# University of Minnesota

Aerospace Engineering and Mechanics

**Spring 2002 Seminar Series**

*Asymptotic Solutions of Fluid-Driven Fractures*

*Abstract*

**The talk will focus on the asymptotic analysis of fracture propagation
driven by a viscous fluid in a linear elastic solid with small toughness. A
priori unknown lag between the fluid and fracture fronts will be taken in
consideration. Upon discussion of the fluid-driven fracture scaling, it will be
shown that two asymptotic regimes exist. The first regime develops when the
fracture propagates under large confining stress or, equivalently, at large
time. This regime corresponds to a fully fluid-filled crack (nearly zero lag).
The other regime characterizes propagation under small (or zero) confining
stress or, equivalently, at small time, and corresponds to the fluid-filled
fraction of the crack being small (the lag accounts for most of the fracture
length. Under conditions of small toughness, both asymptotic cases are singular
perturbation problems. In the large stress/time case, the solution on the scale
of the fracture is given by the zero-toughness zero-lag solution, whereas the
influence of toughness is localized to a tip boundary layer possessing the
linear elastic fracture mechanics singularity at the fracture tip. In the small
stress/time case, the injected fluid forms a thin boundary layer near the
fracture inlet while the solution away from the inlet is provided by the
solution for the crack loaded at the center by a pair of concentrated forces.
The latter are obtained from the solution of the inlet fluid boundary
layer.**

### Friday, April 5, 2002

209 Akerman Hall

2:30-3:30 p.m.

### Refreshments served after the seminar in
227 Akerman Hall.

Disability accomodations provided upon request.

Contact Kristal Belisle, Senior
Secretary, 625-8000.