Overdamped Stress Relaxation in Buckled Rods

Details Overdamped Stress Relaxation in Buckled Rods Overdamped Stress Relaxation in Buckled Rods

2004-02-03

arxiv.org/abs/cond-mat/0402082v1

Phys. Rev. E 70, 031802 (2004)

Physics

Condensed Matter

Soft Condensed Matter

20 pages, 12 figures

Scientific paper

10.1103/PhysRevE.70.031802

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.

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