Skip to main content
SpringerLink
Log in

Peeling of Magneto-responsive Beams with Large Deformation Mediated by the Parallel Magnetic Field

  • Published:
Acta Mechanica Solida Sinica Aims and scope Submit manuscript

Abstract

Elasto-capillarity phenomena are prevalent in various industrial fields such as mechanical engineering, material science, aerospace, soft robotics, and biomedicine. In this study, two typical peeling processes of slender beams driven by the parallel magnetic field are investigated based on experimental and theoretical analysis. The first is the adhesion of two parallel beams, and the second is the self-folding of a long beam. In these two cases, the energy variation method on the elastica is used, and then, the governing equations and transversality boundary conditions are derived. It is shown that the analytical solutions are in excellent agreement with the experimental data. The effects of magnetic induction intensity, distance, and surface tension on the deflection curve and peeling length of the elastica are fully discussed. The results are instrumental in accurately regulating elasto-capillarity in structures and provide insights for the engineering design of programmable microstructures on surfaces, microsensors, and bionic robots.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Availability of Data and Materials

The datasets generated or analyzed during this study are available from the corresponding author upon reasonable request.

References

  1. Ji Y, Luan C, Yao X, Fu J, He Y. Recent progress in 3D printing of smart structures: classification, challenges, and trends. Adv Intell Syst. 2021;3(12):2000271.

    Article  Google Scholar 

  2. Kornbluh R, Pelrine R, Pei QB, Heydt R, Stanford S, Oh SJ, Eckerle J. Electroelastomers: applications of dielectric elastomer transducers for actuation, generation and smart structures. Smart structures and materials 2002: industrial and commercial applications of smart structures technologies. Adv Intell Syst. 2002;3: 4698.

    Google Scholar 

  3. Lu L, Guo P, Pan Y. Magnetic-field-assisted projection stereolithography for three-dimensional printing of smart structures. J Manuf Sci Eng Trans ASME. 2017;139(7): 071008.

    Article  Google Scholar 

  4. Ozer MB, Royston TJ. Optimal passive and hybrid control of vibration and sound radiation from linear and nonlinear PZT-based smart structures. In: Proceedings of SPIE smart structures and materials conference on modeling, signal processing and control. 2002, p. 4693.

  5. Kang J, Liu S, Wang C. Controllable bistable smart composite structures driven by liquid crystal elastomer. Smart Mater Struct. 2022;31:01503.

    Article  Google Scholar 

  6. Xu D, Banerjee S, Wang Y, Huang S, Cheng X. Temperature and loading effects of embedded smart piezoelectric sensor for health monitoring of concrete structures. Constr Build Mater. 2015;76:187–93.

    Article  Google Scholar 

  7. Ebrahimi N, Bi C, Cappelleri DJ, Ciuti G, Conn AT, Faivre D, et al. Magnetic actuation methods in bio/soft robotics. Adv Funct Mater. 2020;31(11):2005137.

    Article  Google Scholar 

  8. Dorfmann A, Ogden RW. Magnetoelastic modelling of elastomers. Eur J Mech A Solids. 2003;22:497–507.

    Article  MathSciNet  Google Scholar 

  9. Dorfmann A, Ogden RW. Nonlinear magnetoelastic deformations of elastomers. Acta Mech. 2004;167:13–28.

    Article  Google Scholar 

  10. Zhao R, Kim Y, Chester SA, Sharma P, Zhao X. Mechanics of hard-magnetic soft materials. J Mech Phys Solids. 2019;124:244–63.

    Article  MathSciNet  Google Scholar 

  11. Mukherjee D, Rambausek M, Danas K. An explicit dissipative model for isotropic hard magnetorheological elastomers. J Mech Phys Solids. 2021;151: 104361.

    Article  MathSciNet  Google Scholar 

  12. Lum GZ, Ye Z, Dong X, Marvi H, Erin O, Hu W, Sitti M. Shape-programmable magnetic soft matter. PNAS. 2016;113(41):E6007.

    Article  Google Scholar 

  13. Barreto DD, Saxena S, Kumar A. A magnetoelastic theory for Kirchhoff rods having uniformly distributed paramagnetic inclusions and its buckling. Int J Solids Struct. 2021;234–235: 111147.

    Google Scholar 

  14. Sano TG, Pezzulla M, Reis PM. A Kirchhoff-like theory for hard magnetic rods under geometrically nonlinear deformation in three dimensions. J Mech Phys Solids. 2022;160: 104739.

    Article  MathSciNet  Google Scholar 

  15. Cheng Y, Li S, Liu J. Abnormal deformation and negative pressure of a hard magnetic disc under the action of a magnet. Sens Actuators A Phys. 2021;332: 113065.

    Article  Google Scholar 

  16. Kim Y, Zhao X. Magnetic soft materials and robots. Chem Rev. 2022;122:5317–64.

    Article  Google Scholar 

  17. Zhao YP, Wang LS, Yu TX. Mechanics of adhesion in MEMS a review. J Adhes Sci Technol. 2003;17(4):519–46.

    Article  Google Scholar 

  18. Bico J, Roman B, Moulin L, Boudaoud A. Elastocapillary coalescence in wet hair. Nature. 2004;432(9):690.

    Article  Google Scholar 

  19. Liu JL, Feng XQ, Xia R, Zhao HP. Hierarchical capillary adhesion of microcantilevers or hairs. J Phys D Appl Phys. 2007;40:5564–70.

    Article  Google Scholar 

  20. Begley MR, Collino RR, Israelachvili JN, McMeeking RM. Peeling of a tape with large deformations and frictional sliding. J Mech Phys Solids. 2013;61:1265–79.

    Article  MathSciNet  Google Scholar 

  21. Chen H, Feng X, Huang Y, Huang Y, Rogers JA. Experiments and viscoelastic analysis of peel test with patterned strips for applications to transfer printing. J Mech Phys Solids. 2013;61:1737–52.

    Article  Google Scholar 

  22. Gong Y, Li S, Liu J. Peeling of an extensible soft microbeam to solid: large deformation analysis. Int J Appl Mech. 2018;10(6): 1850065.

    Article  Google Scholar 

  23. He L, Lou J, Kitipornchai S, Yang J, Du J. Peeling mechanics of hyperelastic beams: bending effect. Int J Solids Struct. 2019;167:184–91.

    Article  Google Scholar 

  24. Liprandi D, Bosia F, Pugno NM. A theoretical–numerical model for the peeling of elastic membranes. J Mech Phys Solids. 2020;136: 103733.

    Article  MathSciNet  Google Scholar 

  25. Shen CS, Wang HF, Du CL. Peeling of a film from a flexible cantilever substrate. Mech Res Commun. 2022;119: 103833.

    Article  Google Scholar 

  26. Yin H, Peng Z, Yao Y, Chen S, Gao H. A general solution to the maximum detachment force in thin film peeling. Int J Solids Struct. 2022;242: 111546.

    Article  Google Scholar 

  27. Ogden L. Nonlinear theory of electroelastic and magnetoelastic interactions. Berlin: Springer; 2014.

    Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (12372027 and 12211530028), the Natural Science Foundation of Shandong Province (ZR202011050038), and Special Funds for the Basic Scientific Research Expenses of Central Government Universities (2472022X03006A).

Author information

Authors and Affiliations

  1. College of Pipeline and Civil Engineering, China University of Petroleum (East China), Qingdao, 266580, China

    Gongqi Cao, Zhangna Xue, Shiyang Liu, Yuchen Jin & Jianlin Liu

Authors
  1. Gongqi Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhangna Xue
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shiyang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yuchen Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jianlin Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

GC contributed to writing—original draft, methodology, and visualization; ZX worked in supervision and software; SL helped in validation and investigation; YJ helped in conceptualization and supervision; and JL contributed to writing—review and editing, validation, and methodology.

Corresponding author

Correspondence to Jianlin Liu.

Ethics declarations

Conflict of Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Consent for Publication

All authors have approved the final manuscript and its submission to the journal.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cao, G., Xue, Z., Liu, S. et al. Peeling of Magneto-responsive Beams with Large Deformation Mediated by the Parallel Magnetic Field. Acta Mech. Solida Sin. (2024). https://doi.org/10.1007/s10338-024-00480-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10338-024-00480-w

Keywords

Search

Navigation