The Analysis Of The Mechanical-electro Nonlinear Deformation And Failure Modes Of Elastic Polymer Membranes

Since 1990's, in the family of electro-active polymers, one kind of special soft smart materials, that is dielectric elastomer, has received considerable attention among researchers and engineers due to its many outstanding mechanical attributes such as large strain, fast response, high efficiency etc.when it is subject to a voltage. These attributes make dielectric elastomer promising for applications as transducers such as actuators, sensors and energy harvesters.The essential part of dielectric elastomer transducers is a dielectric membrane sandwiched between two compliant electrodes.Subject to a voltage, the dielectric membrane reduces its thickness and expands its area, converting electrical energy into mechanical energy. Due to large deformation, nonlinear equations of state, and complicated loads, modeling the electro-mechanical response for dielectric elastomer transducers has been challenging. The main contents of this thesis are as follows:1.The axisymmetric out-of plane nonlinear deformation of an annular elastic membrane is studied in the frame of nonlinear elastic deformation theory. The membrane is initially flat and attached to a disk in the inner circle and to a rigid ring in the outer circle, then a weight is applied to the disk and the membrane deforms into an axisymmetric shape, undergoing large out-of-plane deformation.The governing equations characterizing the out-of plane large deformation of the elastic membrane are derived by combining state equilibrium and thermodynamics.The derived governing equations are solved by using shooting method. The obtained results show that the deformation field in the membrane is very inhomogeneous.This indicates that the membrane doesn't function efficiently, which leads to a material waste.The theory and method presented in this section provide some basic outlines for the problem discussed in the next section.2.This part focuses on investigating the axisymmetric out-of plane nonlinear deformation of an actuator made of electro-active polymer membrane.The mechanical model describing the axisymmetric nonlinear deformation of such annular membrane is formulated, and the equations of equilibrium state characterizing the large deformation of the annular membrane subject to a concentrated force and a voltage are derived by thermodynamics.The derived state equations are solved by using shooting method and the distributions of true stress fields,stretches and true electrical fields are obtained numerically. The obtained numerical results show that the deformation field in the membrane is highly inhomogeneous.The deformation near the central part of the membrane is large while the deformation near the edge of the membrane is small, which leads to the induced electric field in the membrane increases monotonically from the edge to the central part and reaches maximum at the central part of the membrane. This results in the consequence that the membrane near the central part risks the possibility of electric breakdown while the major part of the membrane can still function normally. The inhomogeneity of deformation field leads to the consequence that the membrane does not function efficiently, which results in material waste.3.This part explores the potential modes of failure when the electro-active polymer membrane is subjected to a voltage and a force.The equations of equilibrium of the system are derived by thermodynamics and the criterions for each mode of failure are specified. Using these criterions, we obtain the allowed range of the force and the voltage. In addition, numerical results indicate that pre-stretch may reduce the inhomogeneity. If the design parameters of actuator are chosen suitably, the true electrical field in the membrane may tend to be homogeneous,which may greatly improve the efficiency of the material.The results presented in this paper could provide some guidelines for optimizing the design of such kind commercial actuators.