Nonlinear Longitudinal Strain Waves in a Solid Exposed to Pulsed Laser Radiation

Abstract

The propagation of longitudinal strain waves in a solid with quadratic nonlinearity of elastic continuum was studied in the context of a model that takes into account the joint dynamics of elastic displacements in the medium and the concentration of the laser-induced point defects. The input equations of the problem are reformulated in terms of only the total displacements of the medium points. In this case, the presence of structural defects manifests itself in the emergence of a delayed response of the system to the propagation of the strain-related perturbations, which is characteristic of media with relaxation or memory. The model equations describing the nonlinear displacement wave were derived with allowance made for the values of the relaxation parameter. The influence of the generation, relaxation, and the strain-induced drift of defects and the flexoelectricity on the propagation of this wave was analyzed. It is shown that, for short relaxation times of defects, the strain can propagate in the form of both shock fronts and solitary waves (solitons). Exact solutions depending on the type of relation between the coefficients in the equation and describing both the shock-wave structures and the evolution of solitary waves are presented. In the case of longer relaxation times, shock waves do not form and the strain wave propagates only in the form of solitary waves or a train of solitons. The contributions of the finiteness of the defect-recombination rate and the flexoelectricity to linear elastic moduli and spatial dispersion are determined.