A universal relation for a chemomechanically changing rubber cylinder

Abstract

This work studies a rubber cylinder that is held at a fixed uniaxial stretch, given a small amplitude twist and then increased in temperature to a regime where processes of scission and re-cross-linking of macromolecular network junctions take place. In particular, it examines the relation between the torsional stiffness and the axial force. When the uniaxial stretch and twist are held fixed, it is shown that Rivlin’s universal relation holds, i.e. there is a specific relation between the torsional stiffness and the axial force that is independent of material, temperature and time and depends only on the undeformed cylinder radius and the axial stretch ratio. Modifications to this relation are developed if the twist changes or the temperature is reduced to a level where the processes stop.