Mechanisms of structural relaxation are linked with the metastability of nonequilibrium potential of solid with defects and the generation of collective modes of defects responsible for the plastic strain and damage localization. It is shown that spatial-temporal dynamics of collective modes (auto-solitary and blow-up dissipative structures) provide the anomalous relaxation ability of nonlinear system “solid with defects” in the conditions of the specific type of criticality – structural-scaling transition. These modes have the nature of self-similar solutions of evolution equations for damage parameter (defect-induced strain) and represent the “universality class” providing the four power law for a steady plastic front, splitting of an elastoplastic shock wave front, and elastic precursor decay kinetics. Wide-range constitutive equations reflecting the linkage between defect-induced mechanisms and structural relaxation are used in the numerical simulation for shock wave loading of metals and ceramics in the comparison with experiments.
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