A 2D spring model for the simulation of ultrasonic wave propagation in nonlinear hysteretic media

Delsanto, Pier Paolo; Gliozzi, Antonio; Hirsekorn, Martin; Nobili, Matteo

doi:10.1016/j.ultras.2006.01.002

Cited by 24 publications

(18 citation statements)

References 24 publications

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“…The above-mentioned results on the influence of the various types of hysteresis can be compared to Fig. 5 in the recent paper of Delsanto et al, 22 in which the influence of the type of hysteresis on the nonlinear response of a plane compressional wave traversing a localized defect zone is investigated with the LISA model. Here the different types of hysteresis are introduced by choosing either the volumetric, deviatoric, or shear stress as the driving parameter governing the hysteretic nonlinear response of the interstice elements.…”

Section: Alternative Analysis Of the Nonlinear Signaturesmentioning

confidence: 89%

“…Along the same lines, Bou Matar et al 20 have recently developed a similar approach based on a pseudospectral wave solver. In addition, a multiscale version of the local interaction simulation approach ͑LISA͒ model for nonlinear wave propagation in 1D and higher dimensions has been reported 21,22 for the investigation of the influence of localized damage on the nonlinear behavior of resonance modes in 1D and on the wave propagation characteristics in 2D.…”

Section: Introductionmentioning

confidence: 99%

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Two-dimensional modeling of wave propagation in materials with hysteretic nonlinearity

Vanaverbeke

Abeele

2007

The Journal of the Acoustical Society of America

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A multiscale model for the two-dimensional nonlinear wave propagation in a locally microdamaged medium is presented, and numerical simulations are analyzed in view of nondestructive testing applications. The multiscale model uses a statistical distribution of hysterons and upscales their microscopic stress-strain relations to a mesoscopic level. Macroscopic observations are then predicted by finite integration techniques. The influence of a small region with hysteretic nonlinearity on the generation of harmonics is investigated, and numerical results for different amplitudes of the input signal and different analysis techniques of the response signal are presented. Second, a study is conducted on the interaction of a Rayleigh wave with a microdamaged zone with hysteretic nonlinearity at the surface of an otherwise linear body, and the influence of the microdamaged zone on the surface wave velocity and on the generation of harmonics is examined. It is found that the effect of hysteresis on the Rayleigh wave propagation can be barely seen in the surface wave velocity measurement, but shows up nicely in the wave spectrum. The potential of a nonlinearity based depth profiling technique is explored by evaluating the nonlinear responses at different frequencies for a vertically stratified medium with spatially varying hysteresis properties.

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Section: Alternative Analysis Of the Nonlinear Signaturesmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Two-dimensional modeling of wave propagation in materials with hysteretic nonlinearity

Vanaverbeke

Abeele

2007

The Journal of the Acoustical Society of America

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“…1, a two-dimensional ͑2D͒ approach to the simulation of ultrasonic wave propagation in nonclassical nonlinear ͑NCNL͒ media has been used. 32 The method is described elsewhere 33 and its correctness demonstrated by qualitative and quantitative comparison with experimental data. [34][35][36][37] In particular, the model predicts mode conversion between shear and longitudinal waves, both due to the propagation of a nonplane wave 34 and both that generated at the reflection from an interface between different materials.…”

Section: B the Modelmentioning

confidence: 99%

“…Finally, when a PM space is introduced in order to model the transitions between the two states, regions with nonlinear hysteretic properties are modeled. 29,30,33 …”

Section: B the Modelmentioning

confidence: 99%

Efficiency of time-reversed acoustics for nonlinear damage detection in solids

Gliozzi

Griffa

Scalerandi

2006

The Journal of the Acoustical Society of America

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Time-reversed acoustics ͑TRA͒ has been developed in the last few years as a powerful tool for several applications, based on the theoretical properties emerging from the time reversal invariance of the wave equation. TRA is expected to be a good basis for the development of imaging techniques in the field of nondestructive evaluation. For this purpose, however, data processing is necessary to discriminate between images due to defects ͑in general nonlinear scatterers͒ and images due to linear inclusions, boundaries, etc. We propose here an approach based on the filtering of the time signals. The image of the scatterer is obtained through numerical simulations of the back propagation in a fictitious reference specimen. We validate the approach using the inversion of synthetic data. We also estimate the robustness of the procedure in the presence of constraints that can occur in any experimental procedure.

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“…A finite difference technique based on a spring model has been used in ultrasonics propagation in complex and heterogeneous media by Delsanto and Scalerandi (1998), using local interaction simulation approach (LISA) in one-dimensional and two-dimensional cases. An application with the previous cited spring model combined with the PM space has been used in Delsanto et al (2006). Finite difference schemes like elastodynamic finite integration technique (EFIT) have been used in Van Den Abeele et al (2004) for a resonant bar with localized damage.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear wave propagation in damaged hysteretic materials using a frequency domain-based PM space formulation

Barbieri

Meo

Polimeno

2009

International Journal of Solids and Structures

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a b s t r a c tIn this work, a new and simple numerical approach to simulate nonlinear wave propagation in purely hysteretic elastic solids is presented. Conversely to classical time discretization method, which fully integrates the nonlinear equation of motion, this method utilizes a first-order approximation of the nonlinear strain in order to separate linear and nonlinear contributions. The problem for the nonlinear displacements is then posed as a linear one in which the solid is enforced with nonlinear forces derived from the linear strain. In this manner, a frequency analysis can be easily conducted, leading directly to a well-known frequency spectrum for the nonlinear strain. A mesoscale approach known as Preisach-Mayergoyz space (PM space) is used for the chacterization of the nonlinear elastic region of the solid. A meshless element free Galerkin method is implemented for the discretized equations of motion. Nevertheless, a mesh-based method can be still used as well without loss of generality. Results are presented for bidimensional isotropic plates both in plane stress and in plane strain subjected to harmonic monotone excitation.

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A 2D spring model for the simulation of ultrasonic wave propagation in nonlinear hysteretic media

Cited by 24 publications

References 24 publications

Two-dimensional modeling of wave propagation in materials with hysteretic nonlinearity

Two-dimensional modeling of wave propagation in materials with hysteretic nonlinearity

Efficiency of time-reversed acoustics for nonlinear damage detection in solids

Nonlinear wave propagation in damaged hysteretic materials using a frequency domain-based PM space formulation

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