Snap-through instability analysis of dielectric elastomers with consideration of chain entanglements

Abstract

It is widely recognized that the extension limit of polymer chains has a significant effect on the snap-through instability of dielectric elastomers (DEs). The snap-through instability performance of DEs has been extensively studied by two limited-stretch models, i.e., the eight-chain model and Gent model. However, the real polymer networks usually have many entanglements due to the impenetrability of the network chains as well as a finite extensibility resulting from the full stretching of the polymer chains. The effects of entanglements on the snap-through instability of DEs cannot be captured by the previous two limited-stretch models. In this paper, the nonaffine model proposed by Davidson and Goulbourne is adopted to characterize the influence of entanglements and extension limit of the polymer chains. It is demonstrated that the nonaffine model is almost identical to the eight-chain model and is close to the Gent model if we ignore the effects of chain entanglements and adopt the affine assumption. The suitability of the nonaffine model to characterize the mechanical behavior of elastomers is validated by fitting the experimental results reported in the open literature. After that, the snap-through stability performance of an ideal DE membrane under equal-biaxial prestretches is studied with the nonaffine model. It is revealed that besides the prestretch and chain extension limit, the chain entanglements can markedly influence the snap-through instability and the path to failure of DEs. These results provide a more comprehensive understanding on the snap-through instability of a DE and may be helpful to guide the design of DE devices.