Mathieu Chekroun

Time-domain numerical simulations of multiple scattering to extract elastic effective wavenumbers

Elastic wave propagation is studied in a heterogeneous two-dimensional medium consisting of an elastic matrix containing randomly distributed circular elastic inclusions. The aim of this study is to determine the effective wavenumbers when the incident wavelength is similar to the radius of the inclusions. A purely numerical methodology is presented, with which the limitations usually associated with low scatterer concentrations can be avoided. The elastodynamic equations are integrated by a fourth-order time-domain numerical scheme. An immersed interface method is used to accurately discretize the interfaces on a Cartesian grid. The effective field is extracted from the simulated data, and signal-processing tools are used to obtain the complex effective wavenumbers. The numerical reference solution thus obtained can be used to check the validity of multiple scattering analytical models. The method is applied to the case of concrete. A parametric study is performed on longitudinal and transverse incident plane waves at various scatterer concentrations. The phase velocities and attenuations determined numerically are compared with predictions obtained with multiple scattering models, such as the Independent Scattering Approximation model, the Waterman–Truell model, and the more recent Conoir–Norris model.

Comparison between a multiple scattering method and direct numerical simulations for elastic wave propagation in concrete

Numerical simulations are performed to study the propagation of elastic waves in a 2-D random heterogeneous medium such as concrete. To reduce spurious numerical artefacts to a negligible level, a fourth-order time-domain numerical scheme and an immersed interface method are used together. Effective properties of the equivalent homogeneous medium are extracted and compared to the predictions of a multiple scattering method (ISA), to evaluate the validity of this latter.

DETERMINATION OF THE ORDER OF PASSES OF AN AUSTENITIC WELD BY OPTIMIZATION OF AN INVERSION PROCESS OF ULTRASOUND DATA

Multipass welds made in austenitic stainless steel, in the primary circuit of nuclear power plants with pressurized water reactors, are characterized by an anisotropic and heterogeneous structure that disturbs the ultrasonic propagation and challenge the ultrasonic non‐destructive testing. The simulation in this type of structure is now possible thanks to the MINA code which allows the grain orientation modeling taking into account the welding process, and the ATHENA code to exactly simulate the ultrasonic propagation. We propose studying the case where the order of the passes is unknown to estimate the possibility of reconstructing this important parameter by ultrasound measures. The first results are presented.

Comparisons between multiple scattering methods and time‐domain numerical simulations for elastic waves

Propagation of elastic waves in heterogeneous medium composed of scatterers embedded in a homogeneous matrix is considered. Both matrix and scatterers are isotropic elastic media. The multiple scattering regime is assumed, and the focus is put on the coherent field obtained by averaging several equivalent realizations of disorder. Classical methods, such as Independent Scattering Approximation, Foldy or Waterman‐Truells model, provide expressions of the complex effective wave number of the coherent field, leading to an effective phase velocity and effective damping factor. Two‐dimensional time‐domain numerical simulations are performed for studying the validity of these analytical or semianalytical methods. To reduce spurious effects, such as numerical diffraction, to a negligible level, a high‐order numerical scheme and an immersed interface method are used together. Comparisons between theoretical and numerical values of the effective phase velocity and damping factor are proposed and analyzed in terms...

Numerical modeling of nonlinear modulation of coda wave interferometry in a multiple scattering medium with the presence of a localized micro-cracked zone

The spectral element method is used to perform a parametric sensitivity study of the nonlinear coda wave interferometry (NCWI) method in a homogeneous sample with localized damage [1]. The influence of a strong pump wave on a localized nonlinear damage zone is modeled as modifications to the elastic properties of an effective damage zone (EDZ), depending on the pump wave amplitude. The local change of the elastic modulus and the attenuation coefficient have been shown to vary linearly with respect to the excitation amplitude of the pump wave as in previous experimental studies of Zhang et al. [2]. In this study, the boundary conditions of the cracks, i.e. clapping effects is taken into account in the modeling of the damaged zone. The EDZ is then modeled with random cracks of random orientations, new parametric studies are established to model the pump wave influence with two new parameters: the change of the crack length and the crack density. The numerical results reported constitute another step towards quantification and forecasting of the nonlinear acoustic response of a cracked material, which proves to be necessary for quantitative non-destructive evaluation.The spectral element method is used to perform a parametric sensitivity study of the nonlinear coda wave interferometry (NCWI) method in a homogeneous sample with localized damage [1]. The influence of a strong pump wave on a localized nonlinear damage zone is modeled as modifications to the elastic properties of an effective damage zone (EDZ), depending on the pump wave amplitude. The local change of the elastic modulus and the attenuation coefficient have been shown to vary linearly with respect to the excitation amplitude of the pump wave as in previous experimental studies of Zhang et al. [2]. In this study, the boundary conditions of the cracks, i.e. clapping effects is taken into account in the modeling of the damaged zone. The EDZ is then modeled with random cracks of random orientations, new parametric studies are established to model the pump wave influence with two new parameters: the change of the crack length and the crack density. The numerical results reported constitute another step towards...

Nonlinear Coda Wave Interferometry: Detecting, quantifying, and locating damage in complex solids

In this talk, we report results on the nonlinear interactions of ultrasonic coda waves with lower pump waves, in reverberating or multiple scattering mesoscopic solid media. Using the method of coda wave interferometry (CWI), we analyze the effect of mixing a coda wave with an additional lower frequency pump wave. The extracted CWI parameters, known to be highly sensitive to small geometric or elastic modifications of the tested medium, are shown to be pump-amplitude dependent and to capture finely the results of the nonlinear interactions. Although nonlinear self-action effects with coda waves have been reported in unconsolidated granular media, they are difficult to implement in cracked solids or concrete. Instead, the reported nonlinear CWI class of methods (NCWI) shows robustness, a high sensitivity, and has been applied successfully to various complex media and structures. We show through several examples on « model » media (cracked glass plates) and on concrete structures, that NCWI can be useful fo...