Skip to main content
SpringerLink
Log in

Transient thermo-mechanical analysis for bimorph soft robot based on thermally responsive liquid crystal elastomers

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

Thermally responsive liquid crystal elastomers (LCEs) hold great promise in applications of soft robots and actuators because of the induced size and shape change with temperature. Experiments have successfully demonstrated that the LCE based bimorphs can be effective soft robots once integrated with soft sensors and thermal actuators. Here, we present an analytical transient thermo-mechanical model for a bimorph structure based soft robot, which consists of a strip of LCE and a thermal inert polymer actuated by an ultrathin stretchable open-mesh shaped heater to mimic the unique locomotion behaviors of an inchworm. The coupled mechanical and thermal analysis based on the thermo-mechanical theory is carried out to underpin the transient bending behavior, and a systematic understanding is therefore achieved. The key analytical results reveal that the thickness and the modulus ratio of the LCE and the inert polymer layer dominate the transient bending deformation. The analytical results will not only render fundamental understanding of the actuation of bimorph structures, but also facilitate the rational design of soft robotics.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. WEHNER, M., TRUBY, R. L., FITZGERALD, D. J., MOSADEGH, B., WHITESIDES, G. M., LEWIS, J. A., and WOOD, R. J. An integrated design and fabrication strategy for entirely soft, autonomous robots. nature, 536(7617), 451–455 (2016)

    Article  Google Scholar 

  2. BARTLETT, N. W., TOLLEY, M. T., OVERVELDE, J. T. B., WEAVER, J. C., MOSADEGH, B., BERTOLDI, K., WHITESIDES, G. M., and WOOD, R. J. A 3D-printed, functionally graded soft robot powered by combustion. Science, 349(6244), 161–165 (2015)

    Article  Google Scholar 

  3. GISBY, T. A., O’BRIEN, B. M., and ANDERSON, I. A. Self sensing feedback for dielectric elastomer actuators. Applied Physics Letters, 102, 193703 (2013)

    Article  Google Scholar 

  4. LI, T. F., LI, G. R., LIANG, Y. M., CHENG, T. Y., DAI, J., YANG, X. X., LIU, B. Y., ZENG, Z. D., HUANG, Z. L., LUO, Y. W., XIE, T., and YANG, W. Fast-moving soft electronic fish. Science Advances, 3, e1602045 (2017)

    Article  Google Scholar 

  5. KIM, D., KIM, K. J., TAK, Y., PUGAL, D., and PARK, I. Self-oscillating electroactive polymer actuator. Applied Physics Letters, 90, 184104 (2007)

    Article  Google Scholar 

  6. REN, K. L., BORTOLIN, R. S., and ZHANG, Q. M. An investigation of a thermally steerable electroactive polymer/shape memory polymer hybrid actuator. Applied Physics Letters, 108, 062901 (2016)

    Article  Google Scholar 

  7. LASCHI, C., CIANCHETTI, M., MAZZOLAI, B., MARGHERI, L., FOLLADOR, M., and DARIO, P. Soft robot arm inspired by the octopus. Advanced Robotics, 26, 709–727 (2012)

    Article  Google Scholar 

  8. MENG, H. and LI, G. A review of stimuli-responsive shape memory polymer composites. Polymer, 54(9), 2199–2221 (2013)

    Article  Google Scholar 

  9. PALLEAU, E., MORALES, D., DICKEY, M. D., and VELEY, O. D. Reversible patterning and actuation of hydrogels by electrically assisted ionoprinting. Nature Communications, 4(4), 2257 (2013)

    Article  Google Scholar 

  10. MAEDA, S., KATO, T., KOGURE, H., and HOSOYA, N. Rapid response of thermo-sensitive hydrogels with porous structures. Applied Physics Letters, 106, 171909 (2015)

    Article  Google Scholar 

  11. WANG, C. J., SIM, K., CHEN, J., KIM, H., RAO, Z., LI, Y. H., CHEN, W. Q., SONG, J. Z., VERDUZCO, R., and YU, C. J. Soft ultrathin electronics innervated adaptive fully soft robots. Advanced Materials, 30, 1706695 (2018)

    Article  Google Scholar 

  12. LI, M. E., LV, S., and ZHOU, J. X. Photo-thermo-mechanically actuated bending and snapping kinetics of liquid crystal elastomer cantilever. Smart Materials and Structures, 23, 125012 (2014)

    Article  Google Scholar 

  13. AN, N., LI, M. E., and ZHOU, J. X. Instability of liquid crystal elastomer. Smart Materials and Structures, 25, 015016 (2016)

    Article  Google Scholar 

  14. YANG, T. Z., BAI, X., GAO, D. L., WU, L. Z., LI, B. W., THONG, J. T. L., and QIU, C. W. Invisible sensors: simultaneous sensing and camouflaging in multiphysical fields. Advanced Materials, 27(47), 7752–7758 (2015)

    Article  Google Scholar 

  15. BEHL, M., KRATZ, K., NEOCHEL, U., SAUTER, T., and LENDLEIN, A. Temperature-memory polymer actuators. Proceedings of the National Academy of Sciences of the United States of America, 110(31), 12555–12559 (2013)

    Article  Google Scholar 

  16. WHITE, T. J. and BROER, D. J. Programmable and adaptive mechanics with liquid crystal polymer networks and elastomers. Nature Materials, 14(11), 1087–1098 (2015)

    Article  Google Scholar 

  17. HUANG, Y. A., DING, Y. J., BIAN, J., SU, Y. W., ZHOU, J., DUAN, Y. Q., and YIN, Z. P. Hyper-stretchable self-powered sensors based on electrohydrodynamically printed, self-similar piezoelectric nano/microfibers. Nano Energy, 40, 432–439 (2017)

    Article  Google Scholar 

  18. ZHANG, Y. H., FU, H. R., SU, Y. W., XU, S., CHENG, H. Y., FAN, J. A., HWANG, K. C., ROGERS, J. A., and HUANG, Y. G. Mechanics of ultra-stretchable self-similar serpentine interconnects. Acta Materialia, 61, 7816–7827 (2013)

    Article  Google Scholar 

  19. ZHANG, Y. H., HUANG, Y. G., and ROGERS, J. A. Mechanics of stretchable batteries and supercapacitors. Current Opinion in Solid State and Materials Science, 19(3), 190–199 (2015)

    Article  Google Scholar 

  20. MA, Y. J., FENG, X., ROGERS, J. A., HUANG, Y. G., and ZHANG, Y. H. Design and ap-plication of ‘J-shaped’ stress-strain behavior in stretchable electronics: a review. Lab on a Chip, 17(10), 1689–1704 (2017)

    Article  Google Scholar 

  21. CHEN, H., ZHU, F., JANG, K. I., FENG, X., ROGERS, J. A., ZHANG, Y. H., HUANG, Y. G., and MA, Y. J. The equivalent medium of cellular substrate under large stretching, with applications to stretchable electronics. Journal of the Mechanics and Physics of Solids, 120, 199–207 (2018)

    Article  MathSciNet  Google Scholar 

  22. LIU, Z. and GAO, J. Deformation-pattern-based digital speckle correlation for coefficient of thermal expansion evaluation of film. Optics Express, 19, 17469–17479 (2011)

    Article  Google Scholar 

  23. SUN, Y. X., MA, J. X., LIU, S. B., and YANG, J. L. Analytical solution of transient heat conduction in a bi-layered circular plate irradiated by laser pulse. Canadian Journal of Physics, 95(4), 322–330 (2017)

    Article  Google Scholar 

  24. CHEN, T. M. and CHEN, C. C. Numerical solution for the hyperbolic heat conduction problems in the radial-spherical coordinate system using a hybrid Green’s function method. International Journal of Thermal Sciences, 49(7), 1193–1196 (2010)

    Article  Google Scholar 

  25. NILISHKOV, J. P. Curvature estimation for multilayer hinged structures with initial strains. Journal of Applied Physics, 94(8), 5333–5336 (2003)

    Article  Google Scholar 

  26. CUI, Y., WANG, C. J., SIM, K., CHEN, J., LI, Y. H., XING, Y. F., YU, C. J., and SONG, J. Z. A simple analytical thermo-mechanical model for liquid crystal elastomer bilayer structures. AIP Advances, 8, 025215 (2018)

    Article  Google Scholar 

  27. YU, C. J., DUAN, Z., YUAN, P. X., LI, Y. H., SU, Y. W., ZHANG, X., PAN, Y. P., DAI, L. L., NUZZO, R. G., HUANG, Y. G., JIANG, H. Q., and ROGERS, J. A. Electronically programmable, reversible shape change in two-and three-dimensional hydrogel structures. Advanced Materials, 25(11), 1541–1546 (2013)

    Article  Google Scholar 

  28. TORRAS, N., ZINOVIEV, K. E., CAMARGO, C. J., CAMPO, E. M., CAMPANELLA, H., ESTEVE, J., MARSGALL, J. E., TERENTJEV, E. M., OMASTOVA, M., and KRUPA, I. Tactile device based on opto-mechanical actuation of liquid crystal elastomers. Sensors and Actuators A: Physical, 208, 104–112 (2014)

    Article  Google Scholar 

  29. DuPont. Kapton® HN general-purpose polyimide film (2018) https://www.dupont.com/products/kapton-hn.html

Download references

Author information

Authors and Affiliations

  1. Institute of Solid Mechanics, Beihang University, Beijing, 100191, China

    Yun Cui, Yafei Yin & Yuhang Li

  2. Department of Engineering Mechanics, Soft Matter Research Center, Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou, 310027, China

    Chengjun Wang & Jizhou Song

  3. Materials Science and Engineering Program, University of Houston, Houston, TX, 77204, USA

    K. Sim

  4. State Key Laboratory of Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

    Yuhang Li

  5. Department of Mechanical Engineering, University of Houston, Houston, TX, 77204, USA

    Cunjiang Yu

  6. Department of Electrical and Computer Engineering, University of Houston, Houston, TX, 77204, USA

    Cunjiang Yu

  7. Department of Biomedical Engineering, Texas Center for Superconductivity, University of Houston, Houston, TX, 77204, USA

    Cunjiang Yu

Authors
  1. Yun Cui
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yafei Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chengjun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. K. Sim
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yuhang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Cunjiang Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Jizhou Song
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Yuhang Li, Cunjiang Yu or Jizhou Song.

Additional information

Project supported by the National Basic Research Program (No. 2015CB351901), the National Nat- ural Science Foundation of China (Nos. 11372272, 11622221, 11621062, 11502009, and 11772030), the Doctoral New Investigator Grant from American Chemical Society Petroleum Research Fund of the National Science Foundation (Nos. 1509763 and 1554499), the Opening Fund of State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University (No. SV2018-KF-13), and the Fundamental Research Funds for the Central Universities (No. 2017XZZX002-11)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cui, Y., Yin, Y., Wang, C. et al. Transient thermo-mechanical analysis for bimorph soft robot based on thermally responsive liquid crystal elastomers. Appl. Math. Mech.-Engl. Ed. 40, 943–952 (2019). https://doi.org/10.1007/s10483-019-2495-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-019-2495-8

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation