The Alternative Kirchhoff Approximation in Elastodynamics With Applications in Ultrasonic Nondestructive Testing

Fradkin, Larissa; Djakou, Audrey Kamta; Prior, Christopher; Darmon, Michel; Chatillon, Sylvain; Calmon, Pierre

doi:10.1017/s1446181120000036

Cited by 5 publications

(4 citation statements)

References 11 publications

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“…For planar surfaces, some smoothing modifications of KA can be proposed [69] in the vicinity of critical angles for better validity, but they do not simulate head waves. A modification of KA using an alternative integral formula for the Kirchhoff integral has just been developed [89], and it could be extended to scattering from a rough surface. Nevertheless, this perspective has to be tested and validated, since such a model will generate head waves as if they have been created on successive local non-finite tangential plane.…”

Section: Summary Discussion and Perspectivesmentioning

confidence: 99%

“…The Kirchhoff approximation models bulk waves, and does not take into account surface acoustics waves (SAW) as Rayleigh waves neither head waves. Head waves led to recent researches [70,[86][87][88] and a modification [89] of the Kirchhoff approximation is henceforth proposed for head waves account. Head waves on irregular surfaces can also be modelled [90].…”

Section: Elastic Targets and Applicationsmentioning

confidence: 99%

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Acoustic Scattering Models from Rough Surfaces: A Brief Review and Recent Advances

Darmon

Dorval

Baqué³

2020

Applied Sciences

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This paper proposes a brief review of acoustic wave scattering models from rough surfaces. This review is intended to provide an up-to-date survey of the analytical approximate or semi-analytical methods that are encountered in acoustic scattering from random rough surfaces. Thus, this review focuses only on the scattering of acoustic waves and does not deal with the transmission through a rough interface of waves within a solid material. The main used approximations are classified here into two types: the two historical approximations (Kirchhoff approximation and the perturbation theory) and some sound propagation models more suitable for grazing observation angles on rough surfaces, such as the small slope approximation, the integral equation method and the parabolic equation. The use of the existing approximations in the scientific literature and their validity are highlighted. Rough surfaces with Gaussian height distribution are usually considered in the models hypotheses. Rather few comparisons between models and measurements have been found in the literature. Some new criteria have been recently determined for the validity of the Kirchhoff approximation, which is one of the most used models, owing to its implementation simplicity.

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Section: Summary Discussion and Perspectivesmentioning

confidence: 99%

Section: Elastic Targets and Applicationsmentioning

confidence: 99%

Acoustic Scattering Models from Rough Surfaces: A Brief Review and Recent Advances

Darmon

Dorval

Baqué³

2020

Applied Sciences

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“…2D CIVA FEM is a transient elastodynamic finite element code integrated into CIVA for various applications. Indeed, it allows simulations of crack-like flaws inspections [19,20] with a more precise prediction of head waves than models [21][22][23] developed for canonical shapes; it is subsequently also adapted for concrete modelling [1]. 2D SPECFEM is a numerical code based on the spectral elements numerical method [2] that has also been employed for wave propagation simulation in concrete [13].…”

Section: Evaluation Of 2d Elastic Homogenization Models For Concrete ...mentioning

confidence: 99%

2D Analytical Modelling for Ultrasonic Inspection of Concrete Structures: Effects of Scatterers Position Correlation

Khalid,

Darmon,

Chaix

2024

J. Phys.: Conf. Ser.

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Ultrasonic Non-Destructive Testing (NDT) simulation plays an important role in designing inspections of concrete structures. The concrete structural complexity (presence of different heterogeneities: aggregates, porosities, microcracks …) leads to dispersion and attenuation of the ultrasonic waves, which requires an accurate modelling of the waves scattered from heterogeneities. For that purpose, studying the mean coherent wave characterized by its attenuation and phase velocity is of great interest. Two major approaches (numerical or analytical) exist for modelling the coherent wave. Numerical methods are more efficient but still limited in the 3D case by their computation time. Therefore, semi-analytical homogenization methods are considered a practical solution for a fast 3D simulation. Nevertheless, they may encounter several limitations in estimating the attenuation in dense heterogeneous materials such as concrete. Our goal is to explain and handle these prediction errors. Since the scattered ultrasonic field depends strongly on the obstacles’ positions in concrete, a particular focus is put on the pair correlation function describing the radial distribution of scatterers’ positions around a fixed scatterer (mean concentration at a distance r from this scatterer). Existing homogenization models are employed for simulating coherent wave propagation in concrete use by simplification of a uniform distribution. In order to improve the analytical models, the effects of scatterers’ positions correlation are investigated. In the present work, we propose to evaluate precisely the existing homogenization model that is the most suitable for high scatterers concentration. A comparison between this model and a 2D finite element code under development in the CIVA NDT simulation software is presented.

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“…Moreover, the region of the model's validity has been extended [26] to cover some transition zones surrounding critical rays, where the shear diffracted waves and head waves interfere. Important efforts have been made to propose an analytical modelling of some head waves contributions, notably lateral waves in the TOFD configuration [27,28]: for planar surfaces, lateral waves are head waves propagating along such surfaces, and recent advances have been obtained in their modelling [29][30][31][32][33]; for complex or cylindrical surfaces, lateral waves can include bulk wave contributions [34]. The PTD-based system model [26] can be considered as the most sophisticated and valid semi-analytical approach existing at the present date.…”

Section: Introductionmentioning

confidence: 99%

An Experimental and Theoretical Comparison of 3D Models for Ultrasonic Non-Destructive Testing of Cracks: Part I, Embedded Cracks

2022

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Ultrasonic Non-Destructive Testing (NDT) methods are broadly used for detection and characterization/imaging of cracks. Simulation is of great interest for designing such NDT methods. To model the ultrasonic 3D response of a crack, ultrasonic high frequency asymptotic (semi-analytical) models (such as the Physical Theory of Diffraction—PTD) are known to provide accurate predictions for most classical NDT configurations, and 3D numerical models have also emerged more recently. The aim of this paper is to carry out for the first time an experimental and theoretical comparison of 3D models for ultrasonic NDT of embedded cracks in 3D configurations. Semi-analytical models and a hybrid 3D FEM strategy—combining high-order spectral Finite Elements Method (FEM) for flaw scattering and an asymptotic ray model for beam propagation—have been compared. Both numerical validations and comparisons between simulation and experiments prove the effectiveness of PTD in numerous configurations but validate and demonstrate the improvement provided by the 3D hybrid code, notably for small flaws compared to the wavelength and for shear waves.

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The Alternative Kirchhoff Approximation in Elastodynamics With Applications in Ultrasonic Nondestructive Testing

Cited by 5 publications

References 11 publications

Acoustic Scattering Models from Rough Surfaces: A Brief Review and Recent Advances

Acoustic Scattering Models from Rough Surfaces: A Brief Review and Recent Advances

2D Analytical Modelling for Ultrasonic Inspection of Concrete Structures: Effects of Scatterers Position Correlation

An Experimental and Theoretical Comparison of 3D Models for Ultrasonic Non-Destructive Testing of Cracks: Part I, Embedded Cracks

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