Undular bores generated by fracture.

Abstract

Undular bores, or dispersive shock waves, are nonstationary waves propagating as oscillatory transitions between two basic states, in which the oscillatory structure gradually expands and grows in amplitude with distance traveled. In this work we report an important mechanism of generation of nonlinear dispersive shock waves in solids. We demonstrate, using high-speed pointwise photoelasticity, the generation of undular bores in solid (polymethylmethacrylate) prestrained bars by natural and induced tensile fracture. For the distances relevant to our experiments, the viscoelastic extended Korteweg-de Vries 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 linearization near the nonzero prestrain level. The experimental and theoretical approaches presented open avenues and analytical tools for the study and applications of dispersive shock waves in solids.