Article(id=1246046389726196163, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1246046388547596731, articleNumber=null, orderNo=null, doi=10.19636/j.cnki.cjsm42-1250/o3.2024.034, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1721836800000, receivedDateStr=2024-07-25, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1775010209732, onlineDateStr=2026-04-01, pubDate=1735056000000, pubDateStr=2024-12-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1775010209732, onlineIssueDateStr=2026-04-01, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1775010209732, creator=13701087609, updateTime=1775010209732, updator=13701087609, issue=Issue{id=1246046388547596731, tenantId=1146029695717560320, journalId=1241755870837649424, year='2024', volume='45', issue='6', pageStart='709', pageEnd='856', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1775010209451, creator=13701087609, updateTime=1775010293319, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1246046740390986227, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1246046388547596731, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1246046740390986228, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1246046388547596731, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=748, endPage=758, ext={EN=ArticleExt(id=1246046391290671561, articleId=1246046389726196163, tenantId=1146029695717560320, journalId=1241755870837649424, language=EN, title=Study on the Electromechanical Response of Ogden-Type Conical Dielectric Elastomer Actuators with Linear Permittivity, columnId=1244229834482757770, journalTitle=Chinese Journal of Solid Mechanics, columnName=Research Paper, runingTitle=null, highlight=null, articleAbstract=

This study investigates the electromechanical characteristics of a conical dielectric elastomer actuator in a non-ideal state, specifically focusing on the dielectric constant related to tensile deformation. By using the Ogden elastic strain energy function with multiple material constants and incorporating a linear permittivity that depends on the tensile rate, the constitutive relation for a non-ideal state is further deduced. The model is solved employing the shooting method, allowing for analysis of the mechanical performance and electromechanical stability of conical dielectric elastomers. We observe significant out-of-plane nonlinear axisymmetric deformation when the membrane is subjected to external force and external voltage, both with and without pre-stretch. By changing the voltage while maintaining constant external force, we identify model parameters and assess how varying electrostriction coefficients impact radial strength, circumferential stretch, and the true electric field. As the electrostriction coefficient decreases, tensile deformation in the membrane becomes increasingly uniform under no pre-stretch conditions, and the true electric field distribution tends to become more even. Under prestretch conditions, tensile deformation in the membrane remains stable, and the true electric field distribution is more consistent. When the electrostriction coefficient is sufficiently small, both the tensile deformation and the true electric field distribution tend to be stable, enhancing the overall stability of the dielectric elastomer. It is found that the prestretch condition exhibits greater stability than the no pre-stretch scenario. This research enhances our understanding of the electromechanical properties in non-ideal states, providing a theoretical foundation for the stable operation of conical dielectric elastomers in practical applications. The findings can guide the design of conical dielectric elastomer actuators, assisting engineers in optimizing design parameters to improve the performance and reliability of actuators.

, correspAuthors=Guanghong Miao, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, authorCompany=null, fund=null, authors=null, authorsList=Guanghong Miao, Shun Li, Xiangyu Chu, Cheng Yuan), CN=ArticleExt(id=1246046404905382662, articleId=1246046389726196163, tenantId=1146029695717560320, journalId=1241755870837649424, language=CN, title=具有线性介电常数Ogden型锥形介电弹性体作动器的力电响应研究, columnId=1241831201896469478, journalTitle=固体力学学报, columnName=研究论文, runingTitle=null, highlight=null, articleAbstract=

为研究锥形介电弹性体作动器在非理想状态下的力电特性,本文采用多材料常数Ogden模型,考虑无预拉伸和预拉伸的情况下,通过引入依赖拉伸率的线性介电常数,得到非理想状态下的本构关系. 对薄膜受到外力外电压作用时发生面外非线性轴对称大变形进行数值模拟. 结果表明在预拉伸下,随着电致伸缩系数的减小,薄膜变形,拉伸量呈稳定状态,真实电场分布呈均匀状态,研究结果有利于理解介电弹性体的力电稳定性,更好地指导此类作动器的设计.

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** E-mail:.
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具有线性介电常数Ogden型锥形介电弹性体作动器的力电响应研究
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缪广红 1, ** , 李顺 1 , 楚翔宇 2 , 袁成 2
固体力学学报 | 研究论文 2024,45(6): 748-758
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固体力学学报 | 研究论文 2024, 45(6): 748-758
具有线性介电常数Ogden型锥形介电弹性体作动器的力电响应研究
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缪广红1, ** , 李顺1, 楚翔宇2, 袁成2
作者信息
  • 1安徽理工大学力学与光电物理学院,淮南,232001
  • 2安徽理工大学土木建筑学院,淮南,232001

通讯作者:

Study on the Electromechanical Response of Ogden-Type Conical Dielectric Elastomer Actuators with Linear Permittivity
Guanghong Miao1, ** , Shun Li1, Xiangyu Chu2, Cheng Yuan2
Affiliations
  • 1School of Mechanics and Optoelectronics Physics, Anhui University of Science and Technology, Huainan, 232001
  • 2School of Civil Engineering and Architecture, Anhui University of Science and Technology, Huainan, 232001
出版时间: 2024-12-25 doi: 10.19636/j.cnki.cjsm42-1250/o3.2024.034
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为研究锥形介电弹性体作动器在非理想状态下的力电特性,本文采用多材料常数Ogden模型,考虑无预拉伸和预拉伸的情况下,通过引入依赖拉伸率的线性介电常数,得到非理想状态下的本构关系. 对薄膜受到外力外电压作用时发生面外非线性轴对称大变形进行数值模拟. 结果表明在预拉伸下,随着电致伸缩系数的减小,薄膜变形,拉伸量呈稳定状态,真实电场分布呈均匀状态,研究结果有利于理解介电弹性体的力电稳定性,更好地指导此类作动器的设计.

锥形介电弹性体  /  非理想  /  线性介电常数  /  电致伸缩系数

This study investigates the electromechanical characteristics of a conical dielectric elastomer actuator in a non-ideal state, specifically focusing on the dielectric constant related to tensile deformation. By using the Ogden elastic strain energy function with multiple material constants and incorporating a linear permittivity that depends on the tensile rate, the constitutive relation for a non-ideal state is further deduced. The model is solved employing the shooting method, allowing for analysis of the mechanical performance and electromechanical stability of conical dielectric elastomers. We observe significant out-of-plane nonlinear axisymmetric deformation when the membrane is subjected to external force and external voltage, both with and without pre-stretch. By changing the voltage while maintaining constant external force, we identify model parameters and assess how varying electrostriction coefficients impact radial strength, circumferential stretch, and the true electric field. As the electrostriction coefficient decreases, tensile deformation in the membrane becomes increasingly uniform under no pre-stretch conditions, and the true electric field distribution tends to become more even. Under prestretch conditions, tensile deformation in the membrane remains stable, and the true electric field distribution is more consistent. When the electrostriction coefficient is sufficiently small, both the tensile deformation and the true electric field distribution tend to be stable, enhancing the overall stability of the dielectric elastomer. It is found that the prestretch condition exhibits greater stability than the no pre-stretch scenario. This research enhances our understanding of the electromechanical properties in non-ideal states, providing a theoretical foundation for the stable operation of conical dielectric elastomers in practical applications. The findings can guide the design of conical dielectric elastomer actuators, assisting engineers in optimizing design parameters to improve the performance and reliability of actuators.

conical dielectric elastomer  /  non-ideal  /  linear permittivity  /  electrostriction coefficient
缪广红, 李顺, 楚翔宇, 袁成. 具有线性介电常数Ogden型锥形介电弹性体作动器的力电响应研究. 固体力学学报, 2024 , 45 (6) : 748 -758 . DOI: 10.19636/j.cnki.cjsm42-1250/o3.2024.034
Guanghong Miao, Shun Li, Xiangyu Chu, Cheng Yuan. Study on the Electromechanical Response of Ogden-Type Conical Dielectric Elastomer Actuators with Linear Permittivity[J]. Chinese Journal of Solid Mechanics, 2024 , 45 (6) : 748 -758 . DOI: 10.19636/j.cnki.cjsm42-1250/o3.2024.034
作为电活性聚合物的典型代表之一,介电弹性体(Dielectric elastomer,DE)具有许多优异的性能,包括应变大,能量密度高,响应速度快,重量轻. 因此它们在航空航天,软机器人,生物医学等工程领域[1-3]有着广泛的应用. 介电弹性体作动器是薄膜两面涂上柔性电极形成的. 由于介电弹性体的不可压缩性,施加电压时会在介电弹性体膜上产生Maxwell应力,将电能转化为机械能从而导致弹性体面积变大、厚度变薄. 当电压释放时,由于弹性应力的作用,它又恢复到原来的状态.
针对DE作动器,目前已发展较为完善的理论建模方法和实验技术. Zhao和Suo[4]详细描述了薄膜电击穿现象的非线性力电模型,给出了由应变计算临界场强的计算方法;Michael等[5]对电活性聚合物致动器中的力电耦合现象进行分析,测量了不同预拉伸程度下,丙烯酸弹性体介电膜的介电常数值,观察到介电常数值随预拉伸的增加而减小,矫正了不可压介电材料的本构模型参数;Kais等[6]推导了材料在超弹性特性下的非线性控制方程,并运用数值方法求得了圆形介电薄膜材料在不同预拉伸和电压下的动态解,验证了预拉伸对固有频率的影响;Luo等[7]采用超弹性材料Yeoh模型及ABAQUS仿真软件分析了因介电弹性体膜的横向侧边收缩、卷绕后的周向松弛、层间挤压对圆柱型驱动器轴向力变化情况,试验结果表明卷绕后的周向松弛对轴向力影响最大. Cooley等[8]使用牛顿框架来模拟圆形介电弹性体膜的非线性动力学,考虑了平面运动过程中的动态厚度变化,得到的运动方程具有额外的非线性项,即轴向惯性. 研究了轴向惯性对膜频率响应的影响,以确定正弦电压波动,结果表明轴向惯性对非线性动力学的影响是显著的. 刘等[9]应用多材料参数的Ogden模型对介电弹性体的力电稳定性进行分析探讨,通过数值模拟,证明了材料常数比及电致伸缩系数的适当调节可以令介电弹性体的结构更加稳定. Wang等[10]通过测量介电弹性体(DE)的拉伸性能,确定DE预拉伸指数,然后详细讨论了不同预拉伸指数和不同预紧力下锥形介电弹性体致动器的致动位移和输出力,试验结果表明较大的预拉伸比会导致DE出现不稳定性. Zhu等[11]通过改变预拉伸、电压与压力,调节了薄膜的固有频率,预测了包含超谐波、谐波和次谐波共振的几种振荡模式. Xing等[12]提出了一种由DE作动器驱动的超轻软机械臂,结构具有大变形能力,同时保持扭转刚度,实现了机械臂的超轻量化和大范围连续变形. Cao等[13]采用了双锥形介电弹性体作动器(DCDEA)配置,建立一个数值模型来研究昆虫的仿生扑翼的动态响应. 开发了一个有效的功率研究框架,并根据预拉伸比和间隔长度对DCDEA的功率输出进行了优化. 优化结果表明无预拉伸且间间隔长度为1.4的设计可实现最高的功率输出,功率密度可与昆虫肌肉相媲美. Huang等[14]通过研究聚二甲基硅氧烷材料的锥形DEA并考虑惯性的影响,提出了一种基于非平衡热力学原理的动力学模型. 该动力学模型可以描述锥形DEA的复杂运动特性. 基于实验数据,采用差分进化算法对所建立的动力模型的未定参数进行识别,结果证明了模型的有效性. Jiang等[15]研究开发了一种基于VHB弹性体的锥体DEG,通过将等轴预拉伸与锥体拉伸模式相结合,然后对等轴预拉伸比、输入偏置电压和锥体位移等变量进行定制,优化了其能量收集性能. Cao等[16]考虑具有广义耗散有效载荷的锥形配置DEA,通过有效载荷条件对锥形DEA系列功率输出的影响进行了广泛的研究,且对不同锥形DEA配置的性能进行了基准测试,并说明了这些输出模式背后的基本原理.
现阶段作动器结构主要为圆柱形、矩形,对锥形研究较少. 且大多数是在理想状态进行研究,默认介电常数是一个定量,但在试验过程中介电常数是变化的,不能忽略介电常数带来的影响. 因此本文应用多材料常数的Ogden自由能密度函数耦合线性介电常数的能量密度函数模型,研究锥形介电弹性体在力电激励作用下的面外非线性轴对称大变形,对薄膜变形,环向拉伸,径向拉伸,真实电场进行定量分析.
图1(a)是电活性聚合物薄膜初始状态,薄膜厚度为H,内径为A,外径为B,令薄膜上任意一点到薄膜中心距离为R图1(b)是变形后的状态,介电弹性体膜均匀拉伸,先将半径为a的刚性圆盘牢固地粘附在薄膜的表面,在此步骤结束和以下的拉伸步骤中,内半径a是固定的. 然后DE膜进一步拉伸,将其外边界固定在半径为b的刚性环上,刚性圆盘的中心与预拉伸DE膜的中心重合. 拉伸结束后,在两电极间施加电压Φ,在外力F作用下,薄膜发生面外大变形且关于z轴对称,圆盘向下运动.
Ogden弹性应变能是学者Ogden在1972年最先提出的,常见的弹性应变能模型都是此模型的特例,为此研究更有一般性. 因此本文选用Ogden模型对电活性聚合物在力电作用下的面外非线性轴对称大变形进行研究.
式中μn为Ogden材料常数,qn为无刚量常数,ε为介电常数,表示名义电位移,λ1为径向拉伸量,λ2为环向拉伸量.
真实电场E是电压除以薄膜在变形状态下的厚度:
真实电位移是变形状态下单位面积电极上的电量:
由整个薄膜Helmholtz自由能密度的变分及自由能改变量得到如下平衡方程:
将公式(2)(7)代入(8)得:
将公式(4)(5)(6)代入(9)得:
将(11)代入(10)得:
在理想状态下,介电常数默认是一个定量. 但Suo提出经历大变形的介电常数不是独立的,它依靠弹性体本身的变形. 因此Suo等根据Wissler和Mazza实验[19]提出把介电常数拟合成依赖拉伸率的线性变化函数. Suo在文献[20]得出结论:电致伸缩系数为负数时,与变形有关的介电常数效应部分抑制了Maxwell应力,因此足够负的电致伸缩系数将抑制力电不稳定性. 引入Suo拟合得到介电弹性体的介电常数与拉伸率的关系[20]
式中η为电致伸缩系数,根据实验数据[20]ε=4.68ε0ε0=8.85×10-12 F/m.
将(13)代入方程(1)得:
对平衡方程(8)进行改写,得到如下公式:
将公式(7)(15)代入(8)得:
将公式(5)(6)(17)代入(18)得:
引入上述的无量纲量,即得如下式子:
将公式(5)(11)(17)代入(15)(16)(19)分别可得:
在无量纲外力F/2π1=2恒定不变情况下,取无量纲电压分别为0.10,0.15,0.20,0.25. 电致伸缩系数η取0,-0.053,-0.10,-0.25[20],当η=0时,为分析理想状态下介电弹性体的力电稳定性. 薄膜厚度为0.05,薄膜内径为1,外径为4. 对无预拉伸和预拉伸这两种情况进行稳定性分析,即无预拉伸a/A=1,b/B=1;预拉伸a/A=1.2,b/B=1.9. 本文采用打靶法对模型进行求解,计算中,文献[22]通过试验数据拟合,得到Ogden模型中的材料常数分别为:q1=1.3,q2=5,q3=-2,μ1=0.63 MPaμ2=1.2×10-3 MPa,μ3=-1×10-2 MPa.
图2为不同电致伸缩系数下,薄膜变形离中心O点远近的变化曲线. 可以看出距离中心O点越近,薄膜变形越大,反之则越小. 薄膜变形曲线向内凹,且薄膜变形随着外加电压Φ的增大而增大. 当电致伸缩系数越小时,薄膜的最大变形逐渐减小,不同电压间的薄膜变形差值也逐渐减小,薄膜变形呈稳定趋势.
图3为不同电致伸缩系数下径向拉伸随着距离中心O点由近到远的变化曲线. 可以看出离中心O越近径向拉伸越大,反之则越小. 随着电致伸缩系数减小,最大拉伸值逐渐减小,不同电压间拉伸差值也逐渐减小,径向拉伸呈稳定趋势.
图4为不同电致伸缩系数下环向拉伸随着距离中心O点由近到远的变化曲线. 由于薄膜的内边界和外边界被固定,导致薄膜在内外边界未发生环向变形即r=1,λ2=1;r=4,λ2=1. 由图4(a)(b)(c)可以看出无量纲电压时,环向拉伸先减小后增大;无量纲电压时,环向拉伸先增大后减小. 由图4(d)可知,当电致伸缩系数η=-0.25时,不同电压的环向拉伸呈先减小后增大.
图5为不同电致伸缩系数下真实电场随着距离中心O点由近到远的变化曲线. 电场在薄膜处由内到外呈单调递减的趋势. 电致伸缩系数减小,电场最大值逐渐减小,不同电压间的电场差值也逐渐减小. 电场分布不均匀,导致薄膜内边界处在电击穿边缘时,其他区域仍有很强的承受能力,材料利用率不高.
图6(a)可以看出无量纲电压时,薄膜变形曲线向内凹,无量纲电压时,薄膜变形曲线向外凸,这是因为当外加电压增大到某一临界值时,薄膜的厚度进一步减小,其环向朝外边界的移动逐渐增大,从而导致曲线向外凸. 图6(b)(c)(d)薄膜变形曲线向内凹. 距离中心O点越近,变形越大;反之则越小. 与图2相比,预拉伸减小了薄膜变形的最大值,增大了不同电压间薄膜变形差值. 随着电致伸缩系数减小,不同电压间变形差值逐渐减小,薄膜变形曲线变化更明显,薄膜变形呈稳定状态.
图7可知,径向拉伸离中心O点越近值越大,反之则越小. 与图3相比,预拉伸提高了径向拉伸量,每条曲线上最大值与最小值的差值减小. 当电致伸缩系数减小,不同电压的径向拉伸差值减小,拉伸的最大值与最小值也逐渐减小,径向拉伸呈稳定趋势.
图8(a)可以看出无量纲电压时,环向拉伸呈递增趋势;无量纲电压时,环向拉伸先增大后减小. 由图8(b)(c)(d)可知,环向拉伸全部呈递增趋势. 与图4相比,预拉伸的内边界和外边界环向拉伸值变大;环向拉伸变形在一个固定的范围内,只有在图8(a)中无量纲电压时拉伸变形超出固定范围,但控制在0.1内;不同电压间环向拉伸差值更小,曲线趋于稳定. 当电致伸缩系数减小,不同电压间拉伸差值减小,环向拉伸呈稳定状态.
图9可知,真实电场从内边界到外边界呈先增后减小的趋势. 与图5相比,预拉伸提高了真实电场值,不同电压间真实电场差值更大,电场分布呈均匀趋势. 在图9(a)(b)中无量纲电压时,电场分布不均匀,但随着电致伸缩系数减小,电场分布呈均匀状态,材料利用率得到提高.
本文以Ogden模型为基础,建立了锥形介电弹性体作动器在非理想状态下力电耦合数学模型. 在未拉伸和预拉伸两种情况下,通过改变电致伸缩系数,对弹性体的变形,径向拉伸,环向拉伸,真实电场进行了研究,结论如下:
(1)当η=0时即在理想状态下,对薄膜进行预拉伸,拉伸后减小了薄膜变形,增大了径向拉伸和环向拉伸的变形量,增大了真实电场值.
(2)随着电致伸缩系数的减小,不同电压间的薄膜变形,径向拉伸,环向拉伸,真实电场间的差值逐渐减小,曲线变化趋势逐渐相同,抑制了力电不稳定性.
(3)随着电致伸缩系数减小,预拉伸下薄膜变形,拉伸量,真实电场发生明显的变化,这说明薄膜变形,径向和环向拉伸,真实电场对电致伸缩系数的改变是非常敏感的.
(4)在预拉伸下,电致伸缩系数为负数时,随着电致伸缩系数的减小,薄膜的变形,拉伸量的曲线稳定;真实电场分布均匀,很好地抑制了作动器的力电不稳定性,这与试验[20]对电致伸缩系数的研究得到结论一致. 本文的研究结果能更好地指导此类作动器的设计.
  • 国家自然科学基金项目(11902003)
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doi: 10.19636/j.cnki.cjsm42-1250/o3.2024.034
  • 接收时间:2024-07-25
  • 首发时间:2026-04-01
  • 出版时间:2024-12-25
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  • 收稿日期:2024-07-25
基金
国家自然科学基金项目(11902003)
作者信息
    1安徽理工大学力学与光电物理学院,淮南,232001
    2安徽理工大学土木建筑学院,淮南,232001

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2种不同金属材料的力学参数

Family
属数
Number of
genus
种数
Number of
species
占总种数比例
Percentage of
total species (%)

Genus
种数
Number of
species
占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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