Wave propagation in elastic media with cracks. Part II: Transient nonlinear response of a cracked matrix

The transient dynamic response of an elastic medium containing a random array of aligned penny-shaped cracks is studied. Nonlinearity in the response due to contact between crack faces during the motion is taken into account. The mean value of wave fields is considered and an effective constitutive relation is adopted which contains an internal variable defining the mean opening of the cracks. An integral representation of the effective displacement field is given using the Green function of the uncracked body. One-dimensional nonlinear waves are studied using the solution of the single scattering problem proposed by the authors in a previous paper. Numerical examples showing the role of the characteristic crack dimension on the overall nonlinear response of the cracked medium are presented.