PHENOMENOLOGICAL CONSTITUTIVE MODELS FOR DIELECTRIC ELASTOMER MEMBRANES FOR ARTIFICIAL MUSCLE APPLICATIONS

Open Access
Author:
Yang, Eunice Eun-Young
Graduate Program:
Mechanical Engineering
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
June 19, 2006
Committee Members:
  • Mary I Frecker, Committee Chair
  • Eric M Mockensturm, Committee Chair
  • Alan Snyder, Committee Member
  • H J Sommer Iii, Committee Member
Keywords:
  • electroactive polymers
  • modeling
  • finite element
  • electrostrictive
  • large nonlinear viscoelastic deformations
Abstract:
The primary goal of this research was to develop a better understanding of the large nonlinear viscoelastic deformation of electroactive elastomers subject to high electric fields. This was achieved through experimental characterizations of dielectric material as well as through the development of analytical and finite element hyperelastic and viscoelastic models. Polyacrylate and silicone (polydimethylsiloxane) dielectric materials were considered in this research. The constitutive equations for the large nonlinear hyperelastic deformation of a dielectric elastomer subjected to an electric field was developed using the Mooney-Rivlin and Ogden material models. The analytical model was validated for an annular actuator configuration. It is known that the polyacrylate VHB 4910 dielectric elastomer has significant viscoelastic properties. Hence, to model large nonlinear viscoelastic deformations, Christensen’s viscoelastic theory was used. The analytical viscoelastic material model was validated with experimental results for specimens undergoing uniaxial deformation. Furthermore, non-axisymmetric actuator configurations with cavities in the shapes of an ellipse and rectangle were investigated using a finite element model. An analytical model for dielectric elastomers was developed using the theory of large elastic deformations known as hyperelasticity. From these results a better understanding of how a dielectric elastomer annulus deforms was obtained by understanding the effects of varying Maxwell pressures, pre-stretches, and inner radial pressures, and internal stresses. Through the use of the analytical model, it was found that the radial and circumferential stresses transitions from tensile to compressive stresses at a "critical" Maxwell pressure. The significance of this is the determination of the Maxwell pressure that will cause the elastomer to buckle or wrinkle. Also, the model not only showed that prestretching yields the benefit of greater strain, but that there exists an "optimum" pre-stretch range that would yield a larger percent change in radius for a given incremental increase in the effective Maxwell pressure. In addition, a fixed-free annulus with an inner radial pressure, which may simulate a portion of a simple fluid pump, was modeled. It was found that there exists an operating range of the inner radial pressure and effective Maxwell pressures for the device to be physically as well as mathematically viable. A nonlinear finite deformation viscoelastic model for dielectric elastomer membranes was developed using Christensen’s viscoelastic model in the stretch regime 1.5<ë<3. This model is applicable for small and large nonlinear deformations. In this research, the Mooney-Rivlin elastic material model was utilized. Uniaxial creep tests were conducted to determine the material constants of an exponentially decaying relaxation modulus. The analytical model validated with experimental results from a constant load uniaxial tensile test. The degree of agreement was a function of the relaxation modulus, g(t). A relaxation modulus was found and correlated very well with experimental data within one time constant of the relaxation modulus. The same relaxation modulus could not predict viscoelastic deformations beyond this time constant. A single relaxation function that characterizes the material over a large time [0,t] domain can be obtained by choosing a more complicated mathematical form of the relaxation modulus. Furthermore, the general-purpose finite element (FE) software ABAQUS was used to develop an FE model of non-axisymmetric dielectric elastomer actuators undergoing large nonlinear viscoelastic deformations. Rectangular framed actuators with rectangular and elliptical cavities at the center were investigated. Hyperelastic and viscoelastic material properties were determined from uniaxial constant load tensile and creep test data, respectively. The FE model was validated using experimental data from actuators with uniaxial, in-plane axisymmetric, and in-plane non-axisymmetric deformations. The FE hyperelastic (time-independent) results for uniaxial, in-plane axisymmetric, and in-plane non-axisymmetric deformations correlated well with experimental data. The time-dependent FE results of activated (non-zero electric field) uniaxial and in-plane axisymmetric (annular configuration) deformations correlated well with experimental data. The FE and experimental correlations degraded for time-dependent deformations of non-axisymmetric geometries. The cause for this may be due to the limitations of FE models that use uniaxial test data to define the material properties. Utilization of test results from in-plane tensile tests and in-plane shear tests may improve the FE model to better simulate in-plane deformations. Finally, the FE model was used to model activated strains of cylindrical silicone dielectric elastomer actuators as these materials exhibit negligible viscoelastic behaviors. The material properties were once again defined using uniaxial tensile test data. The activated strains of the cylindrical tubes were subjected to uniaxial tensile tests. As expected, the FE model correlated well uniaxial test data.