  In the present paper we consider the problem of the fragmentation of an
aluminum projectile on a thin steel mesh shield at high-velocity impact in a
three-dimensional (3D) setting. The numerical simulations are carried out by
smoothed particle hydrodynamics method applied to the equations of mechanics of
deformable solids. Quantitative characteristics of the projectile fragmentation
are obtained by studying statistics of the cloud of fragments. The considerable
attention is given to scaling laws accompanying the fragmentation of the
projectile. Scaling is carried out using the parameter K which defines the
number of the mesh cells falling within the projectile diameter. It is found
that the dependence of the critical velocity Vc of fragmentation on the
parameter K consists of two branches that correspond to two modes of the
projectile fragmentation associated with the "small" and "large" aperture of
the mesh cell. We obtain the dependences of the critical velocity Vc on the
projectile diameter and the mesh parameters for the both modes of the
fragmentation. It is shown that the average cumulative mass distributions
constructed at Vc exhibit the property of scale invariance, splitting into two
groups of distributions exactly corresponding to the modes of the projectile
fragmentation. In each group, the average cumulative distributions show good
coincidence in the entire mass region, moreover in the intermediate mass region
the each group of distributions has a power-law distribution with an exponent
tau different from that in the other group. The conclusion about the dependence
of the exponent of the power-law distribution tau on the fragmentation mode is
made.
