The Treloar–Kearsley instability in a swollen or thermally expanded elastomeric sheet

It has been observed in experiments that when a uniformly distributed equal biaxial tensile force is applied to an elastomeric sheet, as it increases the sheet first undergoes homogenous equal biaxial extensions. Then, at some state, the deformation can become an unequal biaxial extension. This event has usually been analyzed as a bifurcation during the deformation of a nonlinear elastic material. The material is regarded as incompressible and its volume does not change. In the present work, it is assumed that the elastomeric sheet first undergoes a uniform increase in volume due to either a temperature increase or swelling induced by a contained fluid. The sheet is then subjected to uniformly distributed equal biaxial forces. The influence of the increased volume on the bifurcation of the subsequent deformation is then investigated. Analyses are carried out using a constitutive equation for thermomechanical response introduced by Chadwick and one for swelling introduced by Pence. The initial volume increase is shown to have a significant effect on bifurcation.