D. Garagash et E. Detournay, SIMILARITY SOLUTION OF A SEMIINFINITE FLUID-DRIVEN FRACTURE IN A LINEAR ELASTIC SOLID, Comptes rendus de l'Academie des sciences. Serie II. Mecanique, physique, chimie, astronomie, 326(5), 1998, pp. 285-292
A similarity solution for a steadily moving semi-infinite fluid-driven
fracture in an impermeable linear elastic solid is described in this
note. The existence of a lag, of a priori unknown length, between the
crack tip and the fluid front is explicitly taken into account. The as
ymptotic behavior of the solution at the tip is consistent with linear
elastic fracture mechanics, whereas its asymptotic behaviour at infin
ity corresponds to a singular solution constructed under the assumptio
n of zero fluid lag. A universal relation between fluid lag and fractu
re toughness is obtained. (C) Academie des Sciences/Elsevier, Paris.