Thermo-electro-magnetostrictive unequal-biaxial taut states in thin elastomeric membranes

Wrinkles, with regular periodic patterns in thin elastomeric membranes, occur to relax in-plane compressive stresses through out-of-plane deformations. Existing studies on such wrinkling have primarily ignored the thermo-electro-magnetostrictive unequal-biaxial taut states, focusing instead on the equal-biaxial deformations of thin membranes. Soft actuators made of electro-magneto-active (EMA) membranes, used mainly in soft robotics, often exhibit a variety of instabilities, which may adversely affect their performance and lead to actuator failure. Conversely, fine-tuned wrinkles in their regular periodic patterns can be used proactively in specific applications that necessitate an intentional loading transformation and dual responsiveness to electromagnetic fields. This paper theoretically develops a physics-based thermo-electro-magnetostrictive unequal-biaxial deformation model of thin EMA membranes, incorporating classical tension field theory to predict the thresholds on the taut domains in the plane of principal stretches. The model solution is then experimentally verified for a readily available thin membrane. In addition, the analytical findings tie an unanswered ideal remark on the deviations of taut states with the biaxiality ratio of the unequal-biaxially deformed wrinkle appearance in thin EMA-based smart membranes.