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Analytical Expression for Fracture Profile in Viscoelastic Crack Propagation

We derive an analytical expression for the strain field during steady-state crack propagation in viscoelastic solids described by the standard linear solid (Zener) model. This expression reveals three regions in the fracture profile and in the strain field ahead of the crack tip, each distinguished by power-law exponents that evolve with distance from the crack tip. These features explain the experimentally observed crack-tip sharpening in rubbers and gels as the crack-propagation velocity increases, often associated with catastrophic failure triggered by a velocity jump. Furthermore, we establish de Gennes' viscoelastic trumpet on a continuum-mechanical foundation, previously based only on a scaling argument.