Bending a gel beam with consideration of entanglements and finite extensibility

Abstract

A hybrid beam containing a gel layer attached on the top of an elastic non-swellable substrate has been normally used to manufacture diverse sensors and actuators. Generally, when the system uses different gels, it is necessary to develop differentiated models for the hybrid beam. Recently, on the basis of the generalized ideal elastomeric gel model, a unified relationship between the gels' swelling and the elastic beam's bending curvature is formulated by Cai, which is separated from some particular swelling mechanisms of gels. He plugged neo-Hookean model and Gent model of the stretching polymer network to the generalized equations. However, the polymer networks usually have many entanglements due to the uncrossability of the network chains as well as a finite extensibility resulting from the full stretching of the network chains. The effect of entanglements cannot be captured by these two models. In this letter, the nonaffine model proposed by Davidson and Goulbourne is adopted to the generalized equations derived by Cai. The results show that entanglements as well as chain extensibility have important influences on the mechanical bending behaviors of the gels' beam.