A novel hydraulic fractures growth formulation
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Propagation of a fluid-driven crack in an impermeable linear elastic medium under axis-symmetric conditions is investigated in the present work. The fluid exerting the pressure inside the crack is an incompressible Newtonian one and its front is allowed to lag behind the propagating fracture tip. The tip cavity is considered as filled by fluid vapors under constant pressure having a negligible value with respect to the far field confining stress. A novel algorithm is here presented, which is capable of tracking the evolution of both the fluid and the fracture fronts. Particularly, the fracture tracking is grounded on a recent viscous regularization of the quasi-static crack propagation problem as a standard dissipative system. It allows a simple and effective approximation of the fracture front velocity by imposing Griffith's criterion at every propagation step. Furthermore, for each new fracture configuration, a non linear system of integro-differential equations has to be solved. It arises from the non local elastic relationship existing between the crack opening and the fluid pressure, together with the non linear lubrication equation governing the flow of the fluid inside the fracture.
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