Variational Based Stability Analysis in Coupled Electro-Mechanics at Finite Strains

Smart or functional materials are in focus in broad fields of recent research. In particular, electroactive polymers (EAPs) with their large actuator strains are used for innovative design in robotics. These materials become practical as soon as the material is robust, reliable and long lived. However, EAPs suffer from different types of instabilities, such as unstable thinning of actuators, local buckling induced by coexistent states and electrical breakdown. One distinguishes between structural instability, i.e. instabilities in the global structural response like buckling or wrinkling and local or material instability, e.g. the formation of microstructures and phase decompositions. These effects are well known and analyzed for purely mechanical phenomena, but not fully developed in the context of electro-mechanically coupled problems. To this end, we develop new variational-based stability criteria in finite electro-elastostatics, by postulating an electro-mechanical quasi-convexity condition for weakly convex energy and weakly convex-concave energy-enthalpy formulations. Starting from distinct variational principles, we develop criteria for local and global stability and construct stability checks, which accompany equilibrium paths for the detection of critical points in finite element models. Numerical examples validate the developed concepts for boundary value problems. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)