一个新的自由能函数对介电高弹薄膜的多组等双轴预拉伸下力电耦合实验的预测

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.

A new free energy model for predicting the qual-biaxial tests of dielectric elastomers

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 λ_i (∂W/∂λ_i)= C(λ ₁, λ ₂)(λ_i²-λ ₁^-2 λ₂^-2), σ_pi = C(λ ₁, λ ₂)(λ _pi²-λ _p1^-2λ_p2^-2)(λ_i/λ _pi), i = 1, 2, are assumed. The new λ_i (∂ W/∂λ_i) and σ_pi are substituted into the equation of equilibrium of dielectric elastomer film σ_pi + εE² = λ_i (∂ W/∂λ_i), i = 1, 2. Under equal-biaxial pre-stretched condition, P₁ = P₂ = P, λ _p1 = λ _p2 = λ_p, C(λ₁, λ ₂) = C(λ). The parameter C(λ)= ε(Vλ²/t₀)²/(λ ²-λ ^-4-(λ _p-λ _p^-4)(λ/λ _p)) 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 + be^√I₁-3, (I₁ = λ ₁² + λ ₂² + λ ₃²) can be determined by data points (λ, C(λ)). By computing the integral of λ_i (∂ W/∂λ_i)= a + be^√I₁-3)(λ_i²-λ ₁^-2 λ ₂^-2), i = 1, 2, a new free energy function W = (a/2)(I₁-3) + be^√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.