Electrode and electroactive polymer layout design using topology optimization

TL;DR

This paper addresses the challenge of simultaneously designing electrode layouts and dielectric EAP structures under electrostatic–electromechanical coupling. It introduces a gradient-based, multi-material topology optimization framework with Exponential Material Interpolation (EMI) and a truncated extended-domain model for surrounding free space, enabling electrode connectivity and targeted field concentration inside the EAP. Through numerical experiments, the authors show that arbitrary electrode/EAP layouts can be generated, producing thin active EAP layers with connected electrodes and strong field localization that drives deformation. The approach integrates PDE-filter regularization, smooth projection, and a CRISP-like density penalty to obtain near-binary designs, offering a practical method for designing soft actuators with controlled electric-field pathways and connectivity.

Abstract

When electrically stimulated, electroactive polymers (EAPs) respond with mechanical deformation. The goal of this work is to design electrode and EAP layouts simultaneously in structures by using density-based, multi-material topology optimization. In this novel approach the layout of electrodes and EAP material are not given a priori but is a result from the topology optimization. Material interpolation based on exponential functions is introduced, allowing a large flexibility to control the material interpolation. The electric field in the surrounding free space is modeled using a truncated extended domain method. Numerical examples that demonstrates the method's ability to design arbitrary EAP and electrode layouts are presented. In these optimized structures, electrode material is continuously connected from the electrical sources to opposite sides of the EAP material and thereby concentrating the electric field to the EAP material which drives the deformation.

Figures (6)

• Figure 1: A solid body $\mathcal{B}_0$ surrounded by a free space $\mathcal{F}_0$ in the material and spatial configurations.
• Figure 2: The penalization function in \ref{['eq:CRISP']} with example values on $\alpha$ and $\delta$.
• Figure 3: The EMI interpolation in \ref{['eq:EMI']} with example values on $\xi^1$, $\xi^2$, and $q$.
• Figure 4: Illustration of the geometry and boundary conditions for the actuator with thickness 1 mm. The square design domain is surrounded by a large free space. The initial design and the two cases for the optimization are presented.
• Figure 5: Optimized design for maximizing vertical displacement $u_{out}^{v}$. a) Deformed structure cut-out where $0.5\leq \Bar{\rho}_1$ and where $\Bar{\rho}_2=0$ indicates electrode material and $\Bar{\rho}_2=1$ EAP. Solid green lines indicates the undeformed configuration. b) Electric potential $\phi$ in the undeformed total domain with the design domain highlighted as a black square and outline of the final design in green. Note that the highest gradient is concentrated to the EAP material. c) Objective function with converged value $g_0=-0.399$ mm at iteration 286. The designs for selected iterations are also shown. d) Volume constraints.