Electroactive polymers (EAPs) are considered as smart materials. Therein, a differentiation between an electric and an ionic EAP will be made. In this contribution, in particular the ionic polymer‐metal composites (IPMCs) are investigated which belong to the class of the ionic EAPs. These kind of materials act as an actuator and a sensor in variety of applications. The actuation application is given by applying an electrical voltage to the electrodes which instantaneously leads to the relocation of the mobile cations towards the cathode. The sensor application is performed by loading the IPMC mechanically which generates an electrical field. For the prediction of the behavior of this material, the theoretical framework of electrodynamics in combination with the Theory of Porous Media has been taken into account, see [1–3]. A numerical example for the 2D sensing behavior is investigated.

In the present contribution, we compare (quantitatively) different mixed least-squares finite element methods (LSFEMs) with respect to computational costs and accuracy. Various first-order systems are derived based on the residual forms of the equilibrium equation and the continuity condition. The first formulation under consideration is a div-grad first-order system resulting in a three-field formulation with total stresses, velocities, and pressure (S-V-P) as unknowns. Here, the variables are approximated in H(div) × H1 × L2 on triangles and in H1 × H1 × L2 on quadrilaterals. In addition to that a reduced stress-velocity (S-V) formulation is derived and investigated. S-V-P and S-V formulations are promising approaches when the stresses are of special interest, e.g., for non-Newtonian, multiphase or turbulent flows. The main focus of the work is drawn to performance and accuracy aspects on the one side for finite elements with different interpolation orders and on the other side on the usage of efficient solvers, for instance of Krylov-space or multigrid type.

AbstractIonic polymer‐metal composites (IPMCs) serve as electro‐mechanical transducers for actuator and sensor applications, see [1]. Typically, they are sandwiched between two impermeable electrodes comprising the polymer network, the liquid, the fixed anions and the mobile cations. The actuation mechanism takes place by applying an electric potential (voltage) and the mobile cations move towards the cathode. Due to the relocation of the cations (electrostatic and ionic forces), a deformation of the IPMC can be observed. In contrast, the sensing mechanism is performed by applying a mechanical load yielding to a concentration redistribution and generating an electrical potential inside the IPMC. In Leichsenring [2], a parametric study has been carried out for the description of an IPMC. Therein, the Theory of Porous Media (TPM) was used, see [3], while the motion of the liquid and the cations were restricted. In the present contribution, the actuation and sensing behavior of an IPMC is presented within the framework of the TPM, see [5]. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Ionomeric polymer–metal composites (IPMCs) consist of an ionomer with bound anionic groups and mobile counterions. They are plated with noble impermeable metal cover layers. By application of an electric voltage, a transport of the mobile ions towards the respective electrode occurs. Due to local electrostatic and ionic forces, a local deformation of the IPMC can be observed. Therefore IPMCs are promising candidates for electrochemical transducers. In the present research, the chemo-electro-mechanical behavior of IPMCs is described within the framework of the theory of porous media. First, the field equations are derived with respect to the second law of thermodynamics. Second, a reduced set of equations for the chemo-electric behavior is formulated and discretized by applying the finite element method. In the numerical investigations a parametric study of the time and space dependent behavior is carried out in order to quantify the influence of different material compositions. Based on this study, the characteristic response of IPMC to the application of an electric voltage can be predicted. Concluding, the obtained computational framework is an excellent tool for the design of electrochemical transducers.

A thermo-electromechanical formulation for the description of ionic electroactive polymers is derived within the framework of the Theory of Porous Media. The model consists of an electrically charged porous solid saturated with an ionic solution. The saturated porous medium is assumed to be incompressible. Different constituents following different kinematic paths are considered such as solid, fluid, anions, cations and free charges. The electromechanical and the electrodynamic field equations are discussed. Based on the second law of thermodynamics, a consistent model is developed. With respect to the closure problem of the model, the needed constitutive relations and evolution equations are presented.

Ionic electroactive polymers are widely used in many engineering fields. These kind of materials can be stimulated to change their shape and size, see [1]. Since, the material under consideration has a complex multiphasic microstructure, such multiphasic materials are best described by a continuum mechanical approach. Thus, the presented model is based on the Theory of Porous Media (TPM), cf. [2]. In this contribution, we consider the Ionic Polymer Metal Composites (IPMCs). Stimulating by an electrical voltage, a structural deformation will be caused. Responsible for this deformation are the mobile ions. The focus of the presented model is to capture this material behavior, e.g. the distribution of the mobile cations. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

AbstractIn this contribution, a multiphase model will be presented in order to simulate ionic electroactive polymers (EAPs). The considered material model is developed within the framework of the Theory of Porous Media (TPM) which consists a thermo‐electro‐mechanical coupling. For the description of the model, a thermodynamically consistent formulation in consideration of the electrostatic forces and the fluid pressure will be derived. The presented model includes a charged polymer (solid) saturated by an electrolyte solvent (fluid). A boundary value problem (plate with a hole) is given. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

In this contribution we present the least‐squares finite element method (LSFEM) for the incompressible Navier‐Stokes equations. In detail, we consider a non‐Newtonian fluid flow, which is described by a power‐law model, see [1]. The second‐order problem is reformulated by introducing a first‐order div‐grad system consisting of the equilibrium condition, the incompressibility condition and the constitutive equation, which are written in residual forms, see [2]. Here, higher‐order finite elements which are an important aspect regarding accuracy for the present formulation are investigated. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

AbstractIn the present contribution we propose an improved mixed least‐squares finite element method (LSFEM) and compare it with standard LSFEMs with respect to performance aspects. In detail, we consider an approach for Newtonian fluid flow, which is described by the incompressible Navier‐Stokes equations. The basis for the associated symmetric minimization problem is a reduced stress‐velocity (s‐v) two‐field approach, see e.g. CAI ET AL. [1] and SCHWARZ & SCHRÖDER [2]. The main idea for the proposed formulation is to add an additional equation, which yields an overconstrained first‐order system. This approach does not introduce additional unknowns, so the advantage of two variables (stresses and velocities) remains. Finally, we present a numerical example in order to show the capability of the proposed formulation. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

AbstractThe focus of this contribution is the examination of the influence of different interpolation orders (especially for the pressure field) by solving the stationary incompressible Navier‐Stokes equations with least‐squares finite elements. We consider two different div‐grad first‐order systems which result in a three‐field formulation with stresses, velocitites and pressure, see e.g. SCHWARZ & SCHRÖDER [1] and BOCHEV & GUNZBURGER [2]. Additionally, a numerical example is presented to show the performance of the considered formulations. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)