A model and numerical study for coiling of Kelvin-type viscoelastic filament

• Derive the strain rate and strain tensors of curved viscoelastic filament.
• Establish 1D governing equations for Kelvin-type viscoelastic filament coiling.
• The model can degenerate to the purely elastic rope coiling problem.
• The multivaluedness of numerical solution appears.
• Study effects of retardation time and other parameters to the coiling frequency.

Coiling problems of elastic rope and viscous jet have been fully studied both experimentally and theoretically, but very few studies exist for viscoelastic material. In this paper, a system of one-dimensional two-point boundary nonlinear equations for Kelvin material coiling is presented. The equations are solved numerically by continuation method. It is found that the coiling frequency depends on the dimensionless retardation time and other continuation parameters involving inertia and gravity. The multivaluedness of the solution is observed in the numerical study.