Fig. 1.

Staggered grid and implementation of cracks. Different symbols denote grid points on which different quantities are allocated as follows; diamonds: horizontal particle velocity and mass density; circles and semicircles: vertical particle velocity and mass density; squares: normal stress, λ, and μ; triangles: shear stress and μ. Here, λ and μ are the Lamé parameters. The region enclosed by the dotted line corresponds to a crack, in which the solid triangles denote the points with zero shear stress. Each pair of gray and black semicircles denotes two close points located on the upper and lower crack faces, respectively, whose separation is much smaller than the grid spacing.