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The most important characteristics of the fragmentation of heterogeneoussolids is that the mass (size) distribution of pieces is described by a powerlaw functional form. The exponent of the distribution displays a high degree ofuniversality depending mainly on the dimensionality and on the brittle-ductilemechanical response of the system. Recently, experiments and computersimulations have reported an energy dependence of the exponent increasing withthe imparted energy. These novel findings question the phase transition pictureof fragmentation phenomena, and have also practical importance for industrialapplications. Based on large scale computer simulations here we uncover arobust mechanism which leads to the emergence of energy dependence infragmentation processes resolving controversial issues on the problem: studyingthe impact induced breakup of plate-like objects with varying thickness inthree dimensions we show that energy dependence occurs when a lower dimensionalfragmenting object is embedded into a higher dimensional space. The reason isan underlying transition between two distinct fragmentation mechanismscontrolled by the impact velocity at low plate thicknesses, while it ishindered for three-dimensional bulk systems. The mass distributions of thesubsets of fragments dominated by the two cracking mechanisms proved to have anastonishing robustness at all plate thicknesses, which implies that thenon-universality of the complete mass distribution is the consequence ofblending the contributions of universal partial processes.

Emergence of energy dependence in the fragmentation of heterogeneous materials