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

作者：Jiang Shi Ming^*

来源：Acta Physica Sinica, 2015, 64(18): 184601.

DOI：10.7498/aps.64.184601

• dielectric elastomer polymer
• electric-mechanical couple
• new free energy function

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 epsilon E-2, 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(lambda(1), lambda(2)) is introduced. and lambda(i) partial derivative W/partial derivative lambda(i) = C(lambda(1), lambda(2)) (lambda(2)(i) - lambda(-2)(1)lambda(-2)(2)), sigma(pi) = C(lambda(1), lambda(2)) (lambda(2)(pi) - lambda(-2)(p1)lambda(-2)(p2)) lambda(i)/lambda(pi), i - 1, 2, are assumed. The new lambda(i) partial derivative W/partial derivative lambda(i) and sigma(pi) are substituted into the equation of equilibrium of dielectric elastomer film sigma(pi) + epsilon E-2 = lambda(i) partial derivative W/partial derivative lambda(i), i = 1, 2. Under equal-biaxial pre-stretched condition, P-1 = P-2 = P, lambda(p1) = lambda(p2) = lambda(p), C(lambda(1), lambda(2)) = C (lambda). The parameter C (lambda) = epsilon(V lambda(2)/t(0))(2)/lambda(2) - lambda(-4) - (lambda(p) - lambda(4)(p))lambda/lambda(p) is obtained. Through analysing the test results of VHB4905 which contains a series of equal-biaxial pre-stretched tests, the data (lambda, C(lambda)) are obtained from the test data (lambda, V). C (lambda) = a + be(root I1-3), (I-1 = lambda(2)(1) + lambda(2)(2) + lambda(2)(3)) can be determined by data points (lambda, C (lambda)). By computing the integral of lambda(i) partial derivative W/partial derivative lambda(i) = = (a + be(root I1-3)) (lambda(2)(i) - lambda(-2)(1)lambda(-2)(2)), i = 1, 2, a new free energy function W = a/2 (I-1 - 3) + b [e(root I1-3)(root I-1 - 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 lambda > 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.

• 出版日期2015-9-20
• 单位同济大学