Mode II intersonic crack propagation in poroelastic media

Abstract

A crack is steadily running in an elastic isotropic fluid-saturated porous solid at an intersonic constant speed c. The crack tip speeds of interest are bounded below by the slower between the slow longitudinal wave-speed and the shear wave-speed, and above by the fast longitudinal wave-speed. Biot's theory of poroelasticity with inertia forces governs the motion of the mixture. The poroelastic moduli depend on the porosity, and the complete range of porosities n ∈ [0, 1] is investigated. Solids are obtained as the limit case n = 0, and the continuity of the energy release rate as the porosity vanishes is addressed. Three characteristic regions in the plane (n, c) are delineated, depending on the relative order of the body wave-speeds. Mode II loading conditions are considered, with a permeable crack surface. Cracks with and without process zones are envisaged. In each region, the analytical solution to a Riemann-Hilbert problem provides the stress, pore pressure and velocity fields near the tip of the crack. For subsonic propagation, the asymptotic crack tip fields are known to be continuous in the body [Loret and Radi (2001) J Mech Phys Solids 49(5):995-1020]. In