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针对软体机器人用水凝胶含摩擦斜向接触问题, 建立了接触力学数值模型, 分析了水凝胶软材料斜向接触时的局部接触大变形及摩擦效应等非线性行为. 基于超弹性材料本构, 推导得到了水凝胶的更新自由能函数. 给出接触计算策略, 数值计算了刚性球状压头正向接触水凝胶和斜向接触水凝胶两个算例, 讨论了经典Hertz接触理论的适用性以及不同摩擦系数对接触区应力分布和接触状态的影响规律. 计算结果表明, 水凝胶的材料非线性以及大变形引起的几何非线性使得经典Hertz接触理论不再适用; 斜向接触时, 摩擦系数的增大会导致水凝胶内部应力的重新分布, 表现为最大应力位置由接触面下方转移到接触表面上, 同时使水凝胶内部和表面出现两个主要高应力区. 此外, 研究还发现当摩擦系数较小时(μ < 0.05), 水凝胶正向接触事件中所有接触点均处于静摩擦到滑动摩擦的极限状态, 而斜向接触事件中接触面的部分区域始终处于稳定静摩擦状态.Focusing on the oblique frictional contact problem of hydrogel for soft robot, a numerical contact model is developed to analyze the nonlinear behaviors including local contact large deformation and friction effect of hydrogel soft material during oblique contact. Based on the constitutive relation of hyperelastic material, the updated free energy function of hydrogel is derived. The contact algorithm is given to compute the contact responses of both collinear contact example and oblique contact example. The applicability of classical Hertz contact theory is discussed. The influence of coefficient of friction on the stress distribution of contact zone and the contact states of contact surface are also investigated. The numerical results show that the material nonlinearity and the geometric nonlinearity (i.e. large deformation) of hydrogel lead to the invalidation of classical Hertz contact theory. For the oblique contact, the internal stress grads of hydrogel will be redistributed as the coefficient of friction increases. Meanwhile, the maximum stress position moves from underside to the contact surface. Two high stress zones occur inside and on the contact surface at the same time, respectively. Besides, when the coefficient of friction is smaller (i.e. μ < 0.05), for the collinear contact all contact points on the contact surface are in critical state from static friction to dynamic friction. But for the oblique contact, some contact points are always in stable static friction state.
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Keywords:
- hydrogel /
- large deformation /
- oblique contact /
- friction
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图 1 水凝胶软体机器人的接触 (a) 示意图; (b) 力学模型; (c) 离散模型
Fig. 1. Hydrogel soft robot’s contact: (a) Schematic diagram; (b) mechanics model; (c) discrete model.
图 3 有限元方法 (a) ABAQUS用户子程序UHYPER; (b) ABAQUS数值计算流程
Fig. 3. Finite element method: (a) ABAQUS user subroutine UHYPER; (b) ABAQUS numerical computation process.
图 4 刚性球状压头-半无限大空间 (a) 接触局部变形示意图; (b) 数值解与经典Hertz理论解的比较
Fig. 4. Rigid spherical indenter-semi-infinite space: (a) Schematic diagram of local contact deformation; (b) comparison between numerical solution and classical Hertz theoretical solution.
图 7 摩擦力导致的应力变化现象 (a) 正向接触; (b) 斜向接触
Fig. 7. Stress changes caused by friction: (a) Collinear contact; (b) oblique contact.
图 8 接触面各点受力分析及接触合力Fc的大小 (a) 接触面各点受力分析图; (b) 不同摩擦系数下接触力Fc的各轴分量
Fig. 8. Force analysis of each point of the contact surface and the magnitude of the contact force Fc: (a) Force analysis diagram of each point of the contact surface; (b) axis components of the contact force Fc under different friction coefficients.
图 9 不同摩擦系数下的各点的合力 (a) 法向接触压力的合力; (b) 切向摩擦力的合力
Fig. 9. Resultant force of each point under different coefficients of friction: (a) Resultant force of normal contact pressure; (b) resultant force of tangential friction force.
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[1] Nagura M, Minourab N 1997 Polym. Gels Networks 5 455
Google Scholar
[2] 卢同庆, 孙丹琪, 王继堃, 杨 孟, 王铁军 2018 中国科学: 技术科学 48 1288
Google Scholar
Lu T Q, Sun D Q, Wang J K, Yang M, Wang T J 2018 Sci. Sin. Tech. 48 1288
Google Scholar
[3] 张恩勉, 李紫秀, 孙蕾, 董点点, 梁毅, 魏钊, 张其清, 陈咏梅 2019 中国科学: 生命科学 49 250
Google Scholar
Zhang E M, Li Z X, Sun L, Dong D D, Liang Y, Wei Z, Zhang Q Q, Chen Y M 2019 Sci. Sin. Vitae 49 250
Google Scholar
[4] Gong J, Higa M, Iwasaki Y, Katsuyama Y, Osada Y 1997 J. Phys. Chem. B 101 5487
Google Scholar
[5] Yuk H, Lin S, Ma C, Takaffoli M, Fang N X, Zhao X 2017 Nat. Commun. 8 14230
Google Scholar
[6] Rus D L, Tolley M T 2015 Nature 521 467
Google Scholar
[7] Kim S, Laschi C, Trimmer B 2013 Trends Biotechnol. 31 287
Google Scholar
[8] 陈恩惠, 杨锦鸿, 李栋, 赵亚溥 2016 物理学报 65 188103
Google Scholar
Chen E H, Yang J H, Li D, Zhao Y P 2016 Acta Phys. Sin. 65 188103
Google Scholar
[9] 巫金波, 温维佳 2016 物理学报 65 188301
Google Scholar
Wu J B, Wen W J 2016 Acta Phys. Sin. 65 188301
Google Scholar
[10] Pilnik W, Rombouts F M 1985 Carbohydr. Res. 142 93
Google Scholar
[11] Shoaib T, Espinosa-Marzal R M, Interfaces 2019 ACS Appl. Mater. Interfaces 45 42722
Google Scholar
[12] Shoaib T, Heintz J, Lopezberganza J, Murobarrios R, Egner S A, Espinosamarzal R M 2018 Langmuir 34 756
Google Scholar
[13] Katta J K, Marcolongo M S, Lowman A M, Mansmann K A 2004 Proceedings of the 30th Annual Northeast Bioengineering Conference, Springfield, MA, USA, April 17–18, 2004 p142
[14] Nakashima K, Sawae Y, Murakami T 2007 Tribol. Lett. 26 145
Google Scholar
[15] Frey M T, Engler A, Discher D E, Lee J, Wang Y 2007 Methods Cell Biol. 83 47
[16] Long R, Hall M, Wu M, Hui C Y 2011 Biophys. J. 101 643
Google Scholar
[17] Yang J, Shen Y 2019 Appl. Math. Modell. 74 94
Google Scholar
[18] Hong W, Liu Z, Suo Z 2009 Int. J. Solids Struct. 46 3282
Google Scholar
[19] Hong W, Zhao X, Zhou J, Suo Z 2008 J. Mech. Phys. Solids 56 1779
Google Scholar
[20] Flory P J, Rehner J 1943 J. Chem. Phys. 11 512
Google Scholar
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