Overdamped Stress Relaxation in Buckled Rods

We present a comprehensive theoretical analysis of the stress relaxation in a multiply but weakly buckled incompressible rod in a viscous solvent. In the bulk two interesting regimes of generic self–similar intermediate asymptotics are distinguished, which give rise to two classes of approximate and exact power–law solutions, respectively. For the case of open boundary conditions the corresponding non–trivial boundary–layer scenarios are derived by a multiple–scale perturbation (``adiabatic’') method. Our results compare well with – and provide the theoretical explanation for – previous results from numerical simulations, and they suggest new directions for further fruitful numerical and experimental investigations.