Undular Bores Generated by Fracture

Abstract

Undular bores, or dispersive shock waves, are non-stationary waves propagating as oscillatory transitions between two basic states, in which the oscillatory structure gradually expands and grows in amplitude with distance travelled. We demonstrate for the first time, using high-speed pointwise photoelasticity, the generation of undular bores in solid (polymethylmethacrylate) pre-strained bars by natural and induced tensile fracture. For the distances relevant to our experiments, the viscoelastic extended Korteweg - de Vries (veKdV) equation is shown to provide very good agreement with the key observed experimental features for suitable choice of material parameters, while some local features at the front of the bore are also captured reasonably well by the linearisation near the nonzero pre-strain level. The experimental and theoretical approaches presented open new avenues and analytical tools for the study and application of dispersive shock waves in solids.

16 pages, 10 figures

References in corpus (5)

• Undular bore theory for the Gardner equation
• Employing pre-stress to generate finite cloaks for antiplane elastic waves
• Deformation and failure maps for PMMA in uniaxial tension
• Modulation theory and resonant regimes for dispersive shock waves in nematic liquid crystals
• Longitudinal bulk strain solitons in a hyperelastic rod with quadratic and cubic nonlinearities

Cited by in corpus (2)

• Soliton-mean field interaction in Korteweg-de Vries dispersive hydrodynamics
• Whitham Shocks and Resonant Dispersive Shock Waves Governed by the Higher Order Korteweg-de Vries Equation