The effect of mechanical tension on the multifractal characteristics of the lateral surface of a Fe₇₇Ni₁Si₉B₁₃ amorphous alloy is studied by scanning tunneling microscopy (STM). It is established that, at small loads, the surface is smoothed out much as a crumpled sheet of paper is smoothed out under tension. With an increase in the load, there appears a tendency to the formation of a fractal structure on the surface.

The change in temperature under adiabatic elastic deformation of solids (thermoelastic effect) at low and high temperatures has been calculated taking into account the quantum properties of thermal dynamics. In the high-temperature range, a quantum-mechanical correction to the classical Kelvin formula has been found. In the low-temperature range, a new formula for the description of the thermoelastic effect has been derived.

The basic principles of the Zhurkov kinetic approach are analyzed in light of the modern idea of self-organization of nonlinear systems under nonequilibrium conditions. It is indicated that the final state before fracture can be described in terms of the model of a self-organized critical state.

The experimental data on the surface relief of loaded ribbons of an amorphous alloy have been obtained. The distributions of surface defects formed under loading have been analyzed using the wavelet transform and box counting method. Moreover, the data on the time accumulation of microcracks in the volume of a loaded granite specimen have been examined. It has been shown that power-law size distributions of defects (scaling) appear on the surface and in the bulk before fracture. It has been revealed that the appearance of the power-law distributions is one of the indications of the formation of the self-organized critical state. The formation of the self-organized critical state in the bulk and on the surface of the material has been considered. It has been established that the formation of the self-organized critical state precedes the fracture of a solid.

A cellular automaton model for describing the fracture of mechanically loaded heterogeneous materials has been constructed. Two extreme scenarios of the fracture process have been revealed, i.e., the dispersion (percolation) scenario, according to which defects accumulate uniformly throughout the volume of the material, and the correlated scenario (growth of predominantly a single source), which have been observed during the fracture of real materials. It has been shown that, in the case of the correlated fracture, a crack grows through the mechanism of ejection of double kinks of its front. In the intermediate case, the process occurs according to both scenarios: first, the slow accumulating (percolation) fracture and, then, the rapid correlated fracture; by the time the latter process begins, a self-organized critical state with a power-law size distribution of cracks typical of it has been formed.