Three-dimensional modeling and numerical predictions of multimodal nonlinear behavior in damaged concrete blocks.

In this paper, the multimodal nonlinear elastic behavior of concrete, which is representative of a consolidated granular material, is modeled numerically. Starting from a local three-dimensional softening law, the initial stiffness properties are re-estimated according to the local strain field. The experiments deal with samples of thermally damaged concrete blocks successively excited around their first three modes of vibration. The geometry of these samples cannot be described by a one-dimensional approximation in these experiments where compressional and shear motions are strongly coupled. Despite this added complexity, the nonlinear behavior for the three modes of vibration of the samples is well captured by the simulations using a single scalar nonlinear parameter appropriately integrated into the elasticity equations. It is shown that without sufficient attention paid to the latter, the conclusions would have brought erroneous statements such as nonlinearity dispersion or strain type dependence.

Quantitative linear and nonlinear resonance inspection techniques and analysis for material characterization: application to concrete thermal damage.

Developed in the late 1980s, Nonlinear Resonant Ultrasound Spectroscopy (NRUS) has been widely employed in the field of material characterization. Most of the studies assume the measured amplitude to be proportional to the strain amplitude which drives nonlinear phenomena. In 1D resonant bar experiments, the configuration for which NRUS was initially developed, this assumption holds. However, it is not true for samples of general shape which exhibit several resonance mode shapes. This paper proposes a methodology based on linear resonant ultrasound spectroscopy, numerical simulations and nonlinear resonant ultrasound spectroscopy to provide quantitative values of nonlinear elastic moduli taking into account the 3D nature of the samples. In the context of license renewal in the field of nuclear energy, this study aims at providing some quantitative information related to the degree of micro-cracking of concrete and cement based materials in the presence of thermal damage. The resonance based method is validated as regard with concrete microstructure evolution during thermal exposure.

Probing the interior of a solid volume with time reversal and nonlinear elastic wave spectroscopy.

A nonlinear scatterer is simulated in the body of a sample and demonstrates a technique to locate and define the elastic nature of the scatterer. Using the principle of time reversal, elastic wave energy is focused at the interface between blocks of optical grade glass and aluminum. Focusing of energy at the interface creates nonlinear wave scattering that can be detected on the sample perimeter with time-reversal mirror elements. The nonlinearly generated scattered signal is bandpass filtered about the nonlinearly generated components, time reversed and broadcast from the same mirror elements, and the signal is focused at the scattering location on the interface.

Quantification of material nonlinearity in relation to microdamage density using nonlinear reverberation spectroscopy: Experimental and theoretical study.

High amplitude vibrations induce amplitude dependence of the characteristic resonance parameters (i.e., resonance frequency and damping factor) in materials with microscopic damage features as a result of the nonlinear constitutive relation at the damage location. This paper displays and quantifies results of the nonlinear resonance technique, both in time (signal reverberation) and in frequency (sweep) domains, as a function of sample crack density. The reverberation spectroscopy technique is applied to carbon fiber reinforced plastic (CFRP) composites exposed to increasing thermal loading. Considerable gain in sensitivity and consistent interpretation of the results for nonlinear signatures in comparison with the linear characteristics are obtained. The amount of induced damage is quantified by analyzing light optical microscopy images of several cross-sections of the CFRP samples using histogram equalization and grayscale thresholding. The obtained measure of crack density is compared to the global macroscopic nonlinearity of the sample and explicitly confirms that the increase in nonlinearity is linked to an increased network of cracks. A change from 1% to 3% in crack density corresponds to a tenfold increase in the signature of nonlinearity. Numerical simulations based on a uniform distribution of a hysteretic nonlinear constitutive relation within the sample support the results.