Science China Technological Sciences

, Volume 61, Issue 7, pp 959–964 | Cite as

Method towards optimal design of dielectric elastomer actuated soft machines

  • Fan Liu
  • WenJie Sun
  • Xuan Zhao
  • ChengHai Li
  • JinXiong ZhouEmail author


Soft machines are combinations of hard and soft active materials, thus the coupling and interaction between soft and hard components dictate the performance of soft machines. Structural optimization has been intensively used for design of conventional hard machines, while, to our best knowledge, few attempts have been made towards optimal design of soft machines. Here, we describe the sizing optimization problem of a dielectric elastomer (DE) actuated mechanical amplifier, and achieve the optimal design through combination of a commercial finite element method (FEM) software and an optimization automation software. We then design, fabricate and demonstrate a locomotive soft machine driven by DE actuator with amplified displacement output. The methodology and results present here open the door towards optimal designs of active materials based soft machines.


soft machine dielectric elastomer structural optimization finite element method mechanical amplifier 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Rus D, Tolley M T. Design, fabrication and control of soft robots. Nature, 2015, 521: 467–475CrossRefGoogle Scholar
  2. 2.
    Kim S, Laschi C, Trimmer B. Soft robotics: A bioinspired evolution in robotics. Trends Biotech, 2013, 31: 287–294CrossRefGoogle Scholar
  3. 3.
    Majidi C. Soft robotics: A perspective—Current trends and prospects for the future. Soft Robot, 2014, 1: 5–11CrossRefGoogle Scholar
  4. 4.
    McEvoy M A, Correll N. Materials that couple sensing, actuation, computation, and communication. Science, 2015, 347: 1261689CrossRefGoogle Scholar
  5. 5.
    Laschi C, Mazzolai B, Cianchetti M. Soft robotics: Technologies and systems pushing the boundaries of robot abilities. Sci Robot, 2016, 1: eaah3690CrossRefGoogle Scholar
  6. 6.
    Ilievski F, Mazzeo A D, Shepherd R F, et al. Soft robotics for chemists. Angew Chem Int Ed, 2011, 50: 1890–1895CrossRefGoogle Scholar
  7. 7.
    Shepherd R F, Ilievski F, Choi W, et al. Multigait soft robot. Proc Natl Acad Sci USA, 2011, 108: 20400–20403CrossRefGoogle Scholar
  8. 8.
    Bartlett N W, Tolley M T, Overvelde J T B, et al. A 3D-printed, functionally graded soft robot powered by combustion. Science, 2015, 349: 161–165CrossRefGoogle Scholar
  9. 9.
    Wehner M, Truby R L, Fitzgerald D J, et al. An integrated design and fabrication strategy for entirely soft, autonomous robots. Nature, 2016, 536: 451–455CrossRefGoogle Scholar
  10. 10.
    Felton S, Tolley M, Demaine E, et al. A method for building selffolding machines. Science, 2014, 345: 644–646CrossRefGoogle Scholar
  11. 11.
    Pelrine R, Kornbluh R, Pei Q, et al. High-speed electrically actuated elastomers with strain greater than 100%. Science, 2000, 287: 836–839CrossRefGoogle Scholar
  12. 12.
    Carpi F, Bauer S, De Rossi D. Stretching dielectric elastomer performance. Science, 2010, 330: 1759–1761CrossRefGoogle Scholar
  13. 13.
    Brochu P, Pei Q. Advances in dielectric elastomers for actuators and artificial muscles. Macromol Rapid Commun, 2010, 31: 10–36CrossRefGoogle Scholar
  14. 14.
    Anderson I A, Gisby T A, McKay T G, et al. Multi-functional dielectric elastomer artificial muscles for soft and smart machines. J Appl Phys, 2012, 112: 041101CrossRefGoogle Scholar
  15. 15.
    Keplinger C, Sun J Y, Foo C C, et al. Stretchable, transparent, ionic conductors. Science, 2013, 341: 984–987CrossRefGoogle Scholar
  16. 16.
    Bauer S, Bauer-Gogonea S, Graz I, et al. A soft future: From robots and sensor skin to energy harvesters. Adv Mater, 2014, 26: 149–162CrossRefGoogle Scholar
  17. 17.
    Stokes A A, Shepherd R F, Morin S A, et al. A hybrid combining hard and soft robots. Soft Robot, 2014, 1: 70–74CrossRefGoogle Scholar
  18. 18.
    Suo Z G. Mechanics of stretchable electronics and soft machines. MRS Bull, 2012, 37: 218–225CrossRefGoogle Scholar
  19. 19.
    Kofod G, Wirges W, Paajanen M, et al. Energy minimization for selforganized structure formation and actuation. Appl Phys Lett, 2007, 90: 081916CrossRefGoogle Scholar
  20. 20.
    Liu F, Zhang Y, Zhang L, et al. Analysis, experiment, and correlation of a petal-shaped actuator based on dielectric elastomer minimumenergy structures. Appl Phys A, 2016, 122: 323CrossRefGoogle Scholar
  21. 21.
    Bendsøe M P, Sigmund O. Design with anisotropic materials. In: Topology Optimization. Berlin, Heidelberg: Springer, 2004. 159–220CrossRefGoogle Scholar
  22. 22.
    Haftka R T, Gürdal Z. Elements of Structural Optimization. Boston: Springer, 1992CrossRefzbMATHGoogle Scholar
  23. 23.
    Lau G K, Lim H T, Teo J Y, et al. Lightweight mechanical amplifiers for rolled dielectric elastomer actuators and their integration with bioinspired wing flappers. Smart Mater Struct, 2014, 23: 025021CrossRefGoogle Scholar
  24. 24.
    Zhao X H, Suo Z G. Method to analyze programmable deformation of dielectric elastomer layers. Appl Phys Lett, 2008, 93: 251902CrossRefGoogle Scholar
  25. 25.
    Suo Z G, Zhao X H, Greene W H. A nonlinear field theory of deformable dielectrics. J Mech Phys Solids, 2008, 56: 467–486MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Zhao X H, Hong W, Suo Z G. Electromechanical hysteresis and coexistent states in dielectric elastomers. Phys Rev B, 2007, 76: 134113CrossRefGoogle Scholar
  27. 27.
    Zhou J X, Hong W, Zhao X H, et al. Propagation of instability in dielectric elastomers. Int J Solids Struct, 2008, 45: 3739–3750CrossRefzbMATHGoogle Scholar
  28. 28.
    Sun W J, Liu F, Ma Z Q, et al. Soft electroactive actuators and hard ratchet-wheels enable unidirectional locomotion of hybrid machine. AIP Adv, 2017, 7: 015308CrossRefGoogle Scholar
  29. 29.
    Sun W J, Liu F, Ma Z Q, et al. Soft mobile robots driven by foldable dielectric elastomer actuators. J Appl Phys, 2016, 120: 084901CrossRefGoogle Scholar
  30. 30.
    Bortot E. Performance optimization of dielectric elastomer generators. Dissertation of Doctoral Degree. Trento: University of Trento, 2015Google Scholar
  31. 31.
    Moretti G, Fontana M, Vertechy R. Model-based design and optimization of a dielectric elastomer power take-off for oscillating wave surge energy converters. Meccanica, 2015, 50: 2797–2813MathSciNetCrossRefGoogle Scholar
  32. 32.
    Price A D, Ask A. Integrated Design Optimization of Dielectric Elastomer Actuators in High-Performance Switchgear. In: Proceedings of the ASME 2014 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. Newport, Rhode Island, 2014. SMASIS2014-7574Google Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Fan Liu
    • 1
  • WenJie Sun
    • 2
  • Xuan Zhao
    • 3
  • ChengHai Li
    • 1
  • JinXiong Zhou
    • 1
    Email author
  1. 1.State Key Laboratory for Strength and Vibration of Mechanical Structures and Shaanxi Engineering Laboratory for Vibration Control of Aerospace StructuresXi’an Jiaotong UniversityXi’anChina
  2. 2.School of Mechanical and Precision Instrument EngineeringXi’an University of TechnologyXi’anChina
  3. 3.School of Aerospace EngineeringTsinghua UniversityBeijingChina

Personalised recommendations