An analytical model for peeling behaviors at the particle-polymer interface in hard-magnetic soft materials

doi:10.1007/s10483-025-3293-8

摘要/Abstract

Abstract:

Hard-magnetic soft materials exhibit significant shape morphing capabilities under non-contact magnetic actuation, yet their particulate composition tends to compromise material toughness. To quantify particle-matrix interactions, we present a mechanics model describing the energy functional of planar magnetic composites. Through the Fourier series, the analytical solutions for stress distribution and interfacial peeling length of a single particle-polymer unit are derived with the Rayleigh-Ritz method under uniaxial tension. The calculated results of stress fields without the magnetic field agree well with those of the finite element method. The effects of external magnetic field strength and particle content on the stress distribution and peeling length are fully explored, and the enhanced analytical outcomes are obtained through numerical prediction. These insights can be used to validate the reliability of engineering designs, including adaptive structures, micro-electro-mechanical sensors, and soft robotic systems.

Key words: hard-magnetic soft material, Rayleigh-Ritz method, particle content, peeling length, particle-polymer interface

中图分类号:

O343.1

. [J]. Applied Mathematics and Mechanics (English Edition), 2025, 46(9): 1649-1662.

Gongqi CAO, Yuchen JIN, Jiguang ZHANG, Zhangna XUE, Jianlin LIU. An analytical model for peeling behaviors at the particle-polymer interface in hard-magnetic soft materials[J]. Applied Mathematics and Mechanics (English Edition), 2025, 46(9): 1649-1662.

图/表 12

参考文献 32

[1]	JI, Y., LUAN, C., YAO, X., FU, J., and HE, Y. Recent progress in 3D printing of smart structures: classification, challenges, and trends. Advanced Intelligent Systems, 3(12), 2170081 (2021)
[2]	KORNBLUH, R., PELRINE, R., PEI, Q., HEYDT, R., STANFORD, S., OH, S., and 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, SPIE, San Diego (2002)
[3]	ZHOU, P. Coupling effects between elastic and electromagnetic fields from the perspective of conservation of energy. Applied Mathematics and Mechanics (English Edition), 42(11), 1649–1662 (2021) https://doi.org/10.1007/s10483-021-2792-9
[4]	OZER, M. B. and ROYSTON, T. J. Optimal passive and hybrid control of vibration and sound radiation from linear and nonlinear PZT-based smart structures. Smart Structures and Materials 2002: Modeling, Signal Processing, and Control, SPIE, San Diego (2002)
[5]	KANG, J., LIU, S., and WANG, C. Controllable bistable smart composite structures driven by liquid crystal elastomer. Smart Materials and Structures, 31, 015003 (2022)
[6]	XU, D., BANERJEE, S., WANG, Y., HUANG, S., and CHENG, X. Temperature and loading effects of embedded smart piezoelectric sensor for health monitoring of concrete structures. Construction and Building Materials, 76, 187–193 (2015)
[7]	EBRAHIMI, N., BI, C., CAPPELLERI, D. J., CIUTI, G., CONN, A. T., FAIVRE, D., HABIBI, N., HOŠOVSKÝ, A., IACOVACCI, V., KHALIL, I. S. M., MAGDANZ, V., MISRA, S., PAWASHE, C., RASHIDIFAR, R., SOTO-RODRIGUEZ, P. E. D., FEKETE, Z., and JAFARI, A. Magnetic actuation methods in bio/soft robotics. Advanced Functional Materials, 31(11), 2005137 (2021)
[8]	LU, H., ZHANG, M., YANG, Y., HUANG, Q., FUKUDA, T., WANG, Z., and SHEN, Y. A bioinspired multilegged soft millirobot that functions in both dry and wet conditions. Nature Communications, 9, 3944 (2018)
[9]	REN, Z., HU, W., DONG, X., and SITTI, M. Multi-functional soft-bodied jellyfish-like swimming. Nature Communications, 10, 2703 (2019)
[10]	SUN, B., JIA, R., YANG, H., CHEN, X., TAN, K., DENG, Q., and TANG, J. Magnetic arthropod millirobots fabricated by 3D-printed hydrogels. Advanced Intelligent Systems, 4(1), 2270005 (2022)
[11]	ISHIYAMA, K., ARAI, K. I., SENDOH, M., and YAMAZAKI, A. Spiral-type micro-machine for medical applications. Proceedings of 2000 International Symposium on Micromechatronics and Human Science, IEEE, Nagoya (2000)
[12]	HWANG, J., KIM, J. Y., and CHOI, H. A review of magnetic actuation systems and magnetically actuated guidewire- and catheter-based microrobots for vascular interventions. Intelligent Service Robotics, 13, 1–14 (2020)
[13]	CHEN, W., YAN, Z., and WANG, L. On mechanics of functionally graded hard-magnetic soft beams. International Journal of Engineering Science, 157, 103391 (2020)
[14]	WANG, L., KIM, Y., GUO, C. F., and ZHAO, X. Hard-magnetic elastica. Journal of the Mechanics and Physics of Solids, 142, 104045 (2020)
[15]	HUANG, W., LIU, M., and HSIA, K. J. A discrete model for the geometrically nonlinear mechanics of hard-magnetic slender structures. Extreme Mechanics Letters, 59, 101977 (2023)
[16]	DORFMANN, A. and OGDEN, R. W. Magnetoelastic modelling of elastomers. European Journal of Mechanics-A/Solids, 22(4), 497–507 (2003)
[17]	DORFMANN, A. and BRIGADNOV, I. A. Constitutive modelling of magneto-sensitive Cauchy-elastic solids. Computational Materials Science, 29(3), 270–282 (2004)
[18]	DORFMANN, A. and OGDEN, R. W. Nonlinear magnetoelastic deformations of elastomers. Acta Mechanica, 167(1), 13–28 (2004)
[19]	KANKANALA, S. V. and TRIANTAFYLLIDIS, N. On finitely strained magnetorheological elastomers. Journal of the Mechanics and Physics of Solids, 52(12), 2869–2908 (2004)
[20]	NADZHARYAN, T. A., STOLBOV, O. V., RAIKHER, Y. L., and KRAMARENKO, E. Y. Field-induced surface deformation of magnetoactive elastomers with anisometric fillers: a single-particle model. Soft Matter, 15, 9507–9519 (2019)
[21]	GARCIA-GONZALEZ, D. and HOSSAIN, M. Microstructural modelling of hard-magnetic soft materials: dipole-dipole interactions versus Zeeman effect. Extreme Mechanics Letters, 48, 101382 (2021)
[22]	GARAI, A. and HALDAR, K. Experiments and modeling of magneto-stiffening effects for magnetoactive polymer. International Journal of Mechanical Sciences, 286, 109860 (2025)
[23]	ROGHANI, M., ROMEIS, D., BORIN, D., and SAPHIANNIKOVA, M. Influence of matrix stiffness on microstructure evolution and magnetization of magneto-active elastomers. Soft Matter, 21, 1416–1425 (2025)
[24]	LEIDNER, J. and WOODHAMS, R. T. The strength of polymeric composites containing spherical fillers. Journal of Applied Polymer Science, 18(6), 1639–1654 (1974)
[25]	ZHOU, Y., HUANG, Z., WANG, J., and WANG, Y. Tensile strength of particle reinforced composite with interfacial debonding. Engineering Fracture Mechanics, 303, 110110 (2024)
[26]	CHEN, J., YAO, Y., and ZHANG, B. The interface debonding in particle-reinforced nonlinear viscoelastic polymer composites. Meccanica, 57, 1353–1367 (2022)
[27]	MATOUS, K., INGLIS, H. M., GU, X., RYPL, D., JACKSON, T. L., and GEUBELLE, P. H. Multiscale modeling of solid propellants: from particle packing to failure. Composites Science and Technology, 67(7-8), 1694–1708 (2007)
[28]	YUAN, R., MA, X., LIANG, L. H., and WEI, Y. Size and interface effects on tensile strength of polymers with nano/micro particle inclusions. Acta Mechanica Solida Sinica, 37, 812–822 (2024)
[29]	KLAUSLER, W. and KALISKE, M. A finite interface element for modeling inclusion-matrix interaction in magneto-active elastomers. International Journal for Numerical Methods in Engineering, 126(3), e7625 (2025)
[30]	SALIM, N. J., ARRETCHE, I., PIERCE, C. D., SMITH, E. J., and MATLACK, K. H. Effect of isotropy and anisotropy: toward understanding the fracture behavior of magnetoactive elastomers. Engineering Fracture Mechanics, 311, 110553 (2024)
[31]	FENG, S. and SUN, L. Microstructure-based magneto-mechanical modeling of magnetorheological elastomer composites: a comparable analysis of dipole and Maxwell methods. Materials, 18(5), 1187 (2025)
[32]	MORENO-MATEOS, M. A., HOSSAIN, M., STEINMANN, P., and GARCIA-GONZALEZ, D. Hard magnetics in ultra-soft magnetorheological elastomers enhance fracture toughness and delay crack propagation. Journal of the Mechanics and Physics of Solids, 173, 105232 (2023)