Reconstruction of interfaces from the elastic farfield measurements using CGO solutions

In this work, we are concerned with the inverse scattering by interfaces for the linearized and isotropic elastic model at a fixed frequency. First, we derive complex geometrical optic solutions with linear or spherical phases having a computable dominant part and an $H^\alpha$-decaying remainder term with $\alpha <3$, where $H^{\alpha}$ is the classical Sobolev space. Second, based on these properties, we estimate the convex hull as well as non convex parts of the interface using the farfields of only one of the two reflected body waves (pressure waves or shear waves) as measurements. The results are given for both the impenetrable obstacles, with traction boundary conditions, and the penetrable obstacles. In the analysis, we require the surfaces of the obstacles to be Lipschitz regular and, for the penetrable obstacles, the Lam\'e coefficients to be measurable and bounded with the usual jump conditions across the interface.Comment: 32 page

Viscoelastic modulus reconstruction using time harmonic vibrations

This paper presents a new iterative reconstruction method to provide high-resolution images of shear modulus and viscosity via the internal measurement of displacement fields in tissues. To solve the inverse problem, we compute the Fr\'echet derivatives of the least-squares discrepancy functional with respect to the shear modulus and shear viscosity. The proposed iterative reconstruction method using this Fr\'echet derivative does not require any differentiation of the displacement data for the full isotropic linearly viscoelastic model, whereas the standard reconstruction methods require at least double differentiation. Because the minimization problem is ill-posed and highly nonlinear, this adjoint-based optimization method needs a very well-matched initial guess. We find a good initial guess. For a well-matched initial guess, numerical experiments show that the proposed method considerably improves the quality of the reconstructed viscoelastic images.Comment: 15 page

Nondestructive Testing Methods Aided Via Numerical Computation Models for Various Critical Aerospace Power Generation Systems

A current critical necessity for all industries which utilize various equipment that operates in high temperature and extreme environments, is the ability to collect and analyze data via non destructive testing (NDT) methods. Operational conditions and material health must be constantly monitored if components are to be implemented precisely to increase the overall performance and efficiency of the process. Currently in both aerospace and power generation systems there are many methods that are being employed to gather several necessary properties and parameters of a given system. This work will focus primarly on two of these NDT methods, with the ultimate goal of contributing to not only the method itself, but also the role of numerical computation to increase the resolution of a given technique. Numerical computation can attribute knowledge onto the governing mechanics of these NDT methods, many of which are currently being utilized in industry. An increase in the accuracy of the data gathered from NDT methods will ultimately lead to an increase in operational efficiency of a given system. The first method to be analyzed is a non destructive emmision technique widely referred to as accoustic ultrasonic thermography. This work will investigate the mechanism of heat generation in acoustic thermography using a combination of numerical computational analysis and physical experimentation. Many of the challenges typical of this type of system are addressed in this work. The principal challenges among them are crack detection threshold, signature quality and the effect of defect interactions. Experiments and finite element based numerical simulations are employed, in order to evaluate the proposed method, as well as draw conclusions on the viability for future extension and integration with other digital technologies for health monitoring. A method to determine the magnitude of the different sources of heat generation during an acoustic excitation is also achieved in this work. Defects formed through industrial operation as well as defects formed through artificial manufacturing methods were analyzed and compared. The second method is a photoluminescence piezospectroscopic (PLPS) for composite materials. The composite studied in this work has one host material which does not illuminate or have photoluminescence properties, the second material provides the luminescence properties, as well as additional overall strength to the composite material. Understanding load transfer between the reinforcements and matrix materials that constitute these composites hold the key to elucidating their mechanical properties and consequent behavior in operation. Finite element simulations of loading effects on representative embedded alumina particles in a matrix were investigated and compared with experimental results. The alumina particles were doped with chromium in order to achieve luminscence capability, and therefore take advantage of the piezospectrscopic measurement technique. Mechanical loading effects on alumina nanoparticle composites can be captured with Photo stimulated luminescent spectroscopy, where spectral shifts from the particles are monitored with load. The resulting piezospectroscopic (PS) coefficients are then used to calculate load transfer between the matrix and particle. The results from the simulation and experiments are shown to be in general agreement of increase in load transferred with increasing particle volume fraction due to contact stresses that are dominant at these higher volume fractions. Results from this work present a combination of analytical and experimental insight into the effect of particle volume fraction on load transfer in ceramic composites that can serve to determine properties and eventually optimize various parameters such as particle shape, size and dispersion that govern the design of these composites prior to manufacture and testing

Phononic Metamaterials for Surface Acoustic Wave Sensing

This thesis investigates the sensitivity of phononic metamaterials to the presence of materials and changes in their environment. The behaviour of surface acoustic waves (SAWs) in periodic arrays of holes was investigated with finite element modelling and experimentally. SAW bandstructures and bandgap attenuation were obtained from simulations of arrays of cylindrical and annular holes which were filled with materials with different SAW velocities. Each type of hole array exhibited two distinct scattering regimes (Mie and Bragg scattering). The dependence of the bandgap frequency on the velocity was found to be stronger for annular holes than for cylindrical holes, suggesting that annular holes are potentially a better route to create tuneable phononic metamaterials. Annular holes also displayed a higher bandgap attenuation than cylindrical holes, meaning that annular hole arrays might be exploited for greater sensitivity in applications such as mass loading sensing. SAW attenuation due to mass loading of air was calculated by measuring SAW amplitude on a SAW device using an oscilloscope system and by laser Doppler vibrometry (LDV). An extraordinary increase of 2 to 3 orders of magnitude in mass loading attenuation was observed at the bandgap frequency when a phononic metamaterial was present, with only 4 resonator elements needed to produce this result. The measurements obtained by both experimental systems displayed similar frequency dependencies of mass loading attenuation coefficients. Some mass loading effects were also reproduced using finite element modelling. These approaches show great promise for improving the sensitivity of SAW pressure sensors. Finally, bandstructures were obtained from finite element simulations for an array of annular holes filled with a small sphere comprised of materials with different SAW velocities. The array exhibited similar scattering regimes as before, with an overlapping region. The dependence of the bandgap frequency on the velocity was found to be stronger when the annular holes contained the sphere than when they are fully-filled, suggesting that annular holes are potentially a good candidate for probing biological cells. Higher bandgap attenuation by up to a factor of 2 was exhibited by the single spherical inclusion compared to fully-filled holes. Since annular holes have more degrees of geometrical freedom than conventional phononic crystals, devices with greater sensitivity might be realised for applications such as biological sensing and lab-on-a-chip diagnostics.Engineering and Physical Sciences Research Council (EPSRC

Small-inclusion asymptotic of misfit functionals for inverse problems in acoustics

The aim of this study is an extension and employment of the concept of topological derivative as it pertains to the nucleation of infinitesimal inclusions in a reference (i.e. background) acoustic medium. The developments are motivated by the need to develop a preliminary indicator functional that would aid the solution of inverse scattering problems in terms of a rational initial 'guess' about the geometry and material characteristics of a hidden (finite) obstacle; an information that is often required by iterative minimization algorithms. To this end the customary definition of topological derivative, which quantifies the sensitivity of a given cost functional with respect to the creation of an infinitesimal hole, is adapted to permit the nucleation of a dissimilar acoustic medium. On employing the Green's function for the background domain, computation of topological sensitivity for the three-dimensional Helmholtz equation is reduced to the solution of a reference, Laplace transmission problem. Explicit formulae are given for the nucleating inclusions of spherical and ellipsoidal shapes. For generality the developments are also presented in an alternative, adjoint-field setting that permits nucleation of inclusions in an infinite, semi-infinite or finite background medium. Through numerical examples, it is shown that the featured topological sensitivity could be used, in the context of inverse scattering, as an effective obstacle indicator through an assembly of sampling points where it attains pronounced negative values. On varying a material characteristic (density) of the nucleating obstacle, it is also shown that the proposed methodology can be used as a preparatory tool for both geometric and material identification

Using a Poroelastic Theory to Reconstruct Subsurface Properties: Numerical Investigation

International audienceThe quantitative imaging of the Earth subsurface is a major challenge in geophysics. In oil and gas exploration and production, aquifer management and other applications such as the underground storage of CO2 , seismic imaging techniques are implemented to provide as much information as possible on fluid-filled reservoir rocks. Biot theory (Biot, 1956) and its extensions provide a convenient framework to connect the various parameters characterizing a porous medium to the wave properties, namely, their amplitudes, velocities and frequency contents. The poroelastic model involves more parameters than the elastodynamic theory, but on the other hand, the wave attenuation and dispersion characteristics at the macroscopic scale are determined by the intrinsic properties of the medium without having to resort to empirical relationships