Mathematical study on the propagation of Griffith crack in a dry sandy strip subjected to punch pressure

Abstract

The present study investigates the features of a moving Griffith crack in a dry sandy infinitely long and finitely thick isotropic strip with moving parallel punches of constant load acting on both of its boundaries owing to plane wave propagation under point loading. Coupled singular integral equations and Cauchy-type singularities are used to formulate the present model, the Dirac delta function is employed to analyse the point load located at the moving crack edge, and the properties of Hilbert transformation are employed to obtain the closed-form expression of the stress intensity factor with constant point loading. For the sake of validation, the obtained results are matched with pre-established and standard results. Numerical simulations and graphical illustrations are performed to analyse the influences of the prevalent parameters, viz., sandiness parameter, punch pressure, distinct point load positions, length and speed of the crack corresponding to the plane wave on the stress intensity factor for the considered dry sandy isotropic material strip.