Mechanical instability of amorphous polymeric networks: Asymmetric deformation under symmetric biaxial tension

Asymmetric deformation of a symmetrically loaded rubber sheet was observed, many years ago, by Treloar in his experiments on natural rubber. The problem has recently been studied by Kearsley, and the possibility of asymmetric deformations in an equi-biaxial state of force is predicted by the use of phenomenological constitutive relations. In the present study, the problem is analyzed in relation to the molecular constitution of rubber networks. It is shown that mechanical instability in symmetrically loaded networks may be possible only for limited choices of molecular parameters such as junction functionality, degree of crosslinking, and the degree of swelling during crosslinking and during deformation. Stability of multiple valued deformations is discussed by thermodynamic considerations of the elastic potential.