Coupled thermo–electro–mechanical nonlinear dynamic analysis of anisotropic visco-hyperelastic DEMES actuators

Abstract

Soft active polymers respond strongly to external fields due to their molecular architecture and material characteristics. Among these, dielectric elastomers-a widely used class of soft active polymers exhibit large electro–mechanical deformation when electrically stimulated. When a pre-stretched dielectric elastomer membrane is bonded to a compliant frame, the assembly naturally relaxes into a dielectric elastomer minimum energy structure (DEMES). In the present study, the dynamic response of such DEMES actuators is analyzed by incorporating the coupled effects of membrane pre-stretch, material anisotropy, and ambient temperature. A Zener rheological model, consisting of a Maxwell element in parallel with a spring, is used to represent the visco–hyperelastic behavior, and an analytical neo-Hookean material-based formulation is developed. A computationally efficient governing model is derived using the non-conservative Euler–Lagrange equation based on the principle of least action. The proposed framework is applied to examine equilibrium configurations, transient response, DC and AC actuation characteristics, periodicity (using Poincaré and phase-portrait analysis), and resonant behavior. The results show that membrane pre-stretch, anisotropy, and temperature significantly influence the oscillation amplitude, permanent deformation, dynamic stability, and resonant frequency. The temperature-dependent behavior of isotropic membranes leads to supercritical pitchfork bifurcation but anisotropic systems show faster convergence and larger deformations under identical conditions. The proposed analytical model offers essential design directions which enable engineers to optimize DEMES-based soft robotic actuators for operation across different environmental settings. © 2026 Elsevier Masson SAS