弹性聚合物薄膜的力电大变形及失效模式分析
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摘要
上世纪九十年代末期,一类特殊的软机敏材料即电活性聚合物引起了学术界及工业界的广泛关注,该类高分子聚合物在电场作用下具有大应变、响应快、能效高等诸多优异的力学性能,可被加工成作动器、传感器及能量采集器,其核心部分是一层在上下表面附着有柔顺电极的聚合物薄膜,受电场作用时,薄膜将减小厚度而扩大面积,从而实现电能和机械能的相互转换。由于电活性聚合物薄膜在电场作用下的变形属非线性大变形,同时薄膜在力电荷载共同作用下存在多种失效模式,因此对其力电响应进行描述充满了挑战性。本文的研究内容如下：
1.基于非线性弹性大变形理论建立了圆环形薄膜在外力作用下的力学模型,研究了一圆环状弹性薄膜的轴对称面外大变形。在未发生变形的参考构形下,平直的圆环状的薄膜的内边界连接一个圆盘,将薄膜的外边界固定在刚性的圆环上。当圆盘上作用一个竖直向下的外力时,薄膜经历面外大变形后形成轴对称的形状。结合状态平衡和热力学,推导得到了描述薄膜经历面外大变形的控制方程。采用了打靶法对控制方程进行求解,得到了薄膜在经历面外大变形时,薄膜内应力场和应变场的分布规律,可以看出薄膜的变形是非常不均匀的,这意味着薄膜在工作时材料的利用率较低,造成了材料的浪费。同时,本章的研究成果从基本理论和计算方法为本文后续的研究工作做了必要的铺垫。
2.以电活性聚合物作动器的基本结构建立的力学模型为基础探讨了电活性聚合物薄膜在力电荷载共同作用下的面外非线性轴对称大变形。利用非线性弹性大变形理论并结合热力学的基本理论,推导得到了圆环形薄膜在受力电载荷作用时产生面外大变形的控制方程,采用打靶法对控制方程进行了数值求解,得到了电活性聚合物薄膜受到力电荷载共同作用时,薄膜内的应力场、应变场和电场的分布规律,结果表明,圆环形薄膜的变形是非常不均匀的,在靠近圆环中心处的薄膜变形较大,而靠近圆环边缘处的薄膜变形较小,导致薄膜中的电场从外向内逐渐变大,从而使得靠近圆环中心处的薄膜处于电击穿的边缘,可能导致的结果是大部分薄膜还可正常工作的时候,处在场强高的某点处的薄膜已经失效。变形场的非均匀性导致薄膜内的大部分材料并没有被有效地利用,造成了材料的浪费。
3.以电活性聚合物作动器简化后的模型为基础,利用热力学基本原理推导得到了系统的控制方程,探讨了作动器在工作中可能存在的失效模式,并给出了各种失效模式的判断准则。本章利用这些准则在给定的条件下,得到了施加在作动器上外力F和电压Φ的有效工作区间。另外,计算结果在作动器工作前对薄膜进行预拉伸,这样可以明显的减小变形后薄膜内电场的不均匀分布的程度,如果作动器的设计参数选择适当,可以达到电场在薄膜中呈现均匀分布的状态,大大提高了材料的利用率。
本文的研究结果对弹性聚合物的基本研究方法及商业化产品的优化设计具有实际的借鉴与指导意义。
Since 1990's, in the family of electro-active polymers, one kind of special soft smart materials, that is dielectric elastomer, has received considerable attention among researchers and engineers due to its many outstanding mechanical attributes such as large strain, fast response, high efficiency etc.when it is subject to a voltage. These attributes make dielectric elastomer promising for applications as transducers such as actuators, sensors and energy harvesters.The essential part of dielectric elastomer transducers is a dielectric membrane sandwiched between two compliant electrodes.Subject to a voltage, the dielectric membrane reduces its thickness and expands its area, converting electrical energy into mechanical energy. Due to large deformation, nonlinear equations of state, and complicated loads, modeling the electro-mechanical response for dielectric elastomer transducers has been challenging. The main contents of this thesis are as follows:
1.The axisymmetric out-of plane nonlinear deformation of an annular elastic membrane is studied in the frame of nonlinear elastic deformation theory. The membrane is initially flat and attached to a disk in the inner circle and to a rigid ring in the outer circle, then a weight is applied to the disk and the membrane deforms into an axisymmetric shape, undergoing large out-of-plane deformation.The governing equations characterizing the out-of plane large deformation of the elastic membrane are derived by combining state equilibrium and thermodynamics.The derived governing equations are solved by using shooting method. The obtained results show that the deformation field in the membrane is very inhomogeneous.This indicates that the membrane doesn't function efficiently, which leads to a material waste.The theory and method presented in this section provide some basic outlines for the problem discussed in the next section.
2.This part focuses on investigating the axisymmetric out-of plane nonlinear deformation of an actuator made of electro-active polymer membrane.The mechanical model describing the axisymmetric nonlinear deformation of such annular membrane is formulated, and the equations of equilibrium state characterizing the large deformation of the annular membrane subject to a concentrated force and a voltage are derived by thermodynamics.The derived state equations are solved by using shooting method and the distributions of true stress fields,stretches and true electrical fields are obtained numerically. The obtained numerical results show that the deformation field in the membrane is highly inhomogeneous.The deformation near the central part of the membrane is large while the deformation near the edge of the membrane is small, which leads to the induced electric field in the membrane increases monotonically from the edge to the central part and reaches maximum at the central part of the membrane. This results in the consequence that the membrane near the central part risks the possibility of electric breakdown while the major part of the membrane can still function normally. The inhomogeneity of deformation field leads to the consequence that the membrane does not function efficiently, which results in material waste.
3.This part explores the potential modes of failure when the electro-active polymer membrane is subjected to a voltage and a force.The equations of equilibrium of the system are derived by thermodynamics and the criterions for each mode of failure are specified. Using these criterions, we obtain the allowed range of the force and the voltage. In addition, numerical results indicate that pre-stretch may reduce the inhomogeneity. If the design parameters of actuator are chosen suitably, the true electrical field in the membrane may tend to be homogeneous,which may greatly improve the efficiency of the material.
The results presented in this paper could provide some guidelines for optimizing the design of such kind commercial actuators.
1.基于非线性弹性大变形理论建立了圆环形薄膜在外力作用下的力学模型,研究了一圆环状弹性薄膜的轴对称面外大变形。在未发生变形的参考构形下,平直的圆环状的薄膜的内边界连接一个圆盘,将薄膜的外边界固定在刚性的圆环上。当圆盘上作用一个竖直向下的外力时,薄膜经历面外大变形后形成轴对称的形状。结合状态平衡和热力学,推导得到了描述薄膜经历面外大变形的控制方程。采用了打靶法对控制方程进行求解,得到了薄膜在经历面外大变形时,薄膜内应力场和应变场的分布规律,可以看出薄膜的变形是非常不均匀的,这意味着薄膜在工作时材料的利用率较低,造成了材料的浪费。同时,本章的研究成果从基本理论和计算方法为本文后续的研究工作做了必要的铺垫。
2.以电活性聚合物作动器的基本结构建立的力学模型为基础探讨了电活性聚合物薄膜在力电荷载共同作用下的面外非线性轴对称大变形。利用非线性弹性大变形理论并结合热力学的基本理论,推导得到了圆环形薄膜在受力电载荷作用时产生面外大变形的控制方程,采用打靶法对控制方程进行了数值求解,得到了电活性聚合物薄膜受到力电荷载共同作用时,薄膜内的应力场、应变场和电场的分布规律,结果表明,圆环形薄膜的变形是非常不均匀的,在靠近圆环中心处的薄膜变形较大,而靠近圆环边缘处的薄膜变形较小,导致薄膜中的电场从外向内逐渐变大,从而使得靠近圆环中心处的薄膜处于电击穿的边缘,可能导致的结果是大部分薄膜还可正常工作的时候,处在场强高的某点处的薄膜已经失效。变形场的非均匀性导致薄膜内的大部分材料并没有被有效地利用,造成了材料的浪费。
3.以电活性聚合物作动器简化后的模型为基础,利用热力学基本原理推导得到了系统的控制方程,探讨了作动器在工作中可能存在的失效模式,并给出了各种失效模式的判断准则。本章利用这些准则在给定的条件下,得到了施加在作动器上外力F和电压Φ的有效工作区间。另外,计算结果在作动器工作前对薄膜进行预拉伸,这样可以明显的减小变形后薄膜内电场的不均匀分布的程度,如果作动器的设计参数选择适当,可以达到电场在薄膜中呈现均匀分布的状态,大大提高了材料的利用率。
本文的研究结果对弹性聚合物的基本研究方法及商业化产品的优化设计具有实际的借鉴与指导意义。
Since 1990's, in the family of electro-active polymers, one kind of special soft smart materials, that is dielectric elastomer, has received considerable attention among researchers and engineers due to its many outstanding mechanical attributes such as large strain, fast response, high efficiency etc.when it is subject to a voltage. These attributes make dielectric elastomer promising for applications as transducers such as actuators, sensors and energy harvesters.The essential part of dielectric elastomer transducers is a dielectric membrane sandwiched between two compliant electrodes.Subject to a voltage, the dielectric membrane reduces its thickness and expands its area, converting electrical energy into mechanical energy. Due to large deformation, nonlinear equations of state, and complicated loads, modeling the electro-mechanical response for dielectric elastomer transducers has been challenging. The main contents of this thesis are as follows:
1.The axisymmetric out-of plane nonlinear deformation of an annular elastic membrane is studied in the frame of nonlinear elastic deformation theory. The membrane is initially flat and attached to a disk in the inner circle and to a rigid ring in the outer circle, then a weight is applied to the disk and the membrane deforms into an axisymmetric shape, undergoing large out-of-plane deformation.The governing equations characterizing the out-of plane large deformation of the elastic membrane are derived by combining state equilibrium and thermodynamics.The derived governing equations are solved by using shooting method. The obtained results show that the deformation field in the membrane is very inhomogeneous.This indicates that the membrane doesn't function efficiently, which leads to a material waste.The theory and method presented in this section provide some basic outlines for the problem discussed in the next section.
2.This part focuses on investigating the axisymmetric out-of plane nonlinear deformation of an actuator made of electro-active polymer membrane.The mechanical model describing the axisymmetric nonlinear deformation of such annular membrane is formulated, and the equations of equilibrium state characterizing the large deformation of the annular membrane subject to a concentrated force and a voltage are derived by thermodynamics.The derived state equations are solved by using shooting method and the distributions of true stress fields,stretches and true electrical fields are obtained numerically. The obtained numerical results show that the deformation field in the membrane is highly inhomogeneous.The deformation near the central part of the membrane is large while the deformation near the edge of the membrane is small, which leads to the induced electric field in the membrane increases monotonically from the edge to the central part and reaches maximum at the central part of the membrane. This results in the consequence that the membrane near the central part risks the possibility of electric breakdown while the major part of the membrane can still function normally. The inhomogeneity of deformation field leads to the consequence that the membrane does not function efficiently, which results in material waste.
3.This part explores the potential modes of failure when the electro-active polymer membrane is subjected to a voltage and a force.The equations of equilibrium of the system are derived by thermodynamics and the criterions for each mode of failure are specified. Using these criterions, we obtain the allowed range of the force and the voltage. In addition, numerical results indicate that pre-stretch may reduce the inhomogeneity. If the design parameters of actuator are chosen suitably, the true electrical field in the membrane may tend to be homogeneous,which may greatly improve the efficiency of the material.
The results presented in this paper could provide some guidelines for optimizing the design of such kind commercial actuators.
引文
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[2]Ashley S..Artificial Muscles.Scientific American,2003,10:53-59.
[3]Kofod G.. Dielectric elastomer actuators[Ph.D].Pitney Bowes Management Services Denmark A/S.2001.
[4]Pelrine R.E.,Kornbluh R.D and Joseph J.P.. Electrostriction of polymer dielectrics with compliant electrodes as a means of actuation. Sensors and Actuators A-Physical,1998,64:77-85.
[5]Pelrine R.E.,Kornbluh R.D.and Pei Q.et al.High speed electrically actuated elastomers with stretch greater than 100%.Science,2000,287:836-839.
[6]Carpi F.,Rossi D.D. and Kornbluh R. et al. Dielectric elastomers as electromechanical transducers:Fundamentals, materials, devices, models and applications of an emerging electroactive polymer technology. Elsevier, UK,2008.
[7]Bar-Cohen Y.,Breazeal C..Biologically inspired intelligent robotics.In: Proceedings of the SPIE Smart Structures and Materials Symposium. San Diego, CA,2003.14-28.
[8]Zhenyi M.,Scheinbeim J.L. and Lee J.W. et al.High field electrostrictive response of polymer. Journal of Polymer Science, Part B:Polymer Physics,1994, 32:2721-2731.
[9]Kornbluh R.,Eckerle J.and Andeen G.Artificial muscle:the next generation of robotic actuators.In:4th World Conference of Robotics Research, Pittsburgh, PA,1991.
[10]Niino T.,Egawa S.and Kimura H..Electrostatic artificial muscle:compact, high-power linear actuators with multiple-layer structures.In:Proceeding of the IEEE Micro Electro Mechanical Systems Workshop,Oiso,Japan,1994:130-135.
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