The signature of nonlinearity in the elastic response of a specimen to an impingent ultrasonic wave is usually determined through Fourier analysis, which provides low amplitude signals, often below noise level. We suggest here an alternative, based on the amplitude dependence of the response of the system. Our procedure is conceptually simple and easy to implement. In addition, it keeps simultaneously into account the nonlinear signature effects on phases, amplitudes, and frequencies of the response. The sensitivity of the approach to the presence of nonlinearity is proven experimentally.

Fast and slow dynamics in the elastic response of damaged materials to external excitations show evidence of an anomalous (hysteretic) elastic behavior. Experimental observations may be used to detect and eventually characterize the damaged state of structural components. At the same time, reliable theoretical models might support data interpretation and development of new experiments. Here, we analyze the resonance frequency shift in undamaged and damaged concrete bars, comparing experimental results and theoretical predictions obtained from a Preisach-Mayergoyz based elastic model.

A spring model for the simulation of the propagation of ultrasonic pulses in arbitrarily complex heterogeneous media is proposed in the framework of the local interaction simulation approach (LISA). The algorithm used allows us to include heuristically additional local interaction mechanisms. In particular, the problem of propagation of pulses across imperfect contact interfaces is considered. A contact quality tensor, which is expected to be connected, although not necessarily in a trivial way, to the bond quality, is introduced directly into the model in order to treat interface flaws, such as delaminations and/or slipping bonds. To demonstrate the applicability of the technique, which is particularly suitable for parallel processing, a few examples of numerical simulation of pulse propagation in media with various kinds of imperfections are presented.

Analyzing the nonlinear part of a signal generated by the response of a sample to an elastic excitation is a powerful tool to gain information on the material microstructure, including the presence of damage. Analysis using band-pass filtering or equivalent methods is often difficult due to the low amplitude of the harmonics contained in the signal. This is the case for the detection of early damage in granular samples with damage induced by a quasistatic loading, as analyzed in this paper. An experimental study, based on the scaling subtraction method, is presented here, showing the possibility of monitoring the variation in the sample nonlinearity during the evolution of damage and allowing linking it to different physical processes. The efficiency of the method in eliminating nonlinear contributions due to the experimental setup is proved through a numerical analysis.

Several materials with mesoscopic characteristics (e.g., defects or intergrain regions) have been shown to share several nonclassical nonlinear features, which distinguish them from classical nonlinear media. Most striking among them is the log-time recovery of the material properties after they have been conditioned by the action of an external perturbation. A simple model based on the description of the mesoscopic features as bond regions between elastic portions is presented here. The implementation of the model is illustrated by the application of a special bi-state protocol, which, by considering also thermally induced transitions between the two basic states, allows to explain all experimentally observed nonclassical nonlinear effects.