Unequal-biaxial taut states of functionally graded dielectric elastomers

A thin dielectric elastomeric (DE) plate with thickness gradients deforms and wrinkles under applied voltages. Such wrinkling, with regular periodic patterns in thin functionally graded DEs, occurs to relax in-plane compressive stresses through out-of-plane deformations. These functionally graded DE-based soft actuators, primarily used in soft robotic applications, exhibit highly localized point loads compared to non-graded soft actuators. DE-based soft actuators frequently exhibit a variety of instabilities, which may adversely affect their functioning and trigger device failure. Conversely, fine-tuned wrinkles can be utilized proactively in specific applications, necessitating an intentional transformation with directional gradients and the truncation of biaxial deformations. This paper presents an experimentally verified continuum physics-based model under a special case for unequal-biaxial deformation in functionally graded DEs. The proposed model integrates classical tension field theory to predict thresholds in taut domains within the plane of principal stretches. The model solutions provide insight into the deviations of taut domains influenced by the graded parameter and the biaxiality ratio in unequal-biaxial deformations of wrinkle formations in this material class.