Dielectric elastomeric actuators (DEAs) have been intensely studied in the recent decades. Their attractive features include large deformation(380%), large energy density(3.4 J/g), light weight, fast response(<1 ms), and high efficiency (80%-90%). They can be used in medical devices, space robotices and energy harvesters. The core part of DEAs is a dielectric elastomeric film with two electordes. When pre-stretched forces are exerted on the film in plane direction and voltage is applied across its thickness, the film achieves a large deformation. Usually the effect of electric field is described by Maxwell stress εE2, and the effect of mechanical field is described by free energy function models (such as Neo-Hookean model, Arruda-Boyce model and Gent model). There are deviations in varying degree between every models and tests of dielectric elastomer. No model works perfectly. In the present paper, a new free energy function model is given to reduce the deviation. According to the main models above, an undetermined parameter C(λ1,λ2) is introduced. and λi?W?λi = C(λ1,λ2)(λ2i -λ-21 λ-22 ), σpi =C(λ1,λ2)(λ2pi -λ-2p1λ-2p2 )λiλpi , i = 1, 2, are assumed. The new λi?W?λi and σpi are substituted into the equation of equilibrium of dielectric elastomer film σpi +εE 2 = λi?W?λi , i = 1, 2. Under equal-biaxial pre-stretched condition, P1 = P2 = P , λp1 = λp2 = λp, C(λ1,λ2) = C(λ). The parameter C(λ) =ε(Vλ2 t0 )2λ2-λ-4-(λp-λ-4p ) λλp is obtained. Through analysing the test results of VHB4905 which contains a series of equal-biaxial pre-stretched tests, the data (λ, C(λ)) are obtained from the test data (λ, V ). C(λ)=a+b e√I1-3, (I1 =λ21+λ22+λ23) can be determined by data points (λ, C(λ)). By computing the integral ofλi?W?λi =(a+b e√I1-3)(λ2i-λ-21 λ-22 ), i=1, 2, a new free energy function W = a2 (I1-3)+b[ e√I1-3(√I1-3-1)+1] (the new model) is achieved. The test results of VHB4905 are fitted by Neo-Hookean, Gent model and the new model. Neo-Hookean model fits well only in small deformation. Gent model fits well only in small-middle deformation, and does not work well when stretch λ > 3.5. The new model fits well in small, middle and large deformation. It is better than Neo-Hookean and Gent model. The new model can give big support in the study of dielectric elastomer materials and structure property, and can be used in engineering practice effectively.%当介电高弹聚合物薄膜被施以面内等双轴预拉伸后, 受到厚度方向的电压作用时, 薄膜在力场和电场共同作用下产生大变形. 电场采用Maxwell应力分析, 力场采用橡胶弹性模型分析. 拟合这类变形的常用橡胶弹性模型主要有Neo-Hookean, Arruda-Boyce, Gent等模型. 这些模型对实验数据的定量拟合存在不同程度的偏差. 通过对实验数据的分析, 结合数学方法, 提出了一个新的自由能函数模型. 通过该模型对VHB4905介电高弹聚合物薄膜的多组等双轴预拉伸电力耦合实验进行拟合, 并以Neo-Hookean, Gent模型作为对照,结果与实验数据拟合很好,比对照模型的偏差明显缩小.
展开▼
