Bending of gel beams: Effect of deflection rate and Hertzian indentation

When the modulus of a gel rod is measured by beam-bending, the modulus that is obtained may be the shear modulus (if the deflection rate is high) or Young's modulus (if the deflection rate is low). This behavior results from the flow of liquid within the rod, as explained previously [J. Non-Cryst. Solids 142 (1,2) (1992) 18-35]. In this paper, the problem is re-examined in more detail, using a new analysis for a cylindrical beam subjected to three-point bending. Criteria are provided for determining the accuracy of the modulus measurement. In particular, it is shown that significant indentation occurs at points of contact with the pushrod and the end supports, and this must be taken into account to get an accurate measure of the elastic modulus of the gel. The analysis is compared to data for silica gel and shown to be in excellent agreement.