Solid Continuum with Thermofluctuation Kinetics of Microcracks. Phase Transition

Abstract

Thermodynamic equations for a solid and a solid continuum under stress are derived on the basis of a multicomponent mean field Markov process for thermofluctuation kinetics of microcracks. The resulting continuum is viscous elastoplastic continuum with damage. It can radiate elastic waves . The existence of phase transitions with microcrack density as an order parameter is proved for a stationary state of a special model of solid. For a finite large system the distribution of the logarithmic power of acoustic emission at a critical point is similar to the distribution of the logarithmic energy of earthquakes.