7 results found
Shi F, Lowe M, Skelton EA, et al., 2018, A time-domain finite element boundary integral approach for elastic wave scattering, Computational Mechanics, Vol: 61, Pages: 471-483, ISSN: 0178-7675
The response of complex scatterers, such as rough or branched cracks, to incident elastic waves is required in many areas of industrial importance such as those in non-destructive evaluation and related fields; we develop an approach to generate accurate and rapid simulations. To achieve this we develop, in the time domain, an implementation to efficiently couple the finite element (FE) method within a small local region, and the boundary integral (BI) globally. The FE explicit scheme is run in a local box to compute the surface displacement of the scatterer, by giving forcing signals to excitation nodes, which can lie on the scatterer itself. The required input forces on the excitation nodes are obtained with a reformulated FE equation, according to the incident displacement field. The surface displacements computed by the local FE are then projected, through time-domain BI formulae, to calculate the scattering signals with different modes. This new method yields huge improvements in the efficiency of FE simulations for scattering from complex scatterers. We present results using different shapes and boundary conditions, all simulated using this approach in both 2D and 3D, and then compare with full FE models and theoretical solutions to demonstrate the efficiency and accuracy of this numerical approach.
Shi F, Lowe M, Craster R, 2017, Diffusely scattered and transmitted elastic waves by random rough solid-solid interfaces using an elastodynamic Kirchhoff approximation, PHYSICAL REVIEW B, Vol: 95, ISSN: 2469-9950
Elastic waves scattered by random rough interfaces separating two distinct media play an important role in modeling phonon scattering and impact upon thermal transport models, and are also integral to ultrasonic inspection. We introduce theoretical formulas for the diffuse field of elastic waves scattered by, and transmitted across, random rough solid-solid interfaces using the elastodynamic Kirchhoff approximation. The new formulas are validated by comparison with numerical Monte Carlo simulations, for a wide range of roughness (rms σ≤λ/3, correlation length λ0≥ wavelength λ), demonstrating a significant improvement over the widely used small-perturbation approach, which is valid only for surfaces with small rms values. Physical analysis using the theoretical formulas derived here demonstrates that increasing the rms value leads to a considerable change of the scattering patterns for each mode. The roughness has different effects on the reflection and the transmission, with a strong dependence on the material properties. In the special case of a perfect match of the wave speed of the two solid media, the transmission is the same as the case for a flat interface. We pay particular attention to scattering in the specular direction, often used as an observable quantity, in terms of the roughness parameters, showing a peak at an intermediate value of rms; this rms value coincides with that predicted by the Rayleigh parameter.
Shi F, Lowe MJS, Craster RV, 2016, Recovery of correlation function of internal random rough surfaces from diffusely scattered elastic waves, Journal of the Mechanics and Physics of Solids, Vol: 99, Pages: 483-494, ISSN: 0022-5096
We propose an ultrasonic methodology to reconstruct the height correlation function of remotely inaccessible random rough surfaces in solids. The inverse method is based on the Kirchhoff approximation(KA), and it requires measuring the angular distribution of diffuse scattering intensities by sending in a narrow band incident pulse. Near field scattering effects are also included by considering the Fresnel assumption. The proposed approach is successfully verified by simulating the scattering from multiple realizations of rough surfaces whose correlation function is known, calculating the mean scattering intensities from these received signals, and then deploying the inverse method on these to reconstruct the original correlation function. Very good agreement between the reconstructed correlation function and the original is found, for a wide range of roughness parameters. In addition, the effect of reducing the number of realizations to approximate the mean intensity are investigated, providing confidence bounds for the experiment. An experiment on a corrugated rough surface is performed with a limited number of scans using a phased array, which further validates the proposed inversion algorithm.
Craster RV, Lowe M, Shi F, et al., 2016, Diffuse scattered field of elastic waves from randomly rough surfaces using an analytical Kirchhoff theory, Journal of the Mechanics and Physics of Solids, Vol: 92, Pages: 260-277, ISSN: 0022-5096
We develop an elastodynamic theory to predict the diffuse scattered field of elastic waves by randomly rough surfaces, for the first time, with the aid of the Kirchhoff approximation (KA). Analytical expressions are derived incorporating surface statistics, to represent the expectation of the angular distribution of the diffuse intensity for different modes. The analytical solutions are successfully verified with numerical Monte Carlo simulations, and also validated by comparison with experiments. We then apply the theory to quantitatively investigate the effects of the roughness and the shear-to-compressional wave speed ratio on the mode conversion and the scattering intensity, from low to high roughness within the valid region of KA. Both the direct and the mode converted intensities are significantly affected by the roughness, which leads to distinct scattering patterns for different wave modes. The mode conversion effect is very strong around the specular angle and it is found to increase as the surface appears to be more rough. In addition, the 3D roughness induced coupling between the out-of-plane shear horizontal (SH) mode and the in-plane modes is studied. The intensity of the SH mode is shown to be very sensitive to the out-of-plane correlation length, being influenced more by this than by the RMS value of the roughness. However, it is found that the depolarization pattern for the diffuse field is independent of the actual value of the roughness.
Shi F, Choi W, Lowe MJS, et al., 2015, The validity of Kirchhoff theory for scattering of elastic waves from rough surfaces, PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 471, ISSN: 1364-5021
Shi F, Choi W, Skelton EA, et al., 2014, A Time-Domain Finite Element Boundary Integration Method for Ultrasonic Nondestructive Evaluation, IEEE TRANSACTIONS ON ULTRASONICS FERROELECTRICS AND FREQUENCY CONTROL, Vol: 61, Pages: 2054-2066, ISSN: 0885-3010
Shi F, Michaels JE, Lee SJ, 2013, In situ estimation of applied biaxial loads with Lamb waves., J Acoust Soc Am, Vol: 133, Pages: 677-687
Spatially distributed arrays of piezoelectric disks are being applied to monitor structural integrity using Lamb waves. Applied loads directly affect waves propagating between array elements because of dimensional changes and the acoustoelastic effect. Resulting changes in phase velocity depend upon the propagation direction as well as the Lamb wave mode and frequency. This paper shows from numerical solutions of the acoustoelastic wave equation for an isotropic plate that it is possible to decouple the effects of a homogeneous biaxial stress into its two principal components. As a consequence of both this decoupling and material isotropy, the acoustoelastic response of a specific mode and frequency is described by only two constants, which can be determined from a uniaxial loading experiment. Using this formulation, a method is developed and verified via simulations to estimate an arbitrary biaxial load from phase velocity changes measured along multiple directions of propagation. Results from uniaxial loading experiments on two different plates further demonstrate the efficacy of the method. It is also shown that opening fatigue cracks may significantly degrade results by interfering with Lamb wave direct arrivals, but that this degradation can be mitigated by using a reduced set of data from unaffected paths of propagation.
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