## Laboratory Rheology

### Scientific lecture

**10 May 2013 (Friday), 14.00, 200 auditory - Lecture of Prof. Gross, Darmstadt, Germany**

**MODELLING AND SIMULATION OF ELECTROACTIVE MATERIALS AND STRUCTURES**

**Prof. Dr.-Ing. Dietmar Gross, Technische Universität Darmstadt**

**ABSTRACT**

Examples of three different materials are discussed in the presentation: Ferroelectrics, Dielectric Elastomers and Ferroelectrets.

Domain switching near a crack tip in ferroelectrics is regarded as a major aspect of local nonlinear behaviour, playing a significant role in the fracture behaviour. A continuum phase field model developed for domain structure evolution in ferroelectrics is used to study the polarization switching near the crack tip. By introducing the spontaneous polarization as an order parameter, the model leads to thermodynamically consistent and electro-mechanically coupled constitutive relations and evolution equations. Using a 2D or 3D implementation of the model in the Finite Element Method, we examine the problem of a stationary crack embedded in a ferroelectric single crystal. Calculations show the domain structure around the crack when a mechanical or electric load is applied. The influence of the domain switching on fracture parameters and various crack face boundary conditions will be discussed.

Dielectric elastomer actuators, consist of an elastomer film, sandwiched between compliant electrodes. Under certain circumstances the elastomer actuator may suffer an electro-mechanical instability. As the applied potential increases, the compression becomes stronger and reduces the thickness further, which in return results in an even higher electric field. Above a critical field this can eventually lead to collapse of the setup. Due to the nonlinearity of the material, the nature of large deformation and the coupling of different physical fields, systematic studies preferably can be done by numerical investigations based on reasonable models. In the present work, the modeling and the numerical simulation of deformable dielectrics are discussed in a coupled electro-mechanical framework. Using numerical simulation, the electro-static contraction of a soft actuator is calculated and verified by the corresponding analytical solution. The operational curve is obtained for a capacitor-like setup using the neo-Hooke material model. The results show that instability occurs above a critical applied electric field. Furthermore, strategies to increase the electromechanical coupling by a modified microstructure are discussed.

Finally, in internal variable based model is proposed to simulate the hysteresis curve of the charge density evolution at the interface in ferroelectrets. In the model a history dependent constitutive relation is used between the internal charge density and the actual electric field of the polymer at the interface. A Maxwell stress based electromechanical model is used for the polymer and for the medium where the Paschen breakdown occurs. The model is presented in the framework of finite deformation which enables the possibility of taking into account the influence of deformation change. By using the nonlinear finite element implementation of the models, a tube-like ferroelectret is simulated. The hysteresis curves of the charge density at the interfaces and the longitudinal piezoelectric constant are calculated showing a good agreement with experimental results. Furthermore, numerical studies are discussed which show the influence of geometry and elastic parameters on the hysteresis and piezoelectricity.

Modified date:14-05-2012