Optimal biaxial prestretch ratios of soft dielectric elastomer actuators for maximal voltage-induced displacement

Prestretch plays an indispensable role in programming the voltage-induced deformation of dielectric elastomer actuators (DEAs). However, lacking rational design methods, the level of prestretch is usually determined through time-consuming experiments and trial-and-error tests. In this paper, we aim to quantitatively determine the optimal biaxial prestretch ratios for maximizing the voltage-induced displacement of interest. Based on the Lagrange method and adjoint sensitivity analysis, we obtain the derivative of the displacement field with respect to the principal prestretch ratios, in which the nonlinearities and complex electromechanical coupling of DEAs are rigorously taken into consideration. The derivative information allows for performing gradient-based optimization at a high convergence rate. We propose a comprehensive optimization framework connecting the nonlinear finite element analysis and sensitivity analysis to iteratively identify the optimal prestretch ratios. We validate our method on two classical types of DEAs, i.e., planar DEAs with fixed boundaries and free-standing three-dimensional dielectric elastomer minimum energy structures (DEMES). The simulation and experiment results both show that remarkable improvements in concerned displacements are obtained compared with the non-optimized designs.