Longitudinal strain waves in a nonlinearly elastic plate with defect generation

Abstract

The evolution of a longitudinal strain wave in a nonlinearly elastic plate is studied theoretically in the context of a model that is based on coupled equation for the elastic-displacement fields in the medium and the concentration of the nonequilibrium laser-generated lattice defects (vacancies and interstitials). The governing nonlinear equations for elastic strain wave were derived with allowance made for the values of the relaxation parameter of a defect subsystem. The influence of the generation, relaxation, and the strain-induced drift of lattice defects on the evolution of this wave is considered. It is shown that, for short defect-relaxation times, the strain wave can propagate in the form of both shock fronts and solitary waves. Exact solutions depending on the type of relation between the coefficients in the equations and describing both the shock-wave structures and the evolution of solitary waves are presented. In the case of longer defect-relaxation times, shock waves do not form and the strain wave propagates only in the form of solitary waves. The amplitudes and velocities of the nonlinear waves depend on the elastic constants and on the properties of the defects’ subsystem in the medium. The contributions of the finiteness of the defect-relaxation rate and the strain-induced drift of defects to the linear and nonlinear elastic modulus, and lattice dissipation and dispersion parameters are found.