Wave Propagation in Damaged Materials Using a New Generalized Continuum Model

An approach is proposed that allows formulating self-consistent problem that includes equations of the material's dynamics and conditions of its damage. It is shown that damage in the material introduces a frequency-dependent damping and dispersion of the phase velocity of ultrasonic acoustic waves that allows estimating damage using the acoustic method. Applied field of deformations leads to the accumulation of damage. A kinetic equation is obtained, whose analysis shows that damage grows exponentially. The parameters of the system for which accumulation of damage can be considered as linear are estimated.