Modeling non-collinear mixing by distributions of clapping microcracks

• Non-collinear mixing by distributions of clapping microcracks is modeled.
• Constitutive relationships for distributions of clapping cracks are presented.
• Linear dependence of scattered waves on the incident field is found.
• Selection rules for nonlinear scattering by quadratic nonlinearity are violated.
• Examples of forward and backscattering for discrimination purposes are presented.

Nonlinear scattering by distributions of clapping cracks in a non-collinear wave mixing setting is modeled. Features of the nonlinear response discriminating distributions of clapping cracks from quadratic nonlinear damage are investigated for distributions of cracks that are parallel to each other or randomly oriented. The effective properties of these distributions are recovered extending an existing model that applies to open cracks. The equation of motion is solved using a perturbation approach, and its solutions are evaluated numerically. Their dependence on the amplitude of the incident field is found to be linear, in contrast with the quadratic dependence characterizing quadratic nonlinearity. The spectrum of the scattered field is shown to contain an infinite number of higher harmonics already at the first order of perturbation. Grating-like structures due to the opening and closing of cracks are responsible for adding diffraction peaks to the directivity functions of waves scattered by open cracks. The locations of the most prominent peaks of these functions do not satisfy the selection rules controlling nonlinear scattering by quadratic nonlinearity. Examples of these are given, together with others showing the possibility of using at least one of several discrimination modalities offered by non-collinear wave mixing.