Stability of an anisotropic dielectric elastomer plate

Abstract A variety of methods have been proposed to improve the performance of dielectric elastomer transducers, which lead to the anisotropic electromechanical behavior of the material. This paper theoretically analyzes the effect of material anisotropy on the diffuse modes of instability in dielectric elastomer plates. As a first step, a transversely isotropic material is considered in the present study. The linearized incremental theory is used and the plate thickness is considered in the stability analysis. The bifurcation equations are solved with Wolfram Mathematica (Wolfram Research, Inc., 2019) [1] to obtain the critical stretches under different electric field. It is found that, compared to the isotropic material, material anisotropy results in larger unstable regions and higher critical stretches above which the plate is stable. It is also shown that material anisotropy has a stronger influence on a thinner plate. As the plate thickness increases, the influence decreases.