Eric Mockensturm

A Nonlinear Model for Dielectric Elastomer Membranes

The material and geometrical nonlinearities of novel dielectric elastomer actuators make them more difficult to model than linear materials used in traditional actuators. To accurately model dielectric elastomers, a comprehensive mathematical formulation that incorporates large deformations, material nonlinearity, and electrical effects is derived using Maxwell-Faraday electrostatics and nonlinear elasticity. The analytical model is used to numerically solve for the resultant behavior of an inflatable dielectric elastomer membrane, subject to changes in various system parameters such as prestrain, external pressure, applied voltage, and the percentage electroded membrane area. The model can be used to predict acceptable ranges of motion for prescribed system specifications. The predicted trends are qualitatively supported by experimental work on fluid pumps [A. Tews, K. Pope, and A. Snyder, Proceedings SPIE, 2003)]. For a potential cardiac pump application, it is envisioned that the active dielectric elastomer membrane will function as the motive element of the device.

Modeling of a dielectric elastomer diaphragm for a prosthetic blood pump

The electromechanical behavior of dielectric elastomers is to be exploited for medical application in artificial blood pumps. It is required that the pump diaphragm achieves a swept volume increase of 70 cc into a systolic pressure of 120 mmHg with the main design objective being volumetric efficiency. As such, a model that accommodates large deformation behavior is used. In order to design prosthetic blood pumps that closely mimic the natural pumping chambers of the heart, a dielectric elastomer diaphragm design is proposed. The elastomers change in shape in response to the applied electric field will permit it to be the active element of the pump just as the ventricular walls are in the natural heart. A comprehensive analytical model that accounts for the combined elastic and dielectric behavior of the membrane is used to compute the stresses and deformations of the inflated membrane. Dielectric elastomers are often pre-strained in order to obtain optimal electromechanical performance. The resulting model incorporates pre-strain and shows how system parameters such as pre-strain, pressure, electric field, and edge constraints affect membrane deformation. The model predicts more than adequate volume displacement for moderate pre-strain of the elastomer.

Nonlinear Vibration of Parametrically Excited, Viscoelastic, Axially Moving Strings

The dynamic response of parametrically excited, axially moving viscoelastic belts is investigated in this paper. Results are compared to previous work in which the partial, not material, time derivative was used in the viscoelastic constitutive relation. It is found that this added steady state dissipation greatly affects both the existence and amplitudes of nontrivial limit cycles. The discrepancy increases with increasing translation speed. To limit the comparison to the additional physics included in the model, the solution procedure of Zhang and Zu [1,2], who applied the method of multiple scales to the governing equations prior to discretization, is retained. The excitation here is provided by physically stretching the belt. In this case, viscoelastic behavior and excitation frequency also affects the amplitude of the tension fluctuations.

Electro-elastic modeling of a dielectric elastomer diaphragm for a prosthetic blood pump

A dielectric elastomer diaphragm is to be designed for potential use in a prosthetic blood pump. Application of an electric field deforms the membrane such that it moves from an initially flat configuration to an inflated state. This motion creates positive displacement of blood from the cardiac chambers thus mimicking the pump-like behavior of the natural heart. A comprehensive large deformation model accounting for the combined dielectric and elastic effect has been formulated. This paper presents recent developments in the model to further incorporate the entire nonlinear range of material elastic behavior and to more accurately represent the applied electric field by keeping the voltage constant as the membrane thickness decreases. The updated model is used to calculate the effects of varying system parameters such as pressure, voltage, prestretch, material constants, and membrane geometry. Analytical results are obtained for biaxially stretched 3M VHB 4905 polyacrylate films.

Viscoelastic model of dielectric elastomer membranes

A non-linear viscoelastic model for finite deformations of dielectric elastomer membranes using Christensens theory of viscoelasticity is developed. For a time efficient numerical solution, the constitutive integral equations with a time dependent kernel (relaxation modulus) are reformulated into a recurrence form using Fengs recurrence formula and solution for the principal stretches are obtained. Uniaxial constant load tensile tests are conducted and compared with theoretical predictions. The model is also valid for small linear deformations.

Piece-Wise Linear Dynamic Systems With One-Way Clutches

One-way clutches and clutch bearings are being used in a wide variety of dynamic systems. Motivated by their recent use as ratchets in piezoelectric actuators and decoupling devices in serpentine belt drives, a method of analysis of systems containing one-way clutches is presented. Two simple systems are analyzed. The goal of the first is the power transmission which would be of concern in an actuator. The goal of the second is decoupling large inertia elements to reduce loads in an oscillating system, the objective of the clutch in a serpentine belt drive. Results show how system parameters can be tuned to meet the desired performance of these piece-wise linear systems.

Modeling electrostatically induced collapse transitions in carbon nanotubes.

Molecular dynamics simulations demonstrate how a mechanically bistable single-walled carbon nanotube can act as a variable-shaped capacitor. If the voltage is tuned so that collapsed and inflated states are degenerate, the tubes susceptibility to diverse external stimuli--temperature, voltage, trapped atoms--diverges following a universal curve, yielding an exceptionally sensitive sensor or actuator. The boundary between collapsed and inflated states can shift hundreds of angstroms in response to a single gas atom inside the tube. Several potential nanoelectromechanical devices could be based on this electrically tuned crossover between near-degenerate collapsed and inflated configurations.

Carbon nanostructures as an electromechanical bicontinuum.

A two-field model provides a unifying framework for elasticity, lattice dynamics and electromechanical coupling in graphene and carbon nanotubes, describes optical phonons, nontrivial acoustic branches, strain-induced gap opening, gap-induced phonon softening, doping-induced deformations, and even the hexagonal graphenic Brillouin zone, and thus explains and extends a previously disparate accumulation of analytical and computational results.

Dynamic analysis of a front-end accessory drive with a decoupler/isolator

In automotive front-end accessory drives (FEAD), the crankshaft supplies power to accessories like alternators, pumps, etc. When the FEAD undergoes forced vibration due to crankshaft excitation, dynamic tension fluctuations can cause the belt to slip on the accessory pulleys. In this paper, an accessory inertia (e.g. alternator) is isolated/separated from the FEAD by placing between the pulley and accessory a combination of a one-way rigid clutch and an isolator spring. The rotational response of a typical FEAD is extended to include this decoupler-isolator. Analytical solutions are obtained by considering it as a piecewise-linearised system about the equilibrium angular displacements. The tension fluctuation of the ordinary FEAD is then compared to that of the system with a decoupler/isolator. The results indicate that within the practical working range of engine speeds, use of either an isolator or a decoupler-isolator could significantly lower the dynamic tension drop across the accessory pulley.

Increasing the Mechanical Work Output of an Active Material Using a Nonlinear Motion Transmission Mechanism

A nonlinear motion transmission mechanism for improving the mechanical work output of an active material drive element is presented. This improvement is achieved by addressing the typical mismatch between the characteristics of a driven load, such as a constant force or spring load, and the active material’s force-displacement behavior; this behavior is described, at a constant drive level, by a linear decrease in the possible force with increasing displacement. The motion transmission mechanism consists of a simple linkage that couples the active material to the load. As the active material does work on the load, the linkage changes the mechanical advantage or leverage of the active material with respect to the load, thereby tailoring the load to best exploit the active material’s force-displacement behavior. A kinematic model is used to predict the maximum quasi-static mechanical work output that can be obtained. Optimization of the model geometry results in a transmission with a theoretical work enhancement of 37% for a constant load, and a theoretical work enhancement that approaches 100% for a spring load. The possibility of work enhancement is verified in an experiment that demonstrates a work output improvement of 27% for the constant load case.