When an elastomeric material is subject to sufficiently high temperature, macromolecular network junctions can undergo time-dependent scission and re-crosslinking (healing). The material system then consists of molecular networks with different reference states. A constitutive framework, based on the experimental work of Tobolsky, is used to determine the evolution of deformation of a solid rubber cylinder spinning at constant angular velocity at an elevated temperature. Responses based on underlying neo-Hookean, Mooney-Rivlin, and Arruda-Boyce models, were solved numerically and compared. Different amounts of healing were studied for each case. For neo-Hookean molecular networks, there may be a critical finite time when the radius grows infinitely fast and the cylinder “blows up.” This time depends on the angular velocity and the rate of re-cross linking. In addition, no solution was possible for angular velocities above a critical value, even without the effects of scission. Such anomalous behavior does not occur for Mooney-Rivlin or Arruda-Boyce network response.
Synthesis of random parameter identification algorithms and estimates of current vessel motion parameters