Impacts of geometry on viscoelastic fracture fields

Fracture in viscoelastic materials is a key phenomenon across numerous natural and industrial applications. We address the question of how geometry impacts the structure of a viscoelastic field surrounding a fracture through a numerical and asymptotic study of the fields surrounding a steadily propagating crack in a Kelvin-Voigt material within a strip. To understand the influence of the strip width, we introduce a fracture Deborah number, D = Vη/LE, to characterize the interplay between crack velocity V, material viscosity η, geometric scale L and elastic modulus E. For small D, the problem reduces to an outer elastic region controlled by the geometry; and an inner viscoelastic zone of universal form and size Vη/E. For high D, our analysis reveals a novel double-decked structure comprising an outer near-one-dimensional deck dominated by a transverse viscous-elastic balance; and an inner deck of size L in which viscous and elastic dynamics continue to remain leading order, but simplify to a `quasi-viscous' constitutive regime in which longitudinal components of the constitutive law become dominantly viscous, but elastic stresses remain leading order in the transverse stresses. The regime necessitates a multiple-scales asymptotic theory to produce consistent matching between the inner and outer decks. The results yield new theoretical insight into how confinement modifies viscoelastic fracture fields and a toolkit for assessing the length scales between different rheological balances.