Jacques Riviere

High-accuracy acoustic detection of nonclassical component of material nonlinearity.

The aim is to assess the nonclassical component of material nonlinearity in several classes of materials with weak, intermediate, and high nonlinear properties. In this contribution, an optimized nonlinear resonant ultrasound spectroscopy (NRUS) measuring and data processing protocol applied to small samples is described. The protocol is used to overcome the effects of environmental condition changes that take place during an experiment, and that may mask the intrinsic nonlinearity. External temperature fluctuation is identified as a primary source of measurement contamination. For instance, a variation of 0.1 °C produced a frequency variation of 0.01%, which is similar to the expected nonlinear frequency shift for weakly nonlinear materials. In order to overcome environmental effects, the reference frequency measurements are repeated before each excitation level and then used to compute nonlinear parameters. Using this approach, relative resonant frequency shifts of 10(-5) can be measured, which is below the limit of 10(-4) often considered as the limit of NRUS sensitivity under common experimental conditions. Due to enhanced sensitivity resulting from the correction procedure applied in this work, nonclassical nonlinearity in materials that before have been assumed to only be classically nonlinear in past work (steel, brass, and aluminum) is reported.

A set of measures for the systematic classification of the nonlinear elastic behavior of disparate rocks

Dynamic acoustoelastic testing is performed on a set of six rock samples (four sandstones, one soapstone, and one granite). From these studies at 20 strain levels 10 −7 <�� < 10 −5 , four measures characterizing the nonlinear elastic response of each sample are found. Additionally, each sample is tested with nonlinear resonant ultrasonic spectroscopy and a fifth measure of nonlinear elastic response is found. These five measures of the nonlinear elastic response of the samples (approximately 3 × 6 × 20 × 5 numbers as each measurement is repeated 3 times) are subjected to careful analysis using model-independent statistical methods, principal component analysis, and fuzzy clustering. This analysis reveals differences among the samples and differences among the nonlinear measures. Four of the nonlinear measures are sensing much the same physical mechanism in the samples. The fifth is seeing something different. This is the case for all samples. Although the same physical mechanisms (two) are operating in all samples, there are distinctive features in the way the physical mechanisms present themselves from sample to sample. This suggests classification of the samples into two groups. The numbers in this study and the classification of the measures/samples constitute an empirical characterization of rock nonlinear elastic properties that can serve as a valuable testing ground for physically based theories that relate rock nonlinear elastic properties to microscopic elastic features.

Resonant ultrasound spectroscopy for materials with high damping and samples of arbitrary geometry

Resonant ultrasound spectroscopy (RUS) is a powerful and established technique for measuring elastic constants of a material with general anisotropy. The first step of this technique consists of extracting resonance frequencies and damping from the vibrational frequency spectrum measured on a sample with free boundary conditions. An inversion technique is then used to retrieve the elastic tensor from the measured resonance frequencies. As originally developed, RUS has been mostly applicable to (i) materials with small damping such that the resonances of the sample are well separated and (ii) samples with simple geometries for which analytical solutions exist. In this paper, these limitations are addressed with a new RUS approach adapted to materials with high damping and samples of arbitrary geometry. Resonances are extracted by fitting a sum of exponentially damped sinusoids to the measured frequency spectrum. The inversion of the elastic tensor is achieved with a genetic algorithm, which allows searching for a global minimum within a discrete and relatively wide solution space. First, the accuracy of the proposed approach is evaluated against numerical data simulated for samples with isotropic symmetry and transversely isotropic symmetry. Subsequently, the applicability of the approach is demonstrated using experimental data collected on a composite structure consisting of a cylindrical sample of Berea sandstone glued to a large piezoelectric disk. In the proposed experiments, RUS is further enhanced by the use of a 3-D laser vibrometer allowing the visualization of most of the modes in the frequency band studied.

Time reversed elastic nonlinearity diagnostic applied to mock osseointegration monitoring applying two experimental models

This study broadens vibration-like techniques developed for osseointegration monitoring to the nonlinear field. The time reversed elastic nonlinearity diagnostic is applied to two mock models. The first one consists of tightening a dental implant at different torques in a mock cortical bone; the second one allows one to follow glue curing at the interface between a dental implant and a mock jaw. Energy is focused near the implant interface using the time reversal technique. Two nonlinear procedures termed pulse inversion and the scaling subtraction method, already used successfully in other fields such as contrast agents and material characterization, are employed. These two procedures are compared for both models. The results suggest that nonlinear elasticity can provide new information regarding the interface, complementary to the linear wave velocity and attenuation. The curing experiment exhibits an overall low nonlinear level due to the fact that the glue significantly damps elastic nonlinearity at the interface. In contrast, the torque experiment shows strong nonlinearities at the focus time. Consequently, a parallel analysis of these models, both only partially reflecting a real case, enables one to envisage future in vivo experiments.

Fast and slow nonlinear elastic response of disparate rocks and the influence of moisture

We study nonlinear elastic phenomena in rocks at the laboratory scale, with the goal of characterizing and understanding observations at crustal scales, for instance, during strong ground motion and earthquake slip processes. A dynamic perturbation of microstrain amplitude in rocks results in a transient elastic softening followed by a log(t)-type relaxation back to the initial unperturbed elastic modulus as soon as the excitation is removed. Here we use Dynamic Acousto-Elastic Testing (DAET) to investigate the relaxation behavior over 7 orders of magnitude in time (from 10-4s to more than 103s). We find that relaxation starts for all samples between 10-3 and 10-2s. Some samples then exhibit a nearly perfect log(t)-relaxation, implying that no characteristic time can be extracted, while some other samples show a preferential relaxation around 0.1s/1s. Such features appear insensitive to the amplitude of the dynamic perturbation and to the moisture content within the sample. The full nonlinear elastic resp...

Nonlinear ultrasound: Potential of the cross-correlation method for osseointegration monitoring

Recently the concept of probing nonlinear elasticity at an interface prosthesis/bone has been proposed as a promising method to monitor the osseointegration/sealing of a prosthesis. However, the most suitable method to achieve this goal is a point of debate. To this purpose, two approaches termed the scaling subtraction method and the cross-correlation method are compared here. One nonlinear parameter derived from the cross-correlation method is as sensitive as a clinical device based on linear elasticity measurement. Further, this study shows that cross-correlation based methods are more sensitive than those based on subtraction/addition, such like pulse inversion and similar methods.

Dynamic acousto-elasticity in Berea sandstone: Influence of the strain rate

In comparison with standard nonlinear ultrasonic methods such as frequency mixing or resonance based measurements that allow one to extract average, bulk variations of modulus and attenuation versus strain level, dynamic acousto-elasticity (DAE) allows to obtain the elastic behavior over the entire dynamic cycle, detailing the full nonlinear behavior under tension and compression, including hysteresis and memory effects. To improve our understanding of these phenomena, this work aims at comparing static and dynamic acousto-elasticity to evaluate the influence of strain rate. To this purpose, we perform acousto-elasticity on a sample of Berea sandstone and a glass beads pack, oscillating them from 0.001 to 10 Hz. These results are then compared to DAE measurements made in the kHz range. We observe that the average decrease in modulus increases with frequency, meaning that conditioning effects are higher at high strain rate, when relaxation characteristic time is higher than the oscillation period. This res...

Dynamic acousto-elastic testing with an ultrasonic tomography probe: Application to fractured rock characterization

We study nonlinear elastic phenomena at the laboratory scale to help interpret the subtle velocity changes observed in the Earth’s crust, for instance, during strong ground motion, earthquake slip processes or Earth tides. Dynamic Acousto-Elastic Testing (DAET) provides unprecedented details on the nonlinear elastic response of consolidated granular media (e.g., rocks, concrete), including tension/compression asymmetry, hysteretic behaviors as well as conditioning and relaxation effects. Such technique uses a pump-probe scheme where a high frequency, low amplitude wave probes the state of a sample that is dynamically disturbed by a low frequency, large amplitude pump wave. While previous work typically involved a single pair of probing transducers, here we use two dense arrays of ultrasonic transducers to image a sample of Westerly granite with a complex fracture. We apply double beamforming to disentangle complex arrivals and conduct ray-based and finite-frequency tomography using both travel time and am...

Extraction of nonlinear elastic material parameters from single-impact nonlinear ring-down spectroscopy

Volumetric microcracking is one of the early symptoms of distress in cementitious materials caused by excessive mechanical stress, chemical attacks, and environmental influences. The microcracks widen, coalesce, and develop into larger cracks with the progress of damage. Visible macro-cracks indicate severe damage that often cannot be mitigated. As such, detection of damage at the early stages of development is essential for designing optimal preventive maintenance programs for concrete structures. Nonlinear acoustics-based nondestructive testing techniques have shown great promise in identification of microscopic cracks in diverse materials including concrete. Impact-based alternatives of conventional techniques are gaining popularity for concrete testing mainly due to their field transportability. In this study, we focus on impact-based nonlinear resonance acoustic spectroscopy (INRAS). We compare the results from multi-impact INRAS, where several impacts of increasing intensities are applied, to those ...

Potential of the scaling subtraction and the cross-correlation methods for osseointegration monitoring

The long-term perspective of this study is to implement in vivo some new noninvasive methods to monitor the bone prostheses sealing or osseointegration (dental implants, hip prostheses). Although the most widely used clinically, X-ray radiography suffers from low sensitivity, limiting for instance its ability to detect early loosening of a prosthesis. The potential of methods developed over the past twenty years and based on linear elasticity measurements has been shown in vitro, but their in vivo effectiveness is still questionable. The objective is to evaluate the potential of methods based on nonlinear elasticity measurement which showed greater sensitivity than the linear elastic response to the presence of weak contacts within a rigid structure, such as cracks. Two different methods called Scaling Subtraction Method and Cross-Correlation Method are compared in this study, using an experimental osseointegration mimicking model. One parameter extracted from the cross-correlation method is shown to be a...