Dynamic Destruction as Analogs of Critical Phenomena in Metal Samples with Various Geometries within a Wide Ranges of Amplitude–Time Characteristics of External Action

The quantitative characteristics of the products of dispersion and the cascade of dissipative structures arising in metals under shock-wave loading are determined. The fractal dimension df and the Hurst exponent H (standardized range of dissipative structures) of the cascade of hydrodynamic modes, the roughness of the fracture surface, and the dispersion products are determined. Destructive processes occurring in loaded samples are numerically simulated using the Lagrangian technique TIM 3D [1, 2]. It is shown that a cascade of dissipative structures at different scale–temporal levels (nanolevel, mesolevel I, mesolevel II, and macrolevel) is a fractal cluster, and it is a percolation cluster on the threshold of a macrofracture, when there is connectivity in the system of dissipative structures [1, 2]. The self-similarity of dissipative structures is due to the self-organization in nonequilibrium systems; and the dynamic fracture and dispersion processes are examples of scale invariance. The scale invariance of the dissipative structures indicates the nonequilibrium system has reached a critical state.