A model for the propagation of strain solitary waves in solids with relaxing atomic defects

Abstract

A model for the propagation of nonlinear dispersive one-dimensional longitudinal strain waves in an isotropic solid with quadratic nonlinearity of elastic continuum is proposed by taking into account the interaction of the longitudinal displacements with the temperature field and the field of concentration of nonequilibrium (recombining) atomic point defects (vacancies and interstitial atoms). The governing nonlinear equation describing the evolution of the self-consistent strain fields is derived. It is shown that the thermoelastic effect on the strain waves manifests itself in the appearance of dissipative terms, which describe the heat transfer and the thermoelastic interaction caused by the strain-induced heat release due to the recombination of atomic defects. The equation that describes the evolution of the amplitude of nonlinear traveling localized waves with time in the single-wave approximation is derived, and on the basis of this equation, the damping increments of these waves are determined with allowance the dissipative losses. The influence of stress-induced decay of defect complexes on the evolution of nonlinear strain waves is considered.