  The most important characteristics of the fragmentation of heterogeneous
solids is that the mass (size) distribution of pieces is described by a power
law functional form. The exponent of the distribution displays a high degree of
universality depending mainly on the dimensionality and on the brittle-ductile
mechanical response of the system. Recently, experiments and computer
simulations have reported an energy dependence of the exponent increasing with
the imparted energy. These novel findings question the phase transition picture
of fragmentation phenomena, and have also practical importance for industrial
applications. Based on large scale computer simulations here we uncover a
robust mechanism which leads to the emergence of energy dependence in
fragmentation processes resolving controversial issues on the problem: studying
the impact induced breakup of plate-like objects with varying thickness in
three dimensions we show that energy dependence occurs when a lower dimensional
fragmenting object is embedded into a higher dimensional space. The reason is
an underlying transition between two distinct fragmentation mechanisms
controlled by the impact velocity at low plate thicknesses, while it is
hindered for three-dimensional bulk systems. The mass distributions of the
subsets of fragments dominated by the two cracking mechanisms proved to have an
astonishing robustness at all plate thicknesses, which implies that the
non-universality of the complete mass distribution is the consequence of
blending the contributions of universal partial processes.
