纯剪切模式介电弹性体发电机发电特性
介电弹性体卷形换能器设计与参数优化
ｃｏｒｒｅｓｐｏｎｄｉｎｇ ｓｉｍｕｌａｔｉｏｎ ｍｏｄｅｌ ｗａｓ ｓｅｔ ｕｐ ｉｎ Ｍ ａｔｌａｂ／Ｓｉｍ ｕｌｉｎｋ ｅｎｖｉｒｏｎｍ ｅｎｔ． Ｔｈｅ ｓｉｍ ｕｌａｔｉｏｎ ｒｅｓｅａｒｃｈ ｏｆ ｔｈｅ ｐｏｗｅｒ ｇｅｎｅｒａｔｉｏｎ ｃｈａｒａｃｔｅｒｉｓｔｉｃｓ ｏｆ ｄｉｅｌｅｃｔｒｉｃ ｅｌａｓｔｏｍｅｒ ｔｒａｎｓｄｕｃｅｒ ａｎｄ ｔｈｅ ｉｎｆｌｕｅｎｃｅ ｏｆ ｄｉｆｆｅｒｅｎｔ ｓｐｒｉｎｇ ｃｏｅｆｌｆｉｃｉｅｎｔｓ ｏｎ ｉｔｓ ｇｅｎｅｒａｔｉｏｎ ｃｈａｒａｃｔｅｒｉｓｔｉｃｓ ｗｅｒｅ ｃａｒｒｉｅｄ ｏｕｔ． Ｔｈｅ ｅｘｐｅｒｉｍｅｎｔａ１ ｒｅｓｅａｒｃｈ ｗａｓ ｄｏｎｅ ｂｙ ｍ ａｋｉｎｇ ｄｉｅｌｅｃｔｒｉｃ ｅｌａｓｔｏｍｅｒ ｒｏｌｌ ｔｒａｎｓｄｕｃｅｒ，ａｎｄ ｃｏｍｐａｒｅｄ ｗｉｔｈ ｔｈｅ ｓｉｍｕｌａｔｉｏｎ ｒｅｓｕｌｔｓ．Ｔｈｅ ｓｉｍｕｌａｔｉｏｎ ａｎｄ ｔｅｓｔ ｒｅｓｕｌｔｓ ｓｈｏｗｅｄ ｔｈａｔ ｔｈｅ ｐｏｗｅｒ ｃｈａｒａｃｔｅｒｉｓｔｉｃｓ ｏｆ ｄｉｅｌｅｃｔｒｉｃ ｅｌａｓｔｏｍ ｅｒ ｒｏｌｌ ｔｒａｎｓｄｕｃｅｒ ｗｅｒｅ ｈｉｇｈｅｒ ｔｈａｎ ｔｈｏｓｅ ｏｆ ｔｈｅ ｇｅｎｅｒａｌ ｔｅｎｓｉｌｅ ｍｏｄｅ ｔｒａｎｓｄｕｃｅｒ． Ｕｎｄｅｒ ｔｈｅ ｓａｍｅ ｃｏｎｄｉｔｉｏｎ ｏｆ ｔｅｎｓｉｌｅ ｍｏｄｅ． ｉｎｉｔｉａｌ ｖｏｌｔａｇｅ ａｎｄ ｔｈｅ ｐｒｅｓｔｒｅｔｃｈ ｌｉｍｉｔａｔｉｏｎｓ． ｔｈｅ ｐｏｗｅｒ ｃｈａｒａｃｔｅｒｉｓｔｉｃ ｗａｓ ｉｎｅｒｅａｓｅｄ ｗｉｔｈ ｔｈｅ ｉｎｃｒｅａｓｅ ｏｆ ｅｌａｓｔｉｃ ｃｏｅｆｆｉｃｉｅｎｔ． Ｔｈｅ ａｂｏｖｅ ｒｅｓｕｌｔｓ ａｂｏｕｔ ｄｉｅｌｅｃｔｒｉｃ ｅｌａｓｔｏｍ ｅｒ ｒｏｌｌ ｔｒａｎｓｄｕｃｅｒ ｐｒｏｖｉｄｅｄ ｔｈｅｏｒｅｔｉｃａｌ ｒｅｆｅｒｅｎｃｅ ｆｏｒ ａｐｐｌｉｃａｔｉｏｎｓ ｏｆ ｄｉｅｌｅｃｔｒｉｃ ｅｌａｓｔｏｍ ｅｒ ｇｅｎｅｒａｔｏｒｓ ｉｎ ｔｈｅ ｆｉｅｌｄ ｏｆ ｖｉｂｒａｔｉｏｎ ｅｎｅｒｇｙ ｈａｒｖｅｓｔｉｎｇ ｉｎ ｔｈｅ ｆｕｔｕｒｅ． Ｋ ｅｙ ｗ ｏｒｄｓ：ｄｉｅｌｅｃｔｒｉｃ ｅｌａｓｔｏｍ ｅｒ； ｒｏｌｌ ｔｒａｎｓｄｕｃｅｒ；ｐｕｒｅ ｓｈｅａｒ； ｓｐｒｉｎｇ； ｅｌｅｃｔｒｏｍｅｃｈａｎｉｃａｌ ｃｏｕｐｌｉｎｇ ｍｏｄｅ
介电弹性体发电实验研究
图３ 实验测试电路原理图 ４实验及 结果分 析 ． 介电弹性体材料 的发 电利 用了可变电容原理 ，当外力作用在具有 预加 电场的介电弹性体材料上使其 变形时 ， 改变 电容 即可发电 ， 因此 弹 性体材料面积的改变将对发 电量产生影响 。图 ４为在其 他条件相 同的 前提下 ， 电极覆盖弹性体材料面积分别 为 １ ｅ ２ ５ｍ ，５ｍ 时 的实验 ５ｒ ， ｃ ｃ ａ ２ ３ 结果 。在 实验中 ， 泄放电阻 为 ２ 偏置 电压 为 １０ Ｖ 材料 拉伸后 为原 Ｇ， ００ ， 始材料长度 的 ３ ， 倍 通过实验得 出 ： ） （ 材料 面积为 １ｃ ， 出电压 ａ ５ｍ 时 输 高于偏置 电压 ８ Ｖ （ ） ０ ；ｂ 材料面积为 ２ ｃ ２ 输 出电压高 于偏 置电压约 ５ ｍ 时， 为 １０ ； ） ３ Ｖ （ 材料面积为 ３ｃ ２ ， ｃ ５ ｍ 时 输出电压高于偏置电压约 为２ ５ 。由 ２Ｖ 实验数据可知 ， 当拉伸量一定 时， 出电荷 电压 与材料 面积成 正比。 输
研 究。
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４ ．— ０ ． ． —
科技信息
博 士 ・ 家论 坛 专
住宅在建筑之前找过 风水 师看过风水 ， 住宅及 院落的主体位置 、 与 周 围关系 、 动土 时间等 的确定都是根据风水先生的要求 房屋建成之后 也请 风水先 生过 目， 并做相应 的法事。在“ 进屋 ” 前按 照习俗摆酒设宴 。 南北两 面墙 正对房 屋门 口的位 置 ， 墙高逐渐升高 ， 风水上有“ 在 挡煞 ” 的 寓 意。 ４、 应对海南气候条件的住宅特征分析 ４１海南 台风概 况 ． 由于海南岛地理位置的特殊性 ， 平均 每年 至少都会遇见一 次台风 ， 素来有 “ 台风走廊 ” 称 。据 １ ５ ～ ０ ３ 气象 资料统 计 ， 之 ９ ０ ２０ 年 海南 岛 自 １５ ９０年以来共发生有危害 的台风 ８ ４次 ， 平均每年 １ ８次 ； ． ５ 多年平均影 响海南的台风有 ７７次 ， ． 年均登 陆 ２ ． ６次。大部分 台风都是 从海南岛的
介电弹性体发电机自偏置机理研究
介电弹性体发电机自偏置机理研究介电弹性体发电机自偏置机理研究引言：随着能源需求的不断增长和能源危机的逼近，人们对可再生能源的研究越来越重视。
近年来，介电弹性体发电技术逐渐受到关注。
介电弹性体是一种具有特殊电与机械性能的材料，利用其特性可转化为电能。
介电弹性体发电机是一种利用介电弹性体的变形产生电能的装置。
本文旨在探索介电弹性体发电机自偏置的机理，进而提高其发电效率。
1. 介电弹性体发电机的原理介电弹性体发电机利用介电材料的变形产生电能。
当施加外力或者机械变形于介电材料时，产生应变，由于介电材料的电弹性效应，引起材料内部电势的变化。
这种内部电势变化将导致电荷的分离和积累，从而产生电流。
通过外部电路连接收集电荷并驱动电子设备或储存电能。
2. 介电弹性体发电机的自偏置现象自偏置现象是指介电弹性体发电机在没有施加外力的情况下仍能够产生电能的特性。
这是由于介电弹性体本身具有的非线性特性导致的。
在没有施加外力的情况下，介电弹性体发电机的内部电势处于平衡状态，电荷均匀分布。
但是当介电弹性体发电机被扭曲或施加机械压力时，介电弹性体发生变形，电势变化导致内部电荷的分离。
一旦外力移除，介电弹性体会返回原始形状，但电荷分布却不会完全恢复平衡状态，而是在一定程度上保持分离状态。
这种分离状态预先生成的电场和电势差引发了自偏置现象。
3. 自偏置机理的探究自偏置机理的探究对于进一步提高介电弹性体发电机的效率至关重要。
（1）晶格缺陷理论：晶格缺陷是介电弹性体内部自偏置现象的重要因素。
介电弹性体中晶格缺陷的产生和储存是通过超过材料内部弹性极限引起的。
晶格缺陷的产生会克服晶体的结构稳定性，因此产生电荷的能力也更大。
这个过程通常需要一定的时间来存储电荷。
（2）电迁移现象：电迁移现象是另一个影响自偏置机理的因素。
当电荷分离状态产生时，电荷首先从导电层向非导电层迁移。
电迁移速率取决于介电材料内部化学成分、材料的电导率和电场强度。
电迁移现象与晶格缺陷理论共同作用，共同影响自偏置机理。
基于Neo-Hooken的介电弹性体单轴拉伸发电特性研究
农 业 机 械 学 报
ｄｏｉ：１０．６０４１／ｊ．ｉｓｓｎ．１０００—１２９８．２０１６．０３．０５５
第４７卷第３期
基
的介 电弹性体 单轴拉伸发 电刘 爱 飞 金 丽 丽 江 孝 琪
（浙 江 师 范 大 学 工 学 院 ，金 华 ３２１０００）
ｅｌｅｃｔｒｏｍ ｅｃｈａｎｉｃａｌ ｃｏｕｐｌｉｎｇ ｍｏｄｅｌ
引 言
介 电 弹 性 体 发 电 机 （Ｄｉｅｌｅｃｔｒｉｃ ｅｌａｓｔｏｍｅｒ ｇｅｎｅｒａｔｏｒ，ＤＥＧ）是 一种 基于 可变 电容原 理 的新 型 微
发 电机 … ，其 三层 式构 造 的 中问层 为 介 电弹性 体 材 料 （ＤＥ）。作 为一 种 新 型 智 能材 料 ，ＤＥ具 有超 大 变 形 、高 理论 比能量 密 度 、高 效 率 、超 短 反 应 时 间及 高 疲 劳 寿命 等特 点 。众 多研究 表 明 ，ＤＥ既是 一 种
Ｐｏｗｅｒ Ｇｅｎｅｒａｔｉｎｇ Ｃｈａｒａｃｔｅｒｉｓｔｉｃｓ ｏｆ Ｕｎｉａｘｉａｌ Ｔｅｎｓｉｌｅ ｆｏｒ ＤＥＧ Ｂａｓｅｄ ｏｎ Ｎｅｏ ——Ｈ ｏｏｋｅｎ Ｍ ｏｄｅｉ
Ｃａｏ Ｊｉａｎｂｏ Ｇｅ Ｃａｉｊｕｎ Ｅ Ｓｈｉｊｕ Ｌｉｕ Ａｉｆｅｉ Ｊｉｎ Ｌｉｌｉ Ｊｉａｎｇ Ｘｉａｏｑｉ
摘 要 ：为研 究 介 电 弹性 体 发 电机 （ＤＥＧ）在 单 轴 拉 伸 下 的发 电特 性 ，结 合 Ｎｅｏ—Ｈｏｏｋｅｎ模 型建 立 了 ＤＥＧ在 单 轴 拉 伸 下 的 机 电 耦 合 数 学 模 型 ，运 用 Ｍａｔｌａｂ／Ｓｉｍｕｌｉｎｋ软 件 建 立 了 ＤＥＧ 的 单 轴 发 电仿 真 模 型 ，对 ＤＥＧ 的 发 电过 程 及 拉 伸 力 、拉 伸 率 、初 始 电压 与 电势 差 之 间 的关 系进 行 了仿 真研 究 ，通 过 搭 建 ＤＥＧ发 电 测 试 试 验 台 ，进 行 了 试 验 研 究 并 与 仿 真 结果 进 行 对 比 。仿 真 和试 验 结 果 表 明在 单 轴 拉 伸 收 缩 发 电过 程 中 ，ＤＥＧ两 端 电 压 先 降 后 升 ；在 初 始 拉 伸 时 和 即将 拉 伸 至最 大 时 电压 有 两 个 突变 点 ；电 势 差 随 着 初 始 电压 、拉 伸 力 的增 加 而近 似线 性 增 加 。 关 键 词 ：介 电 弹 性 体 发 电 机 ；单 轴 拉 伸 ；发 电 机 理 ；机 电耦 合 模 型 中 图分 类 号 ：ＴＢ３８１ 文献 标 识 码 ：Ａ 文 章 编 号 ：１０００．１２９８（２０１６）０３—０３８９－０６
介电弹性体性能分析及应变模拟
中国科学技术大学硕士学位论文表卜１ＥＡＰ，ＳＭｇＥＡｃ的性能比较表特性电敏感聚合物（ＥＡＰ）形状记忆合金（ＳＭＡ）电敏感陶瓷（ＥＡＣ）致动应变＞１０％＜８％短疲劳寿命０．１．０．３％应力（ＭＰａ）０．１－３大约７００３０－４０响应速度微秒（／ａｓ）到秒秒（ｓ）到分钟（ｍｉｎ）微秒（卢ｓ）到秒（ｓ）密度１－２．５９／ｃｃ５－６９／ｃｃ６－８９／ｃｃ。
驱动电压２Ｖ：６ＫＶＮＡ５０，８００Ｖ消耗能量毫瓦瓦瓦断裂韧度弹性的弹性的脆弱的电敏感聚合物材料的性能吸引了许多不同学科的工程师和科学家的注意。
ＥＡＰ的人工肌肉概念可以应用在仿生动物和生物的运动上，这也大大激励了仿生学的开创者。
在可预知的将来，ＥＡＰ驱动的机器人机构将使工程师能够创造出只有在科幻小说中才能出现的设备。
在２００３年，已经报道了巨大的成就，其中包括第一个商用产品的出现以及可能使用ＥＡＰ制作出的手臂，它有望胜过人类手臂。
一个这样的商用产品已经在２００２年１２月出现了，它是日本Ｅａｍｅｘ公司的机器鱼，如图１．１所示。
没有电池或者发动机，它也可以游泳，它使用了对激励弯曲的ＥＡＰ材料。
它使用感应卷来提供能量，该能量卷从上到下绕满了鱼槽并施加了电压。
这种机器鱼是该领域的一座里程碑，因为它是第一例报道过的使用电敏感材料致动器的商用产品。
图ｌ一１第一个商用的ＥＡＰ产品一机器鱼中国科学技术大学硕士学位论文图１．２是一个离子ＥＡＰ的响应例子。
在图１－２中，一个海星形状的ＩＰＭＣ（离子聚合物一金属合成物）显示了明显的弯曲。
弯曲方向依赖于电压极性。
图ｌ－２ＩＰ眦多指海星最值得一提的是在２００４年美国新墨西哥州举行的ＥＡＰＡＤ会议的ＥＡＰ．ｉｎ－Ａｃｔｉｏｎ会议上，美国环境机器人公司展示了ＥＡＰ驱动的角力手臂，如图１－３所示。
这种角力手臂有和人类平均手臂的一样的大小和形状，它使用传导聚丙烯腈ＥＡＰ来驱动。
这种ＥＡＰ材料在实验中产生了近乎２００％的线性应变以及比人类肌肉还要大的力量。
基于Neo-Hooken的介电弹性体单轴拉伸发电特性研究
基于Neo-Hooken的介电弹性体单轴拉伸发电特性研究曹建波;葛彩军;鄂世举;刘爱飞;金丽丽;江孝琪【摘要】为研究介电弹性体发电机(DEG)在单轴拉伸下的发电特性,结合Neo-Hooken模型建立了DEG在单轴拉伸下的机电耦合数学模型,运用Matlab/Simulink软件建立了DEG的单轴发电仿真模型,对DEG的发电过程及拉伸力、拉伸率、初始电压与电势差之间的关系进行了仿真研究,通过搭建DEG发电测试试验台,进行了试验研究并与仿真结果进行对比.仿真和试验结果表明在单轴拉伸收缩发电过程中,DEG两端电压先降后升;在初始拉伸时和即将拉伸至最大时电压有两个突变点;电势差随着初始电压、拉伸力的增加而近似线性增加.【期刊名称】《农业机械学报》【年(卷),期】2016(047)003【总页数】6页(P389-394)【关键词】介电弹性体发电机;单轴拉伸;发电机理;机电耦合模型【作者】曹建波;葛彩军;鄂世举;刘爱飞;金丽丽;江孝琪【作者单位】浙江师范大学工学院,金华 321000;浙江师范大学工学院,金华321000;浙江师范大学工学院,金华 321000;浙江师范大学工学院,金华 321000;浙江师范大学工学院,金华 321000;浙江师范大学工学院,金华 321000【正文语种】中文【中图分类】TB381介电弹性体发电机(Dielectric elastomer generator, DEG)是一种基于可变电容原理的新型微发电机[1]，其三层式构造的中间层为介电弹性体材料(DE)。
作为一种新型智能材料，DE具有超大变形、高理论比能量密度、高效率、超短反应时间及高疲劳寿命等特点[2-4]。
众多研究表明，DE既是一种良好的仿生驱动材料[5-7]，也可逆向应用于发电领域，可以用来构造形式多样、成本低廉的新型发电机，在可再生能源发电及微机电系统等领域将具有广阔的应用前景[8-11]。
国内外学者对DEG发电特性展开了相关研究[1,12-14]，但大多只给出了DEG的单轴、双轴拉伸力学模型，未与电学模型相结合，且推导过程较为简略，未对所得模型进行试验验证。
介电弹性体发电原理分析及应用
介电弹性体发电原理分析及应用作者：刘志运周芸悦来源：《机电信息》2021年第17期摘要：介电弹性体（Dielectric Elastomer，DE）是一种电活性聚合物，是一种表现出对电场响应的大应变材料。
现介绍了介电弹性体中基质材料的结构特性，并详细分析了介电弹性体发电的基本原理、发电技术及其相比现有传统发电技术所具备的优势。
根据近年来人们对介电弹性体的研究，总结并提出了介电弹性体未来发展中可能存在的问题以及应用前景。
关键词：介电弹性体;发电原理;应用0 引言介电弹性体研究自20世纪90年代中期开始，作为一类重要的功能材料，介电弹性体各方面已得到各国学者广泛研究，如非线性光学、铁电、压电元件和电致伸缩性等。
近年来，通过改变形状来响应磁场、电场、压力等外部刺激的聚合物研究越来越多，电活性聚合物可能是被研究最多的一类，介电弹性体作为电活性聚合物的一种，具有张力大、工作原理简单的特点。
介电弹性体在外部电场的刺激下可改变其结构形状或体积。
当物体外部承受电能的刺激动作停止时，即可自动恢复或回到原来的物体形状或缩小体积，从而自动产生机械应力和运动应变，将外部电能自动转化为电动机械的性能，机电转换效率高。
1 介电弹性体中基质材料的结构特征1.1 聚丙烯酸酯类弹性体聚丙烯酸酯弹性体，一种由丙烯酸乙酯和其他丙烯酸酯共聚而成的合成橡胶，外加少量（约5%）另一种含有活泼鹵素的化合物，如氯，用于弹性体的其他丙烯酸酯包括丙烯酸正丁酯、丙烯酸甲氧乙酯和丙烯酸乙酯，这些化合物具有良好的耐热、耐臭氧、耐光和耐油性[1]。
目前，使用最广泛的以丙烯酸酯为基础的DES是商用丙烯酸酯材料，如3M商用胶带VHB 4910和VHB 4905。
亚克力材料因其低廉的价格、优异的性能、对顺应电极的良好附着力等优点而受到许多研究者的青睐。
在高预应变水平下，亚克力材料的最大应力和驱动应变分别达到7.7 MPa和380%，预拉伸后亚克力材料的电击穿强度达到了空前的水平[2]。
介电弹性体
Synthesizing a New Dielectric Elastomer Exhibiting Large Actuation Strain and Suppressed Electromechanical Instability without PrestretchingXiaofan Niu,Hristiyan Stoyanov,Wei Hu,Ruby Leo,Paul Brochu,Qibing PeiDepartment of Materials Science and Engineering,University of California,Los Angeles(UCLA),420Westwood Plaza, 3111Engineering V,Los Angeles,California90095Correspondence to:Q.Pei(E-mail:qpei@)Received6September2012;accepted1October2012;published online19October2012DOI:10.1002/polb.23197ABSTRACT:Prestrain provides high actuation performance in dielectric elastomers(DEs)but increases the bulk,mass,and fa-tigue of the resulting actuators.Based on our experiments on prestrain-locked interpenetrating polymer films and the model developed by Zhao and Suo,materials with a certain stress–strain relationship should be capable of high strain without pre-strain by suppressing electromechanical instability(EMI).Here, we report the synthesis of an acrylic elastomer capable of achieving high actuation performance without prestrain.DE films were directly fabricated by ultraviolet curing of precursors comprising a mixture of acrylate comonomers.Varying the amount of crosslinker comonomer in the precursor allowed us to tune the stress–strain relationship and completely suppress EMI while maintaining high strain performance.Addition of plasticizing agents increased strain sensitivity.The result is a new DE,synthesized from scratch,capable of high actuation strain(>100%),high energy density(>1J gÀ1),and good tem-perature and frequency response without requiring prestretch-ing.The material can be fabricated using conventional coating techniques and the process can allow for high volume through-put of stacked DE actuators.V C2012Wiley Periodicals,Inc. J.Polym.Sci.,Part B:Polym.Phys.2013,51,197–206KEYWORDS:actuation;crosslinker;crosslinking;dielectric elas-tomer;dielectric properties;elastomers;electromechanical instability;prestrain-freeINTRODUCTION Dielectric elastomers(DEs)are a new kind of smart material that can provide efficient electrical–me-chanical energy transduction.1–4Often referred to as artificial muscles,DE actuators(DEAs)have the advantages of large electromechanical strain,high energy density,high coupling efficiency,relatively fast response speed,light weight,and silent operation.The potential for DEAs to mimic or provide better performance than human muscles is quite promis-ing.2,5In recent years,many novel applications based on DEAs have emerged,such as robotics,6diffraction gratings,7 vibration control,8and haptic feedback.9,10The first commer-cially available product made utilizing a DEA,a haptic feed-back accessory for mobile devices,has been released by Arti-ficial Muscle recently.11Although the DEA community has significantly grown,the selection of materials is rather limited.One of the two most widely used DE materials is a commercial product of3M,the VHB TM series acrylic elastomeric tape,manufactured for gen-eral industrial adhesion applications.Highly prestretched VHB films provide excellent actuation strain and energy den-sity,1but suffer from viscoelastic losses.12Attempts to mod-ify this system include forming a second interpenetrating polymer network(IPN)to maintain the prestrain needed for good actuation performance.13Further improvements are considered difficult because the crosslinked elastomer net-work in VHB has already been formed in the commercial product.Silicone elastomers,the other widely used DE mate-rial,are available from various suppliers in one or two parts before curing.Because of better known structures and cur-ing mechanisms,many modifications can be done to silicone elastomers such as blending with high permittivity nanofil-lers14,15and grafting with high polarity side groups.16DE materials also include preswollen thermoplastic gels (TPEG),17PVDF-TrFE copolymers,18and acrylonitrile butadi-ene synthetic rubber.19A general protocol during employment of most DE materi-als to obtain actuation strains greater than33%is pre-stretching.1,20It is known to suppress the electromechani-cal instability(EMI)of the elastomeric material when being actuated and improve its breakdown strength and energy density.20–23However,prestretching complicates the device structure,limits the application,and lowers the lifetime of DEAs because of the stress relaxation and fa-tigue in the biaxially prestretched material as well as the stress concentration along the rigid frame supporting the prestrain.Additional Supporting Information may be found in the online version of this article. V C2012Wiley Periodicals,Inc.The use of material approaches that produce similar or better actuation performance as highly prestretched DEAs but with-out the requirement of prestretching has been an important topic in the DE research field and a pressing issue for the commercialization of DEAs.UV curing of formulated acrylates is known as an effective method for fabricating high-perform-ance coatings,inks,and adhesives.24We found it also well suited for designing new DEs because,first of all,the formula-tion can be adjusted with almost limitless possibilities to achieve materials ranging from extremely soft or gel-like elas-tomers,to rigid,scratch-resist materials.Second,the deploy-ment of such materials can be easily accomplished by indus-trial thin film coating techniques such as blade coating,slot die coating,and spin coating.The form factor of cured materi-als(thin films with a few to tens of micrometers thickness) meets the requirement of DEs.The ability to tune the compo-sition also allows for an adjustable adhesion between different layers of coatings,which will ease the fabrication of DE devi-ces,such as multilayer stack DEA.25Here,we report the syn-thesis of a new series of DEs fabricated from UV radiation po-lymerization(UV-DE).By customizing the crosslink density in the material and using a plasticizer,we are able to adjust its mechanical as well as electromechanical properties to achieve either stable large strain snap-through or a total suppression of EMI.22No prestretching is required during either the fabri-cation or application of the material to achieve high-perform-ance actuation.The electromechanical behavior of the material can be well explained by the thermodynamic theory intro-duced by Zhao and Suo for large-strain deformation.The rapid stiffening of the material above a certain stretch ratio is found critical for overcoming EMI.EXPERIMENTALChemicals and Prepolymer SolutionsCN9021(difunctional acrylic esters resin),isodecyl acrylate (IDA),isobornyl acrylate(IBOA),trimethylolpropane triacry-late(TMPTA),1,6-hexanediol diacrylate(HDDA),and dibu-toxyethoxyethyl formal(DBEF)were obtained from Sartomer Company and used as received.2,2-Dimethoxy-2-phenylace-tophenone(DMPA)and benzophenone(BP)were purchased from Acros and used as received.The acrylate monomers and a photoinitiator were mixed thoroughly by mechanical stirring to form a homogeneous prepolymer solution. Elastomer Film PreparationTwo methods were used to prepare elastomer films for ten-sile and actuation tests.For tensile stress–strain tests,a pre-polymer solution was coated on a Teflon plate with a con-trolled thickness by a doctor’s blade.Then,it was cured on a UV curing conveyor equipped with a 2.5W cmÀ2Fusion 300S type‘‘H’’UV curing bulb,at a speed of6.0feet per mi-nute for two passes.The film was gently peeled off.For actuation tests,the prepolymer solution was spin-coated onto a plastic Petri dish at a speed of800rpm for18s and then cured under the same conditions mentioned above.Car-bon grease(NyoGel756G,Nye Lubricants)was smeared onto both sides of the films as compliant electrodes.The3M VHB material was used as a reference material in our study and was referred to as VHB4905.Similarly,the modified VHB material with IPN was fabricated as reported previously13and was referred to as IPN4905.Tensile TestsType IV dumbbell-shaped samples were made with a cutting die,defined in ISO37.Tensile tests were carried out on a TA RSA3dynamic mechanical analyzer(DMA)at a strain rate of 3.33mm sÀ1.At least three repetitive samples were tested for each formulation.Dynamic Mechanical AnalysisThe dynamic mechanical properties,including loss factor(tan d),of the elastomer films were measured with a TA RSA3 DMA.Samples with a measured thickness of around0.3mm were cut in10-mm wide strips with a razor blade and loaded onto the equipment with a15-mm gap between the thin film grips.All tests were carried out at1Hz frequency,<2% strain,and a temperature ramping rate of7 C minÀ1. Actuation TestsThe electroded elastomer films were attached to a diaphragm chamber made of aluminum with a10-mm circular opening onto which the thin DE films were mounted.A bias air pres-sure of2.5Torr was applied such that when the DE films were actuated,they deform out of plane to form a raised dome shape.The active area of the DE films was flat and circular with a diameter of6.35mm(before actuation).A high-voltage power supply fabricated in-house was used to drive the actua-tors.A digital camcorder was used to record the actuation pro-cess.The actuation strain was measured from the video frame-by-frame and calculated by an equation already reported.13 The strain values for a particular voltage were taken after the constant driving voltage has been applied for5s.The nominal electric field was calculated by dividing the applied voltage by the initial thickness of the elastomer film.The breakdown field was calculated by dividing the applied voltage by the instanta-neous thickness of the elastomer film at maximum strain.At least three repetitive samples were tested for each formulation. Permittivity MeasurementElastomer films of known thickness were coated with silver grease(MGChemicals,Cat.No.8463)to form circular electro-des with a diameter of12.7mm.Capacitance was measured using a GwInstek LCR-819LCR meter at1V excitation and 12Hz frequency.Relative permittivity e of the materials was calculated by:e¼Cz=e0A;(1) where C is the measured capacitance,z is the thickness of the elastomer film,e0is the vacuum permittivity,and A is the effective area.RESULTS AND DISCUSSIONGeneral Guidelines Designing UV-DEThe electrically driven strain in DEs is produced by the elec-trostatic force of free charges on the electrodes.The actua-tion(or Maxwell)pressure(p)is given by:p¼e0e E2¼e0eðV=zÞ2(2) where E is the applied electric field,which is equal to the applied voltage V divided by thickness z.1The electrome-chanical strain can be estimated,using a linear assumption for the elasticity of material,by:s z¼Àp=Y¼Àe0eðV=zÞ2=Y(3)s A¼1=ð1þs zÞÀ1(4) where s z is the strain in the thickness direction,s A is the area strain,and Y is the modulus of the elastomer.1Because of the nonlinearity of the elastomer,the modulus of the elas-tomer changes along with stretching.The apparent modulus of the elastomer at the actuation strain should be used to calculate the strain.Therefore,the actual performance of DEAs is determined by a few factors:the hyperelastic stress–strain response(stiff-ness–strain relationship),stretchability(elongation at break and reversibility),the macroscopic permittivity(dielectric constant)of the polymer,and dielectric breakdown strength (the maximum field applied without causing arcing).These parameters govern material selection and processing.Viscoe-lasticity or dynamic mechanical loss factor plays a key role in response speed and energy efficiency.Most DE materials investigated so far exhibit EMI,or pull-in failure,at an elec-tric field much lower than the polymers’intrinsic breakdown field strength or actuation performance potential.With these considerations in mind,we formulated DE pre-cursor solutions containing a prepolymer(oligomer),reac-tive diluents,photoinitiators,and other additives.In gen-eral,the oligomer,or a blend of a few oligomers,is selected as the framework responsible for the basic mechanical properties of the material system.Reactive diluents,includ-ing monofunctional and/or multifunctional acrylates,are used to adjust rheology,provide crosslinking,and precisely tune the mechanical properties of the material.Photoinitia-tors are used to initialize the polymerization.Additives can be added into the precursor solutions when special require-ments must be met.Table1summarizes the formulations screened in this work.Here,CN9021acrylic ester resin was chosen as the oligomer.It is a urethane acrylate compound comprising a flexible polyether diol segment,a relatively flexible aliphatic diisocyanate segment in its structure,and a high molecular weight.The resulting homopolymer of CN9021has high flexibility,low modulus,and is moisture resist.26DMPA and BP were synergistically used as coinitia-tors to achieve complete bulk and surface curing in thin films.27A few reactive diluents were used,including IDA to reduce the viscosity of the precursor solutions,lower the modulus of the copolymers,and increase hydrophobicity. IBOA was used to improve the toughness,and TMPTA to provide the baseline crosslinking.24HDDA was used as the main crosslinker to adjust the mechanical and electrome-chanical properties of the material.DBEF was used as a plasticizer.Effect of CrosslinkerRadiation polymerization is known to form a complex net-work structure in a heterogeneous way with microgel forma-tion.28However,qualitative analysis of the crosslink density can still be performed by analyzing the equilibrium swelling ratio as well as the gel fraction of the elastomer.The swel-ling ratio Q is defined as cubic of the ratio of the diameter of a swollen elastomer disc to its initial diameter.The gel frac-tion is defined as the ratio of the mass of the deswollen elas-tomer over its initial mass and measures the weight loss during swelling.Figure1(a)shows such data of a series of UV-DE elastomers,with various crosslinker concentrations. C0-P0,with no additional crosslinkers,has the largest Q of 8.37and the smallest gel fraction of75.7%.Q decreases drastically to4.57in C2-P0and then slightly decreases along with further increases in the amount of crosslinker,to3.11 in C5-P0containing5%by weight of HDDA.The gel fraction increases to88.7%in C4-P0and saturates after that.The high gel fractions in this series indicate that the polymer net-works formed are close to ideal.29According to Flory–Reh-ner theory,30if the degree of swelling is large,the average molecular weight between crosslinks,M c,can be defined as:M c¼2q V1Q5=3=ð1ÀKÞ(5) where q is the density of the polymer network,V1is the molar volume of the solvent,and K is a constant depending on temperature,polymer,solvent,and their interaction.The crosslink density,which is inversely proportional to M c, therefore,has a negative correlation to Q.With a higher HDDA concentration,the crosslink density in the UV-DE ma-terial system is effectively increased.The oligomer and monomers have been effectively incorporated into the cross-linked network and thus will contribute to the better rub-bery elasticity in such materials.Figure1(b)shows the nominal stress versus uniaxial stretch curves of UV-DE materials with different crosslinker concen-trations.VHB4905and IPN4905fabricated by a method pre-viously reported13were chosen as reference materials.The tensile strength is improved from2.46MPa in C0-P0to4.38 MPa in C5-P0.The stretch ratio at break is compromised from7.13in C0-P0to2.73in C5-P0.The modulus of theTABLE1Formulations(Parts of Weight)and Nomenclature of Prepolymer Solutions and Corresponding Elastomer FilmsName CN9021HDDA DBEF IDA IBOA TMPTA DMPA BP C0-P07000235110.5 C2-P07020215110.5 C3-P07030205110.5 C4-P07040195110.5 C5-P07050185110.5 C5-P1070510185110.5 C5-P2070520185110.5 C5-P3070530185110.5elastomer at small stretch ratios (k <1.1)increases along with crosslink density,from C0-P0similar to nonpres-tretched VHB4905,to C5-P0similar to IPN4905.The behav-ior is due to additional chemical bonds between polymer chains that prevent them from shearing,which can be derived by thermodynamics and rubbery elasticity,and even used as a measurement of crosslink density.31Another im-portant feature of the UV-DE is the stiffening after a critical stretch ratio.As the crosslink density increases,a smaller stretch is needed in UV-DE to drive the elastomer into its non-Gaussian region,wherein the noncrystallizable elastomer starts to have stress redistribution and causes substantial stiffening.32,33Such critical stretch ratio shifts to a smaller value at a higher crosslink density,which makes the mechan-ical properties of the elastomer to shift from being VHB-like to IPN-like in nature.The modulus increase with increasing crosslink density is further demonstrated in Figure 2.The observed storage modulus of UV-DE varies in between the values of nonpres-tretched VHB4905and IPN4905.Also observed is a higher glass transition temperature (T g )in the highly crosslinked elastomers.A smaller free volume in higher crosslinked elas-tomers,which leads to a confined chain movement,isresponsible for the higher T g .Also because of this confine-ment,the amplitude of the chain segment movement is lim-ited.As a result,the loss peak of highly crosslinked elasto-mers is flattened compared to those with lower crosslink pared with nonprestretched VHB4905(tan d ¼0.642),the UV-DE materials have up to 76%decrease in the loss factor (C2-P0,tan d ¼0.157)at room temperature.It indicates that the material is expected to have a better elec-tromechanical frequency response.The electromechanical performance of UV-DE materials is compared to prestretched VHB4905(300%by 300%biax-ially)and IPN4905in Figure 3.VHB4905has a maximum strain of 163%.Very little EMI can be observed in the biax-ially prestretched VHB material.In IPN4905,the stiffness of the second polymer network is responsible for balancing the prestrain applied to the first network,so no EMI is observed even when the material is freestanding.The observed actua-tion strain is 67%.The UV-DE materials,with no prestretch-ing applied during actuation,show various electromechanical behaviors.C0-P0has a large maximum strain of 318%,and a significant EMI snap-through from 23%at 21.0V l m À1to 262%at 25.8V l m À1,with three intermediate states in between.This large strain snap-through is very similar to a giant strain snap-through in VHB reported recently,34where adjustment of chamber pressure was used to suppress EMI.The EMI is suppressed in C2-P0,where the snap-through is from 31%at 44.1V l m À1to 102%at 54.5V l m À1.The maximum strain decreases to 125%.If more crosslinker is used,as in C5-P0,the maximum strain is further reduced to 89%.No significant strain snap-through can be observed,which indicates that EMI has been completely suppressed.The similarity of C5-P0and IPN4905is further evidenced by the observed electromechanical properties.The ultimate electromechanical behavior and permittivity have been summarized in Figure 4,from a full set of actua-tion tests of UV-DE materials with variouscrosslinkerFIGURE 2(Top)Storage modulus and (bottom)loss factor of UV-DE with different crosslinker concentrations compared with the reference VHB4905and IPN4905materials.FIGURE 1(a)Swelling ratio Q (h )and gel fraction (n )and (b)nominal stress versus stretch ratio relationship of UV-DE with different crosslinker concentrations.concentrations.The apparent electrical breakdown field,defined by the voltage applied divided by the thickness at the maximum strain,increases monotonically,from 114V l m À1in C0-P0to 236V l m À1in C5-P0.The increase could be explained as the synergic effect of the suppression of EMI (explained below)and improvement of the intrinsic break-down field.On the other hand,the maximum area strain s A shows a nonlinear decrease along with increased crosslink density,from 318%in C0-P0,125%in C2-P0,to 70%in C3-P0,a minimum of 56%in C4-P0,and then increasing to 89%in C5-P0.As seen in Figure 3,EMI is responsible for the large strains in the lightly crosslinked elastomers (C0-P0).A small fluctuation in electric field can thin down the elastomer by a significant amount.Although not fully sup-pressed,the EMI becomes less significant in materials with higher crosslink densities (C2-P0,C3-P0,and C4-P0).Larger forces are needed to initiate the strain snap-through due to the stiffening effect in such materials.If the crosslink density is further increased (C5-P0),EMI will no longer be the main electrical breakdown mechanism and intrinsic dielectricbreakdown will take over.The increased intrinsic breakdown strength will allow the material to attain a higher strain.Further explanation of the suppression of EMI in the non-prestretched UV-DE materials can be given by the model developed by Zhao and Suo.22According to this model,DEs can be divided into type I,II,and III,depending on their voltage-stretch curve U (k ),breakdown-stretch curves U B (k ),and the intersections of these two curves:U ðk Þ¼H k À2ffiffiffiffiffiffiffiffiffiffiffiffiffir ðk Þ=ep (6)U B ðk Þ¼E B H k À2(7)where k is the stretch,H the original thickness,r (k )the stress–strain relationship,and E B the electric breakdown strength of the material.This model successfully explains the effects of prestretching,23prestrain-locked IPN,22and the giant strain under varying chamber pressures.34Figure 5(a)shows the voltage-stretch curves of UV-DE materials with various crosslink densities,as well asnonprestretchedFIGURE 3(Top)Electromechanical strain versus applied electric field relationships of UV-DE with different crosslinker concentra-tions.(Bottom)Pictures of the actuated elastomer films.VHB4905and IPN4905.An original thickness of 50l m and the permittivity measured by LCR have been used as model parameters.The inset shows the true stress and uniaxial stretch relationships of these materials.VHB4905is compli-ant at small stretches and does not display any significant stiffening up to k ¼9.5(limit of test equipment).As a result,its voltage-stretch curve reaches a peak and then monotoni-cally decreases.As such,nonprestretched VHB4905is a typi-cal type II dielectric,which will fail due to EMI.On the other hand,IPN materials are reported to have a type III dielectric behavior,where the minimum on the voltage-stretch curve is eliminated by the steep stiffening of the stress–strain rela-tionship,and is monotonically increasing.The UV-DE materials show both types of behaviors,accord-ing to their different crosslinker amounts.The one with no additional crosslinker,C0-P0,has a lowest Young’s modulus at small stretches (k <1.1).It has a stiffening effect after k ¼4.75and a minimum can be found on the corresponding voltage-stretch curve.As the amount of HDDA increases,the Young’s modulus of the material at small stretches increases,while the stiffening effect tends to show up earlier and steeper.The minimum on the voltage-stretch curves alsoshifts to a smaller stretch and finally diminishes in C5-P0,similar with IPN4905.The Zhao–Suo model predicts that C5-P0will have a similar electromechanical behavior as the IPN material,which matches well with the experimental observa-tion shown in Figure 3.Note that no prestretching is involved during the fabrication and testing of the new DE materials.The intersections of the voltage-stretch curves and break-down-stretch curves in UV-DE materials can be used to fit or predict the ultimate electromechanical properties,as shown in Figure 5(b).The electric breakdown strengths of the materials are determined by dividing the nominal electric field at failure by the thickness strain.In C0-P0two curves intersect at k ¼2.24,which is beyond the maximum on the curve (k ¼1.30),but much smaller than the minimum on the voltage-stretch curve (k ¼4.75).This indicates a possi-ble metastable strain snap-through along the voltage-stretch curve from the peak at k ¼1.30.Therefore,C0-P0shouldbeFIGURE 4(a)Maximum electromechanical strain (h )and breakdown field (n )and (b)permittivity of UV-DE with different crosslinkerconcentrations.FIGURE 5(a)Voltage versus stretch U (k )curves and (b)inter-section of U (k )and breakdown field versus stretch U B (k )curves of UV-DE with different crosslinker concentrations.categorized as a type II dielectric.Similarly,in C2-P0,the intersection at k ¼1.92is between the maximum (k ¼1.30)and the minimum (k ¼2.60),but much closer to the mini-mum.It is still a metastable type II dielectric,while the sta-bility of the strain after snap-through is better than the C0-P0case (Supporting Information Fig.S1).In C5-P0,the inter-section is at k ¼1.71.As the minimum is eliminated,it can be categorized as a type III dielectric,which is able to totally suppress EMI.The theoretically predicted values deviate from the experimental strain values,but they follow the same trend.The deviation is probably due to the problematic assumption of estimating biaxial actuation strain with a uni-axial stretch in a much stiffer system.Effect of PlasticizersIncreasing crosslink density can suppress EMI and improve breakdown field,while still allowing a useful large strain.One problem is the high modulus brought in by the high crosslink density.Although not a linear term,the modulus could be taken as a measurement of sensitivity of the mate-rial to an electric field,as explained previously in literature.1A lower modulus is preferred so that a lower field is neededfor the material to be deformed.Although the overall viscoe-lasticity has been reduced,the glass transition temperature increases with higher crosslink density,and viscoelastic behavior still limits the frequency response of the UV-DE.Plasticizers are known as an effective low-molecular-weight additive to plastics and rubbers that can lower the T g and make the material more flexible.35,36Although the flexible monomer IDA can serve as an internal plasticizer to a cer-tain level,we choose DBEF as an external plasticizer of the UV-DE system because of its good low temperature perform-ance,good compatibility with acrylate elastomers,as well as low volatility.35,36Based on the highly crosslinked UV-DE (C5-P0),the effect of DBEF on the crosslink density is studied again with equilib-rium swelling tests [Fig.6(a)].In the calculation of gel frac-tions,the weight of the plasticizers was excluded,as the plasticizers are small molecules without reactive functional groups and will not be incorporated into the network.As the plasticizer concentration increases,the swelling ratio increases slightly and the gel fraction decreases slightly.The reason could be the double bond concentration has been diluted by the plasticizer.Also,the ether-based plasticizer has a higher chain transfer constant,which could sacrifice the efficiency of the incorporation of double bond into the polymer network.Overall,the swelling ratio with 30parts of DBEF is still comparable with sample with four parts of HDDA and no plasticizer.As such,plasticizing with DBEF has no significant effect on the network structure of UV-DE.Basic stress–strain relationships of plasticized UV-DE [Fig.6(b)]show that plasticized materials have a lower modulus,higher elongation,and a lower tensile strength.Plasticizers present improve the mobility of polymer chains,resulting in soften-ing.35The stiffness increase with stretching is still present,although the slope decreases with higher plasticizer loading.Voltage-stretch curves of the plasticized UV-DE materials (Supporting Information Fig.S2)show similar shapes as C5-P0.A longer ‘‘necking’’after the maximum at k $1.3indi-cates that the suppression of EMI becomes less effective when too much plasticizer is used.Another important improvement of using plasticizers is the lower T g .As shown in Figure 7,T g ,defined by the peak of me-chanical loss factor,has shifted from 7.8 C for C5-P0to À30.5 C for C5-P30.Because of the free volume increase in plasticized materials with lower T g ,35a number of mechanical properties have been tuned.The storage modulus at 25 C decreased from 1.8MPa of C5-P0to 0.4MPa of C5-P30.The loss factor at 25 C decreased from 0.28for C5-P0to 0.05for C5-P30,which is much lower than that of VHB4905(0.64at 25 C)and comparable with most of silicone elastomers (0.06for CF19-2186).1The electromechanical frequency response is a complex process that involves the loss factor,modulus at small strains,and the nonlinear modulus change as the mate-rial is stretched.Although more comprehensive studies are still being carried out,the improvement in loss factor and modulus at small strains already demonstrates that plasticiz-ing with DBEF is promising for improving the electromechani-cal frequency response of UV-DEmaterials.FIGURE 6(a)Swelling ratio Q (h )and gel fraction (n )and (b)nominal stress versus stretch ratio relationship of UV-DE with different plasticizer concentrations.。
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纯剪切模式介电弹性体发电机发电特性鄂世举;金建华;曹建波;蔡建程;夏文俊【摘要】为研究介电弹性体发电机的发电特性,基于COMSOL有限元软件建立了在纯剪切拉伸方式下的介电弹性体发电机有限元仿真机电耦合模型.该模型基于Y eo h超弹性材料本构,同时耦合发电机膜内静电力,根据可变电容理论对发电机电容变化及发电效果进行研究.设计了可Y向预拉伸的纯剪切拉伸装置,并在不同预拉伸条件下对发电机薄膜样本进行了拉伸实验,分析了其电容变化及发电效果.对比了仿真数据与实验结果,仿真模型的电容变化与实验测得的电容变化情况基本吻合,仿真模型一个周期内的输出电压变化与实验测得的电压变化基本吻合.实验及仿真结果表明,在相同的拉伸条件下,Y向预拉伸增大了初始电容及电容变化速率,且当Y向预拉伸λ=1时的上升电压为83 V,而λ=2时的上升电压达到252 V,改善了发电性能.本文提出的介电弹性体发电机新的研究方法为发电机样机设计提供了新的思路.【期刊名称】《光学精密工程》【年(卷),期】2018(026)007【总页数】11页(P1708-1718)【关键词】有限元建模;纯剪切;Y向预拉伸;机电特性【作者】鄂世举;金建华;曹建波;蔡建程;夏文俊【作者单位】浙江师范大学工学院 ,浙江金华321004;浙江师范大学工学院 ,浙江金华321004;浙江师范大学工学院 ,浙江金华321004;浙江师范大学工学院 ,浙江金华321004;浙江师范大学工学院 ,浙江金华321004【正文语种】中文【中图分类】TP394.1;TH691.91 引言电活性聚合物(Electroactive Polymer， EAP)是一种新型的功能性材料，可广泛应用于驱动器、传感器和发电领域[1-4]。
介电弹性体(Dielectric Elastomer，DE)是EAP材料中最具代表性的一类，包括聚丙烯酸酯、硅橡胶及天然橡胶等，具有变形大、质量轻、能量密度高及柔顺性好等特点。
从原理上，介电弹性体发电机(Dielectric Elastomer Generator， DEG)是一种具有“三明治”式三层结构的可变电容器，上、下两层是柔性电极，中间是介电弹性体。
在施加偏置电压时，通过拉伸、收缩介电弹性体将施加的机械能转化为电能[5-6]。
DEG的能量密度比其他传统发电机(压电、电磁发电机)至少高了一个数量级，并且机电转换效率在理论上高达80～90%，展现了DEG在发电领域广阔的前景[7]，可应用于人体的生物能，如鞋跟发电机、膝盖能量收集器，风能、海洋能发电等场合[8]。
利用有限元方法及相关软件，建立多种类型的仿真模型，是研究DEG性能的主要理论手段[9-10]，但有限元编程的复杂性大大增加了仿真研究的难度。
COMSOL有限元软件可避免其他有限元软件复杂的编程工作，且在多物理场耦合方面功能强大。
如Deodhar等[11]基于COMSOL软件对圆锥形介电弹性体驱动器进行了机电耦合特性的仿真，并将DE的超弹性和电极考虑其中。
至今为止，针对DEG发电方面的有限元仿真研究仍较少。
形变方式对DEG的发电效果有着显著地影响[12]。
薄膜型DEG的形变方式可分为平面内变形和平面外变形。
平面内变形包括单轴拉伸、纯剪切拉伸、等双轴拉伸和菱形形变等[13-14]。
平面外变形是对薄膜施加平面外的载荷使其造成平面外的形变如圆锥型、球型等[15-17]。
在对DEG的实验研究中，大多以平面内变形作为形变方式，其中单轴拉伸、纯剪切拉伸、等双轴拉伸方式最为典型。
等双轴拉伸方式虽然能使DEG的形变量显著提高，进而提升发电量，但是在实际实验及应用中，等双轴拉伸方式的实现较为困难，其拉伸装置也较为复杂[18-19]。
单轴拉伸方式最为简单，但发电效果较差。
预拉伸是指在施加研究载荷之前对薄膜进行的不同程度拉伸，以提升薄膜性能[20-21]。
预拉伸的研究集中于介电弹性体驱动器(Dielectric Elastomer Actuator，DEA)方面，而对DEG方面的研究较少。
综合考虑DEG的形变及预拉伸对其性能的影响，本文在纯剪切模式下，在COMSOL有限元软件环境中建立了基于Yeoh超弹性材料本构的有限元模型，搭建实验平台并拟合获得了Yeoh超弹性材料参数，继而对DEG的力学特性和电学特性进行了研究。
2 理论模型形变方式和预拉伸方式如图1所示，单轴拉伸方式是一端固定一端施加载荷，纯剪切拉伸方式是在单轴拉伸的基础上，两侧边施加辊支撑约束(限制Y轴方向位移)，而等双轴拉伸方式是一端固定，其余三边施加相等的载荷。
预拉伸主要有3种方式：图1(b)是仅X向预拉伸，预拉伸方向与之后的研究载荷方向一致，一般用于单轴拉伸方式；图1(c)是仅Y向预拉伸，预拉伸方向与之后的研究载荷方向垂直，一般用于纯剪切拉伸方式；图1(d)是X向和Y向共同的双向预拉伸，一般用于等双轴拉伸。
本文主要针对第2种，对Y向预拉伸进行研究。
(a)初始薄膜(a)Iinitial membrane(b)单轴拉伸和X向预拉伸(b)Uniaxial tension and pre-stretch in X direction(c)纯剪切拉伸和Y向预拉伸(c)Pure shear tension and pre-stretch in X direction(d)等双轴拉伸和双向预拉伸(d)Biaxial tension and pre-stretch in X and Y direction图1 单轴、双轴、纯剪切拉伸及3种预拉伸形式示意图Fig.1 Schematic diagram of uniaxial， biaxial， pure shear tension and three ways of pre-stretch基于DEG的发电过程及机理，DEG的模型是一种综合考虑其力学特性和电学特性的机电耦合模型。
为简化模型，假定DE为理想弹性体，有以下几个假设[22]：不可压缩性；介电常数恒定；DE为超弹性材料且不考虑粘弹性行为；各项同性。
2.1 DEG力学模型DE是一种超弹性材料，而对于超弹性材料，材料中的能量(功)仅仅取决于变形的初始状态和最终状态，并独立于变形(载荷)路径，因而应变能函数是描述超弹性材料应力-应变本构关系的有效方式[23]。
超弹性本构模型包括Neo-Hooken、Gent、Ogden以及Yeoh等模型。
这些超弹性本构模型由应变能密度WS来定义，是左柯西应变张量不变量I1，I2，I3的函数：WS=W(I1，I2，I3)。
上述超弹性模型中，Yeoh计算量小，能准确地描述超弹性材料在大形变下的状态[24]，因而本文选用Yeoh对DEG进行建模。
基于材料的不可压缩性假设，其应变能密度WS为：WS=C10(I1-3)+C20(I1-3)2+C30(I1-3)3，(1)，其中：λ1，λ2，λ3是各方向的主拉伸率，C10，C20，C30为材料参数，一般由实验数据拟合获得。
根据弹性力学理论，对于超弹性材料，其柯西主应力δi由应变能对拉伸率λi求导给出：(i=1，2，3)，(3)其中p是静水压力，由动力学边界条件给出。
依据纯剪切拉伸方式，则动力学边界条件以及各主拉伸率关系如下：δ1=δ，δ2≠0，δ3=0，(4)λ1=λ，λ2=1，λ3=λ-1.(5)根据推导得出，在纯剪切模式下基于Yeoh模型的1方向主应力：δ1=2(λ2-λ-2)[C10+2C20(λ2+λ-2-2)+3C30(λ2+λ-2-2)2].(6)定义T为名义应力，在纯剪切模式下有名义应力与真实应力的关系：δ1=λT1，则：T1=2(λ-λ-3)[C10+2C20(λ2+λ-2-2)+3C30(λ2+λ-2-2)2].(7)下文中利用公式(7)来拟合实验测得的数据，从而获得Yeoh本构模型参数C10，C20，C30。
2.2 DEG电学模型基于可变电容原理建立DEG的电学模型。
类比平行板电容器有：Q=CU，C=ε0ε，其中：Q是DEG两端电荷，C是可变电容，A是薄膜面积，d是薄膜厚度。
ε是相对介电常数，定为常数4.7，ε0是真空介电常数，其值为8.854 2×10-12 F/m。
由式(8)可知，在相对介电常数恒定时，电容C仅与薄膜的面积和厚度有关。
当薄膜拉伸时，面积变大，厚度减小，则C变大，相反当薄膜收缩时C减小。
因而在拉伸过程中，电容C随着时间的变化而变化，是时间t的函数，可用C(t)来表示。
DEG两端电压的变化源于电容的变化，而电容的变化源于外力引起薄膜几何形状(面积、厚度)的变化。
即当外界施加的力改变时，便可造成DEG两端输出电压的变化。
其中，电容作为机械能到电能的中间环节，将DEG的力场与电场进行耦合。
如图2所示是经典DEG升压电路，由电源、二极管、电阻、DEG模型组成。
其中电源U0作为偏置电压，其值为1 000 V，u是DEG两端电压，i是电流，R是串联电阻，其值为200 MΩ，二极管的作用是当DEG两端电压u≥U0时，DEG两端电荷不会返回到偏置电源。
图2 经典DEG升压电路Fig.2 Classic DEG energy harvesting circuit因而当薄膜拉伸时，电源给DEG充电，电荷积聚在薄膜上下两面电极区域。
当薄膜收缩时，二极管反向截止，DEG两端的电荷Q保持不变，C减小的同时，电压u增大，从而达到升压发电的效果。
电压变化的微分方程由下式表示：，(9)i=dQ/dt.(10)根据基尔霍夫电压定律，由图2电路得：U0=iR+u.(11)综上，式(8)～(11)组成了DEG的电学模型。
3 仿真模型根据上述理论模型，在COMSOL Multiphysics有限元环境中进行仿真研究。
COMSOL有限元软件以其强大的多物理场耦合特性而著称。
利用软件中的预置模块：结构力学模块、AC/DC(静电)模块以及常微分和微分代数方程模块对DEG的机电耦合特性进行仿真。
其中，结构力学模块用来定义DEG的超弹性本构、DEG 的力学边界约束、以及其在机电载荷下的形变；静电模块用来施加电学边界条件如偏置电压、表征DEG的电容、DEG两端电压等电学特性。
常微分和微分代数方程模块用来仿真拉伸收缩过程中DEG的发电效果，即输出电压的变化。
3.1 几何模型及边界条件定义DEG的几何模型尺寸的长和宽分别为120 mm和80 mm，厚度为0.5 mm，其中上、下表面各有一个的矩形暗色区域表征柔性电极，长和宽分别为70 mm和50 mm，如图3所示。
其中的中间矩形区域为DEG有效工作区域，用于施加偏置电压。
因柔性电极对薄膜的力学影响较小，故本文不考虑电极的影响。
图3 DEG几何模型示意图Fig.3 Schematic diagram of geometric model of DEG模型在X、Y、Z 3个方向上都有约束或者形变，因而无法简化为2D模型。