Dynamic inflation of elastomeric spherical membranes undergoing time dependent chemorheological changes in microstructure

Abstract

When an elastomeric object is subjected to loads while at a sufficiently high temperature, it deforms and undergoes changes in its macromolecular microstructure consisting of time dependent scission of macromolecular network junctions, recoiling of the affected molecules and crosslinking to form new networks with new reference configurations. A constitutive theory has been developed in previous work that accounts for the interaction of deformation and chemorheological changes. This constitutive theory is used to study the dynamical response of a spherical elastomeric membrane under internal pressure at a temperature high enough for the scission/cross-linking process to occur. Quasi-static response at a constant pressure and temperature, studied in previous work, showed that, the membrane radius increases with time due to creep that results from the scission. There can be a finite time when the membrane diameter undergoes a very rapid, or even infinite, rate of increase. This event depends on the properties of the molecular networks, the rate of formation of new networks, and the history of the increase in the membrane diameter. This present work investigates this effect when membrane inertia is included. It is found that the inclusion of inertia eliminates the sudden rapid increases in radius. The motion is also shown to depend on a characteristic time for scission relative to a characteristic time that represents the effects of inertia. Numerical results are presented for the case when the networks act as Mooney–Rivlin materials.