Overdamped Stress Relaxation in Buckled Rods
arXiv:cond-mat/0402082 · doi:10.1103/PhysRevE.70.031802
Abstract
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.
20 pages, 12 figures
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