Similarity solution of a semi-infinite fluid-driven fracture in a linear elastic solid

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 asymptotic behavior of the solution at the tip is consistent with linear elastic fracture mechanics, whereas its asymptotic behaviour at infinity corresponds to a singular solution constructed under the assumption of zero fluid lag. A universal relation between fluid lag and fracture toughness is obtained.