Session: 02-04: Modeling and Simulation of Active Materials

Paper Number: 91710

91710 - Finite Element Analysis of the Nonlinear Material Behavior of Ferroelectrics Under Complex Load Scenarios 

The piezoelectric effect in ferroelectric materials offers a wide range of applications in engineering. Especially in actuator and sensor technologies, this material class is really common. In order to use the piezoelectric effect, the domains in the material have to be orientated under the effect of a strong electric field. During this poling process, strong mechanical stresses can occur in the material. These stresses can induce cracks, cause damage in the structure before the component has been used for any application. Another important effect that must be taken into account is the change in polarization state due to strong mechanical compressive loading, which is commonly called mechanical depolarization.

For the optimized design of actuators and sensors a structural mechanics analysis is needed in order to understand the complex residual stresses and poling states in piezoceramic devices. For the description of the material behavior of ferroelectrics, only a few models are available in literature which capture all coupling effects. The more sophisticated ones of these models are those using microscopically motivated internal state variables. We present such a thermodynamically consistent model which perfectly fits into the variational structure of dissipative standard materials. In this framework, the material behavior is described in terms of an energy storage function and a dissipation potential in order to take into account dissipative effects, e.g. irreversible polarization and strains in ferroelectrics. Based on such variational principles it is quite straightforward to derive suitable finite element formulations for the solution of the global boundary value problem of the coupled electro-mechanical continuum.

The material behavior under complex load scenario is discussed based on numerical examples. It will be shown that the material model is able to capture all material nonlinearities in ferroelectrics: dielectric hysteresis, butterfly hysteresis, ferroelastic hysteresis and mechanical depolarization. The robustness of the outlined methods is demonstrated by investigations of the poling processes in structures with strong electric field inhomogeneities caused by complex electrode layouts.

Presenting Author: Felix Sutter Karlsruhe Institute of Technology