3D elastic plane-wave diffraction by a stress-free wedge for incident skew angles below the critical angle in diffraction

Chehade, Samar; Darmon, Michel; Lebeau, Gilles

doi:10.1016/j.jcp.2020.110062

Cited by 2 publications

(5 citation statements)

References 31 publications

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“…According to the authors' opinion, this technique constitutes a very power tool for the accurate approximate solutions of arbitrary WH equations. We remark that the GWHEs are algebraic, while in [17], the solution is obtained by functional equations written in terms of singular integral operators and solved by numerical technique. We assert that the semianalytic solution using the Fredholm factorization method allows physical insights by asymptotics in spectral domain.…”

Section: Equivalence Theorem In Elasticity: a Field In A Lossy Region Is Uniquely Specified By The Sources Within The Region Plus The Conmentioning

confidence: 99%

“…In the following, we assume that the geometry of the elastic wave-motion problem as well as the eventual boundary conditions are invariant along the z-direction, thus, without loss of generality, when a source depends on an e−jαo z factor, also the total field depends on the same factor, i.e. bold-italicψt=bold-italicψtfalse(x,y,zfalse)=ffalse(x,yfalse) e−jαo z, see for instance [17] before (2.8). Of course, the same behaviour can be obtained by applying a Fourier transform also along the z-direction and assuming an incident plane wave with a particular skew direction that yields e−jαo z.…”

Section: First-order Differential Equations For Continuous Components...mentioning

confidence: 99%

“…In particular, by applying the traction-free boundary conditions (Txy=Tyy=Tyz=TXY=TYY=TYZ=0), (5.11)–(5.13) becomes GWHEs formulating the three-dimensional elastic wedge problem considered in [17]. This formulation is important because it allows to get semianalytical solutions via the Fredholm factorization method as developed by the authors in [4].…”

Section: Explicit Form Of the Functional Equations For Non-planar (Th...mentioning

confidence: 99%

“…New developments of this method are reported in [16], where double Fourier transforms are introduced to obtain the kernels of the singular integral equations. In [17], the method is extended to three-dimensional problems, however, the proposed functional equations in spectral domain are again written in terms of singular integral operators and not in an algebraic form. The concept of spectral representation of the displacements on the wedge faces is applied also by Gautesen's group works [14,[18][19][20] that, according to our opinion, have produced the best practical results in the solution of the two-dimensional elastic isotropic wedge problem [14].…”

Section: Introductionmentioning

confidence: 99%

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The generalized Wiener–Hopf equations for the elastic wave motion in angular regions

Daniele

Lombardi

2022

Proc. R. Soc. A.

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In this work, we introduce a general method to deduce spectral functional equations in elasticity and thus, the generalized Wiener–Hopf equations (GWHEs), for the wave motion in angular regions filled by arbitrary linear homogeneous media and illuminated by sources localized at infinity. The work extends the methodology used in electromagnetic applications and proposes for the first time a complete theory to get the GWHEs in elasticity. In particular, we introduce a vector differential equation of first-order characterized by a matrix that depends on the medium filling the angular region. The functional equations are easily obtained by a projection of the reciprocal vectors of this matrix on the elastic field present on the faces of the angular region. The application of the boundary conditions to the functional equations yields GWHEs for practical problems. This paper extends and applies the general theory to the challenging canonical problem of elastic scattering in angular regions.

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Section: Equivalence Theorem In Elasticity: a Field In A Lossy Region Is Uniquely Specified By The Sources Within The Region Plus The Conmentioning

confidence: 99%

Section: First-order Differential Equations For Continuous Components...mentioning

confidence: 99%

Section: Explicit Form Of the Functional Equations For Non-planar (Th...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The generalized Wiener–Hopf equations for the elastic wave motion in angular regions

Daniele

Lombardi

2022

Proc. R. Soc. A.

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“…GTD is preferred to KA for simulating scattering by crack edges (notably for TOFD configurations [8,9]) but fails in the near-incident and specular reflection directions (shadow boundaries). A GTD solution has also recently been proposed for wedge scattering [10][11][12]. Several system models based on KA [3] or GTD [13,14] were conceived first for 2D configurations and then developed in 3D for KA [1,5] and for GTD [15], then using an incremental Huygens model [16].…”

Section: Introductionmentioning

confidence: 99%

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

2022

Self Cite

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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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3D elastic plane-wave diffraction by a stress-free wedge for incident skew angles below the critical angle in diffraction

Cited by 2 publications

References 31 publications

The generalized Wiener–Hopf equations for the elastic wave motion in angular regions

The generalized Wiener–Hopf equations for the elastic wave motion in angular regions

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

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