Applied Mathematics and Mechanics >
Surface effects on buckling instability and large deformation of magneto-active soft beams
Received date: 2025-01-04
Revised date: 2025-01-19
Online published: 2025-04-07
Supported by
Project supported by the National Natural Science Foundation of China (Nos. 12202009 and 12002004)
Copyright
Magneto-active soft materials, composed of hard-magnetic particles embedded in polymeric matrices, have found widespread applications in soft robotics, active metamaterials, and shape-morphing structures across various length scales due to their ability to undergo reversible, untethered, and rapid deformation in response to magnetic actuation. At small scales, surface effects play a crucial role in the mechanical behavior of these soft materials. In this paper, we theoretically investigate the influence of surface effects on the buckling instability and large deformation of magneto-active soft beams under a uniform magnetic field. The theoretical model is derived according to the principle of minimum potential energy and numerically solved with the finite difference method. By employing the developed theoretical model, parametric studies are performed to explore how surface effects influence the buckling instability and large deformation of magneto-active soft cantilever beams with varying geometric parameters under different uniform magnetic fields. Our results reveal that the influence of surface effects on the mechanical behavior of magneto-active soft beams depends not only on the geometric parameters but also on the magnetic field strength. Specifically, when the magnetic field strength is relatively small, surface effects reduce the deformation of magneto-active soft beams, particularly for beams with smaller thicknesses and larger length-to-thickness ratios. However, when the magnetic field strength is sufficiently large, and the beam's deformation becomes saturated, surface effects have little influence on the deformation. This work uncovers the role of surface effects in the mechanical behavior of magneto-active soft materials, which could provide guidelines for the design and optimization of small-scale magnetic-active soft material-based applications.
Lu LU, Min LI, Shuang WANG . Surface effects on buckling instability and large deformation of magneto-active soft beams[J]. Applied Mathematics and Mechanics, 2025 , 46(4) : 617 -632 . DOI: 10.1007/s10483-025-3233-8
| [1] | KIM, Y. and ZHAO, X. Magnetic soft materials and robots. Chemical Reviews, 122(5), 5317–5364 (2022) |
| [2] | WANG, L., ZHENG, D., HARKER, P., PATEL, A. B., GUO, C. F., and ZHAO, X. Evolutionary design of magnetic soft continuum robots. Proceedings of the National Academy of Sciences, 118(21), e2021922118 (2021) |
| [3] | HU, W., LUM, G. Z., MASTRANGELI, M., and SITTI, M. Small-scale soft-bodied robot with multimodal locomotion. nature, 554(7690), 81–85 (2018) |
| [4] | ZHANG, Q., CHERKASOV, A. V., XIE, C., ARORA, N., and RUDYKH, S. Nonlinear elastic vector solitons in hard-magnetic soft mechanical metamaterials. International Journal of Solids and Structures, 280, 112396 (2023) |
| [5] | CHEN, T., PAULY, M., and REIS, P. M. A reprogrammable mechanical metamaterial with stable memory. nature, 589(7842), 386–390 (2021) |
| [6] | ALAPAN, Y., KARACAKOL, A. C., GUZELHAN, S. N., ISIK, I., and SITTI, M. Reprogrammable shape morphing of magnetic soft machines. Science Advances, 6(38), eabc6414 (2020) |
| [7] | CUI, J., HUANG, T. Y., LUO, Z., TESTA, P., GU, H., CHEN, X. Z., NELSON, B. J., and HEYDERMAN, L. J. Nanomagnetic encoding of shape-morphing micromachines. nature, 575(7781), 164–168 (2019) |
| [8] | LUM, G. Z., YE, Z., DONG, X., MARVI, H., ERIN, O., HU, W., and SITTI, M. Shape-programmable magnetic soft matter. Proceedings of the National Academy of Sciences, 113(41), E6007-E6015 (2016) |
| [9] | YAN, D., ABBASI, A., and REIS, P. M. A comprehensive framework for hard-magnetic beams: reduced-order theory, 3D simulations, and experiments. International Journal of Solids and Structures, 257, 111319 (2022) |
| [10] | WANG, L., KIM, Y., GUO, C. F., and ZHAO, X. Hard-magnetic elastica. Journal of the Mechanics and Physics of Solids, 142, 104045 (2020) |
| [11] | YANG, Y., LI, M., and XU, F. A 3D hard-magnetic rod model based on co-rotational formulations. Acta Mechanica Sinica, 38(9), 222085 (2022) |
| [12] | CHEN, W., YAN, Z., and WANG, L. On mechanics of functionally graded hard-magnetic soft beams. International Journal of Engineering Science, 157, 103391 (2020) |
| [13] | CHEN, W. and WANG, L. Theoretical modeling and exact solution for extreme bending deformation of hard-magnetic soft beams. Journal of Applied Mechanics, 87(4), 041002 (2020) |
| [14] | CHEN, W., WANG, G., LI, Y., WANG, L., and YIN, Z. The quaternion beam model for hard-magnetic flexible cantilevers. Applied Mathematics and Mechanics (English Edition), 44(5), 787–808 (2023) https://doi.org/10.1007/s10483-023-2983-8 |
| [15] | TAN, K., CHEN, L., YANG, S., and DENG, Q. Dynamic snap-through instability and damped oscillation of a flat arch of hard magneto-active elastomers. International Journal of Mechanical Sciences, 230, 107523 (2022) |
| [16] | DEHROUYEH-SEMNANI, A. M. On bifurcation behavior of hard magnetic soft cantilevers. International Journal of Non-Linear Mechanics, 134, 103746 (2021) |
| [17] | XING, Z. and YONG, H. Numerical study on the instabilities of hard-magnetic soft materials with viscoelastic effects. Mechanics of Materials, 179, 104602 (2023) |
| [18] | PEZZULLA, M., YAN, D., and REIS, P. M. A geometrically exact model for thin magneto-elastic shells. Journal of the Mechanics and Physics of Solids, 166, 104916 (2022) |
| [19] | YAN, D., AYMON, B. F., and REIS, P. M. A reduced-order, rotation-based model for thin hard-magnetic plates. Journal of the Mechanics and Physics of Solids, 170, 105095 (2023) |
| [20] | MILLER, R. E. and SHENOY, V. B. Size-dependent elastic properties of nanosized structural elements. Nanotechnology, 11(3), 139 (2000) |
| [21] | JING, G., DUAN, H. L., SUN, X., ZHANG, Z., XU, J., LI, Y., WANG, J., and YU, D. Surface effects on elastic properties of silver nanowires: contact atomic-force microscopy. Physical Review B—Condensed Matter and Materials Physics, 73(23), 235409 (2006) |
| [22] | STYLE, R. W., HYLAND, C., BOLTYANSKIY, R., WETTLAUFER, J. S., and DUFRESNE, E. R. Surface tension and contact with soft elastic solids. Nature Communications, 4(1), 2728 (2013) |
| [23] | MORA, S., PHOU, T., FROMENTAL, J. M., PISMEN, L. M., and POMEAU, Y. Capillarity driven instability of a soft solid. Physical Review Letters, 105(21), 214301 (2010) |
| [24] | GURTIN, M. E. and MURDOCH, A. I. A continuum theory of elastic material surfaces. Archive for Rational Mechanics and Analysis, 57, 291–323 (1975) |
| [25] | GURTIN, M. E. and MURDOCH, A. I. Surface stress in solids. International Journal of Solids and Structures, 14(6), 431–440 (1978) |
| [26] | WANG, S., LI, X., YI, X., and DUAN, H. Morphological changes of nanofiber cross-sections due to surface tension. Extreme Mechanics Letters, 44, 101211 (2021) |
| [27] | LU, P., HE, L., LEE, H., and LU, C. Thin plate theory including surface effects. International Journal of Solids and Structures, 43(16), 4631–4647 (2006) |
| [28] | LI, M., ZHANG, H. X., ZHAO, Z. L., and FENG, X. Q. Surface effects on cylindrical indentation of a soft layer on a rigid substrate. Acta Mechanica Sinica, 36, 422–429 (2020) |
| [29] | LI, M., YAN, Y., XU, S., WANG, G., WU, J., and FENG, X. Q. Surface effect on the necking of hyperelastic materials. Current Applied Physics, 38, 91–98 (2022) |
| [30] | WANG, G. F. and FENG, X. Q. Effects of surface elasticity and residual surface tension on the natural frequency of microbeams. Applied Physics Letters, 90(23), 231904 (2007) |
| [31] | WANG, G. F. and FENG, X. Q. Surface effects on buckling of nanowires under uniaxial compression. Applied Physics Letters, 94(14), 141913 (2009) |
| [32] | HE, J. and LILLEY, C. M. Surface effect on the elastic behavior of static bending nanowires. Nano Letters, 8(7), 1798–1802 (2008) |
| [33] | WANG, Q., LIU, M., WANG, Z., CHEN, C., and WU, J. Large deformation and instability of soft hollow cylinder with surface effects. Journal of Applied Mechanics, 88(4), 041010 (2021) |
| [34] | ZHANG, L., ZHAO, J., NIE, G., and LIU, J. Propagation of Rayleigh-type surface waves in a layered piezoelectric nanostructure with surface effects. Applied Mathematics and Mechanics (English Edition), 43(3), 327–340 (2022) https://doi.org/10.1007/s10483-022-2824-7 |
| [35] | FENG, X., KE, L., and GAO, Y. Love wave propagation in one-dimensional piezoelectric quasicrystal multilayered nanoplates with surface effects. Applied Mathematics and Mechanics (English Edition), 45(4), 619–632 (2024) https://doi.org/10.1007/s10483-024-3104-9 |
| [36] | DUAN, H., WANG, J., and KARIHALOO, B. L. Theory of elasticity at the nanoscale. Advances in Applied Mechanics, 42, 1–68 (2009) |
| [37] | CHEN, G. Y., THUNDAT, T., WACHTER, E., and WARMACK, R. Adsorption-induced surface stress and its effects on resonance frequency of microcantilevers. Journal of Applied Physics, 77(8), 3618–3622 (1995) |
| [38] | LU, P., SHEN, F., SHEA, S. O., LEE, K., and NG, T. Analysis of surface effects on mechanical properties of microcantilevers. Materials Physics and Mechanics, 4, 51–55 (2001) |
| [39] | XU, Q., JENSEN, K. E., BOLTYANSKIY, R., SARFATI, R., STYLE, R. W., and DUFRESNE, E. R. Direct measurement of strain-dependent solid surface stress. Nature Communications, 8(1), 555 (2017) |
| [40] | SORIANO-JEREZ, Y., GOURLAOUEN, E., ZERIOUH, O., CERóN-GARCíA, M. D., ARRABAL-CAMPOS, F. M., RUIZ-MARTíNEZ, C., FERNáNDEZ, I., GALLARDO-RODRíGUEZ, J. J., GARCíA-CAMACHO, F., and MOLINA-GRIMA, E. Role of dynamic surface tension of silicone polyether surfactant-based silicone coatings on protein adsorption: an insight on the ‘ambiguous’ interfacial properties of fouling release coatings. Progress in Organic Coatings, 186, 108079 (2024) |
| [41] | SCHULTZ, C. W., NG, C. L., and YU, H. Z. Superhydrophobic polydimethylsiloxane via nanocontact molding of solvent crystallized polycarbonate: optimized fabrication, mechanistic investigation, and application potential. ACS Applied Materials & Interfaces, 12(2), 3161–3170 (2019) |
| [42] | LI, S., ZHANG, J., HE, J., LIU, W., WANG, Y., HUANG, Z., PANG, H., and CHEN, Y. Functional PDMS elastomers: bulk composites, surface engineering, and precision fabrication. Advanced Science, 10(34), 2304506 (2023) |
/
| 〈 |
|
〉 |
Email Alert
RSS