Surface effects on buckling instability and large deformation of magneto-active soft beams

doi:10.1007/s10483-025-3233-8

Abstract

Abstract:

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.

Key words: magneto-active soft material, surface effect, buckling instability, large deformation

2010 MSC Number:

O342

Lu LU, Min LI, Shuang WANG. Surface effects on buckling instability and large deformation of magneto-active soft beams. Applied Mathematics and Mechanics (English Edition), 2025, 46(4): 617-632.

TrendMD

Figures/Tables 9

Fig. 1

Table 1

Comparison of the normalized tip deflections (δy/L) of a magneto-active cantilever beam under a uniform magnetic field"

$α = π / 2$			$α = π$
$\| M \| \| B a \| / G$	Ref. [13]	Present	$\| M \| \| B a \| / G$	Ref. [13]	Present
$0.752 9 × 10 − 3$	0.362 9	0.362 6	$1.881 × 10 − 3$	0.710 0	0.710 8
$2.267 0 × 10 − 3$	0.659 5	0.661 3	$2.620 × 10 − 3$	0.806 0	0.805 6
$5.621 0 × 10 − 3$	0.805 8	0.804 3	$3.714 × 10 − 3$	0.752 1	0.752 0
$9.400 0 × 10 − 3$	0.854 2	0.851 8	$5.619 × 10 − 3$	0.639 8	0.639 7
$15.040 0 × 10 − 3$	0.887 7	0.883 2	$9.381 × 10 − 3$	0.502 8	0.502 9
$18.820 0 × 10 − 3$	0.901 4	0.895 7	$15.100 × 10 − 3$	0.397 3	0.397 5

Table 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

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