fast, and bidirectional bending of slide-ring polymer materials. Adv Intell Syst. 2020; 2(4): 1900155.

[26] Chen Z, Ma Z, Tang J, Xiao Y, Mao J, Cai Y, et al. Adaptively reconstructing network of soft elastomers to increase strand rigidity: Towards free-standing electro-actuation strain over 100. Mater Horiz. 2021; 8(10): 2834-2841.

[27] Fu M, Dissado L, Chen G, Fothergill J . Space charge formation and its modified electric field under applied voltage reversal and temperature gradient in XLPE cable. IEEE Trans Dielect Electr Insul. 2008; 15(3): 851-860.

[28] Lv Z, Ma Y, Zhang C, Peng J, Wu K, Dissado LA . The simultaneous evolution of space charge and conduction current in LDPE. IEEE Trans Dielect Electr Insul. 2021; 28(2): 616-624.

[29] Kornbluh RD, Pelrine R, Pei Q, Oh S, Joseph J . Ultrahigh strain response of field-actuated elastomeric polymers. In: Bar-Cohen Y, editor. Smart Structures and Materials 2000: Electroactive Polymer Actuators and Devices (EAPAD); 2000 Mar 6-9; Newport Beach, USA. Bellingham: SPIE. 2000. p. 51-64.

[30] Kastanis D, Tasis D, Papagelis K, Parthenios J, Tsakiroglou C, Galiotis C . Oxidized multi-walled carbon nanotube film fabrication and characterization. Adv Compos Lett. 2007; 16(6): 096369350701600606.

[31] Xiong SF, Zhang CC, Jin BJ, Guo BC . Liquid crystalline dielectric elastomer with thermo-and light-guided multimodal electrical actuations. Chin J Polym Sci. 2026; 44: 1457-1464.

[32] Pu J, Meng Y, Xie Z, Peng Z, Wu J, Shi Y, et al. A unimorph nanocomposite dielectric elastomer for large out-of-plane actuation. Sci Adv. 2022; 8(9): eabm6200.

[33] Li A, Cuvin P, Lee S, Gu J, Tugui C, Duduta M, et al. Data-driven long-term energy efficiency prediction of dielectric elastomer artificial muscles. Adv Funct Mater. 2024; 34(42): 2406710.

[34] Dong H, Chen Z, Zhuo J, Tang R, Peng J, Wang L, et al. Biomimetic gradient structured dielectric elastomer actuators for long-term large out-of-plane actuation. ACS Mater Lett. 2025; 7(5): 2002-2009.

[35] Zhang Y, Song Z, Yu W, Wang C, Dong C, Wu J, et al. Dielectric elastomer with covalently charged interpenetrated polyacrylate network for large actuation strain under low driving electric field. Chem Eng J. 2025; 520: 165877.

[36] Sun B, Ling Y, Wang K, Zhang Q, Li Y, Wang H, et al. All-in-one luminescent dielectric elastomer actuator driven by a single electrical stimulus with large out-of-plane actuation and fast response. Small. 2026; 22(19): e10346.

[37] Wang H, Tan MWM, Poh WC, Gao D, Wu W, Lee PS, et al. A highly stretchable, self-healable, transparent and solid-state poly(ionic liquid) filler for high-performance dielectric elastomer actuators. J Mater Chem A. 2023; 11(26): 14159-14168.

[38] Han Y, Zhang Y, Huang P, Shi B, Xie E, Xue C, et al. A dielectric elastomer containing bicomponent core-shell nanoparticles with enhanced electromechanical properties for flexible crawling robots. ACS Appl Polym Mater. 2024; 6(11): 6667-6678.

[39] Borayek R, Zhang P, Willy HJ, Zedan M, Zhu J, Ding J . Programmable, UV-printable dielectric elastomers actuate at low voltage without prestretch and supporting frames. ACS Appl Electron Mater. 2020; 2(12): 4042-4053.

[40] Lau GK, Heng KR, Ahmed AS, Shrestha M . Dielectric elastomer fingers for versatile grasping and nimble pinching. Appl Phys Lett. 2017; 110(18): 182906.

[41] Zhao J, Niu J, McCoul D, Leng J, Pei Q . A rotary joint for a flapping wing actuated by dielectric elastomers: Design and experiment. Meccanica. 2015; 50(11): 2815-2824.

[42] Zhao Q, Zou W, Luo Y, Xie T . Shape memory polymer network with thermally distinct elasticity and plasticity. Sci Adv. 2016; 2(1): e1501297.

[43] Fang Z, Zheng N, Zhao Q, Xie T . Healable, reconfigurable, reprocessable thermoset shape memory polymer with highly tunable topological rearrangement kinetics. ACS Appl Mater Interfaces. 2017; 9(27): 22077-22082.

[44] Yamawake K, Hayashi M . The role of tertiary amines as internal catalysts for disulfide exchange in covalent adaptable networks. Polym Chem. 2023; 14(6): 680-686.