Quantum-statistical approach to dynamic problems of solid mechanics

The present article reviews a quantum-statistical approach to dynamic problems in solid mechanics, when macroscopic defects, nucleation and propagation are not decisive in the irreversible deformation and fracture of a solid. The basic principles to construct quantum and quantum-statistical models of an irreversible deformed or fractured solid are discussed. A general quantum-statistical model of irreversible deformations and fracture of a solid under dynamic (shocking) loading is considered. The connection between the quantum-statistical approach and fractal solid mechanics is discussed. It is shown that the quantum-statistical approach is useful for an adequate description of various behavior patterns and fracture phenomena in irreversible deformed solid under dynamic loading. Some future research trends in this area are suggested as well as potential applications in basic and applied research. (Author)