  We study the kinetics of nonlinear irreversible fragmentation. Here
fragmentation is induced by interactions/collisions between pairs of particles,
and modelled by general classes of interaction kernels, and for several types
of breakage models. We construct initial value and scaling solutions of the
fragmentation equations, and apply the "non-vanishing mass flux "criterion for
the occurrence of shattering transitions. These properties enable us to
determine the phase diagram for the occurrence of shattering states and of
scaling states in the phase space of model parameters.
