Cracks induced by rebar corrosion are among the most important causes of performance deterioration in reinforced concrete elements. Even though several methods have been developed to detect the amount and location of corrosion-induced cracks, the sensitivity to small closed cracks located well below the concrete surface is still an issue to be faced. In this paper, we show the high sensitivity of nonlinear ultrasonic measurements performed using the Scaling Subtraction Method to point out that, under certain conditions, nonlinear indicators might prove to be very efficient and suitable to identify small variations in the element microstructure, such as those due to corrosion crack initiation.

The reciprocity theorem is a general statement valid for elastic media, and it has been applied to the solution of elastic wave equations, transducers calibration, time reversal acoustics, etc. However, localized nonlinear scatterers are expected to break reciprocity even though the effect is, in several cases, negligible. Here the dependence of the reciprocity break on the presence of a localized damage and the influence of its relative position has been experimentally investigated. It will be shown that the break of reciprocity, usually considered a disadvantage, can be exploited as an imaging tool for localized cracks detection.

Concrete, particularly if damaged, exhibits a peculiar nonlinear elastic behavior, which is mainly due to the coupling between nonequilibrium and nonlinear features, the two of which are intrinsically connected. More specifically, the formulation of a constitutive equation able to properly predict the dynamic behavior of damaged concrete is made difficult by the concomitant presence of two mechanisms: The modification of the microstructure of the medium and the transition to a new elastic state caused by a finite amplitude excitation (conditioning). Memory of that new state is kept when the excitation is removed, before relaxation back to the original elastic state takes place. Indeed, besides accounting for linear and nonlinear parameters, a realistic constitutive equation to be used in reliable prediction models should take into account nonequilibrium effects. Specific parameters, sensitive to finite amplitude excitations, should be introduced to provide information about conditioning effects. In this paper, experimental results indicating that nonlinearity of damaged concrete is memory-dependent will be presented and the implications of such findings in the development of physical models, with relevant outcomes for the characterization of hysteretical features, will be discussed.

The effects of localized nonlinearities on the reciprocity principle in the context of ultrasounds and nonlinear elasticity are discussed in this paper. Experiments will be presented to prove that a localized crack in a concrete beam causes a break of reciprocity in the ultrasonic response to a mechanical excitation. The link between non-reciprocity and asymmetry in the nonlinear response will be demonstrated and discussed as a tool for NonDestructive Evaluation.

Understanding the mechanisms and modalities of damage progression close to discontinuities in solids, such as joints, is of great importance for applications in different fields. The interaction between damage and elasticity causes a nonlinear elastic response of the sample to a stress excitation (e.g. in the ultrasonic frequency range). Extracting physical or mechanical information on the sample properties from recorded ultrasonic signals requires a realistic model and an efficient detection method, as it will be discussed in this paper. We study here the successive phases that concrete samples with discontinuities enter by progressively increase the applied external load. Considerations on the mechanisms of damage progression are derived from experimental data using a Preisach–Mayergoyz space approach, developed in order to capture all the observed behaviors.

As largely demonstrated by many authors, localized cracks in heterogeneous media act as nonlinear scatterers; consequently, when an heterogeneous medium is perturbed by a mechanical excitation, its elastic response shows nonlinear features, dependent on the amplitude. Experiments presented here will show that the presence of localized nonlinear scatterers not only breaks the proportionality of the elastic response, but also affects the reciprocity principle, which thus, in some conditions, is no longer valid. Experiments performed on a concrete beam with a significant crack have demonstrated that the reciprocity principle holds true only when the amplitude of excitation is low or when the distance between the crack and the source/receiver is comparable (i.e. source/receiver are symmetric in space with respect to the crack). Besides highlighting the break of reciprocity, experiments have proved its dependence on the amplitude of excitation and on the position of the emitting and receiving transducers with respect to the crack. By taking advantage of these features, a nonlinear tomography of a cracked fibre-reinforced concrete beam was performed, allowing to reproduce an image of the scanned surface and to locate the position of the crack. The sensitivity of the approach to locate small localised nonlinear features is being investigated.

One of the signatures of the presence of cracks in a sample is the nonlinearity in its elastic response to an impingent ultrasonic wave. The Fourier analysis is often inadequate to monitor the evolution of nonlinearity, since the signal-to-noise ratio of higher order harmonics is very low. In order to overcome this drawback, we suggest an alternative procedure to extract nonlinearity indicators from a recorded ultrasonic signal, based on the amplitude dependence of the response of the system. The procedure is first described and then used to analyse the evolution of the nonlinearity due to cracks induced by a quasi-static loading in mortar samples. Our approach allows to distinguish the compaction phase from the micro-damage progression and the pre-rupture phases.

The definition and measurement of the nonlinear elastic properties of a sample is of great importance for a large number of applications, including characterization of material performances and damage detection. However, such measurements are often influenced by spurious effects due to a combination of nonlinearity and nonequilibrium phenomena. We will present experimental data to show how nonlinearity due to small cracks in concrete samples increases as a consequence of conditioning, i.e., after having perturbed them with a constant amplitude excitation. In addition, our experimental data highlight “memory effects,” i.e., they show that when the excitation is removed, the elastic modulus does not return instantaneously to the initial value.

Elastic hysteresis in solids is a complex matter which may affect a wide range of applications. As observed in rocks, it is the result of the interplay between nonlinear and nonequilibrium phenomena, such as conditioning, relaxation, and memory. Here we will propose a theoretical nondeterministic framework in which nonequilibrium effects are a natural consequence of the model. Experimental results will be shown to demonstrate that the separation of such effects is fundamental to extract truthful information on nonlinearity.

An experimental study was conducted on different concrete cylinders damaged in compression. The evolution of damage was followed by means of linear and nonlinear ultrasonic methods, with the purpose to provide a better understanding of mechanical degradation processes in concrete and highlight the potentialities and limitations of the Non-Destructive Techniques used.

The presence of damage or cracks modifies the elastic properties of a sample, introducing nonlinear components in the elastic response to an ultrasonic excitation. Among other effects, we discuss here conditioning and memory, i.e. the transition of the sample to a new (non equilibrium) elastic state when perturbed by a strain, even at a relatively low amplitude. A quantification of these phenomena can be the basis for a novel Nondestructive Method to evaluate the integrity of a structural or mechanical component.

The Scaling Subtraction Method (SSM) has been proposed in recent years as an effective nonlinear nondestructive technique to evaluate the damage level in concrete and other media and monitor its progression as a function of external actions. Here we show experimental data to prove the robustness of the method with respect to the variation of a number of factors related to either the environmental and testing conditions or the size and geometrical characteristics of the elements tested, as well as to the type of damage and the excitation frequency. An experimentally-derived evolution law is also presented as a first attempt to describe compressive damage progression in concrete in a unified approach.

Phenomenological Universality (PUN) represents a new tool for the classification and interpretation of different non-linear phenomenologies in the context of cross-disciplinary research. Also, they can act as a "magnifying glass" to finetune the analysis and quantify the difference among similarly looking datasets. In particular, the class U2 is of special relevance since it includes, as subcases, most of the commonly used growth models proposed to date. In this contribution we consider two applications of special interest in two subfields of Elasto-dynamics, i.e. Fast- and Slow-Dynamics, respectively. The results suggest that new equations should be adopted for the fitting of the experimental results and that fractal-dimensioned variables should be used to recover the scaling invariance, which is invariably lost due to non-linearity.

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.

The presence of discontinuity surfaces in concrete structures, i.e. two or more layers in contact, may be an existing situation with evident relapses on damage formation and progression. Differences occur depending on the type of discontinuity, which could be a thin weaker layer or a pre-existing crack. The behavior of pre-existing interfaces is here studied by means of the Scaling Subtraction Method, a Nonlinear Ultrasonic Non-Destructive Technique, that revealed to be effective in describing the mechanical evolution of concrete samples with discontinuity surfaces under the effects of compressive loads.

The evolution of concrete behavior in the proximity of a joint under the effect of varying external pressures is studied by means of a novel nonlinear ultrasonic technique denoted as Scaling Subtraction Method. The results obtained show that the proposed method is effective in describing the occurrence of micro-structural changes near the joint and detect potential conditions for crack opening and damage initiation.

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 procedure is described and used to analyse the variation of the nonlinearity in a concrete bar subject to quasi-static loadings of increasing amplitude. The sensitivity of the approach allows to distinguish the compaction phase (up to a load of 30% of the rupture loading) from a microdamage progression (up to a load of 60%) and the pre-rupture phases.