Ordinary state-based peri-ultrasound modeling to study the effects of multiple cracks on the nonlinear response of plate structures.

Since it is almost impossible to carry out a comprehensive parametric investigation experimentally for internal cracks with different geometry and orientation, a good numerical modeling and simulation technique is necessary to have a clear understanding of the physics of wave propagation and its interaction with cracks. Such investigation is helpful for structural health monitoring (SHM) with ultrasonic techniques. This work presents a nonlocal peri-ultrasound theory based on ordinary state-based (OSB) peridynamics for modeling elastic wave propagation in three-dimensional (3-D) plate structures containing multiple cracks. A relatively new and promising nonlinear ultrasonic technique called Sideband Peak Count - Index (or SPC-I) is adopted to extract the nonlinearity generated from the interactions between elastic waves and multiple cracks. Effects of three main parameters - the distance between the acoustic source and the crack, the crack spacing and the number of cracks are investigated using the proposed OSB peri-ultrasound theory together with the SPC-I technique. For each of these three parameters investigation, different crack thicknesses were considered - 0 mm (crack-free), 1 mm (thin crack), 2 mm (intermediate thickness) and 4 mm (thick crack); thin and thick cracks are defined after comparing the crack thickness value with the horizon size mentioned in the peri-ultrasound theory. It is found that for obtaining consistent results the acoustic source should be placed at least one wavelength away from the crack and crack spacings also play an important role on the nonlinear response. It is concluded that the nonlinear response diminishes when the cracks become too thick, and thin cracks show higher nonlinearity than that of thick cracks and no cracks. Finally, the proposed method which is combining the peri-ultrasound theory and SPC-I technique is used for monitoring cracks' evolution process. The numerical modeling results are compared with the experimental findings reported in the literature. Consistent qualitative trends in SPC-I variations predicted numerically and obtained experimentally are observed, thus it gives confidence in the proposed method.