Shear crack propagation along weak planes in solids: a finite deformation analysis incorporating the linear harmonic potential

Recent molecular dynamics simulations of dynamic crack propagation have shown that a shear crack propagating at a sub-Rayleigh speed may have a finite crack opening, but the crack opening vanishes once the crack tip velocity exceeds the shear wave speed. This observation is at odds with classical linear elastic solutions which indicate that a pure shear crack should have zero opening. To understand this discrepancy, we develop in this paper a …