Scission induced by circular shear and heat conduction in an elastomeric cylinder

Constitutive equations for the thermo-mechanics of elastomeric materials generally assume that they do not undergo microstructural change. A constitutive theory is discussed here which accounts for such changes arising from continuous scission of macromolecular junctions of elastomeric networks due to deformation and high temperatures and the subsequent cross-linking of molecules into new networks with new reference states. The total stress is the superposition of the stresses in the remainder of the original network and in each subsequently formed network. Each network acts as a temperature-dependent non-linear elastic material. The interaction of this material response with inhomogeneous deformation and temperature fields is studied for finite circular shear of a cylinder. Numerical results illustrate how the mechanical response of the cylinder depends on the temperature dependence of both the scission–cross-linking process and the properties of the elastic networks.