arXiv subjects

Christopher M. Kube

Publications and source records attributed to Christopher M. Kube.

6 recordsLinked to original sources

arXiv2026

A pure stress formulation for modeling elastic waves using central finite differences

A pure stress-based finite difference formulation is introduced for modeling elastic wave propagation in linear elastic solids with spatial heterogeneity. The approach derives from the strong form of the elastodynamic equation of motion, in which stress is the only dependent variable. A standard second-order central difference scheme is applied to discretize the equation of motion, allowing the space-time-dependent evolution of stress components to be modeled. Numerical dispersion analysis is performed for homogeneous, elastically isotropic materials. Simulations are then carried out for a spatially heterogeneous case consisting of a bimaterial with stiffness heterogeneity. This bimaterial case allows comparison with known closed-form solutions for reflection and transmission coefficients and with an analogous displacement-based finite difference model. Simulations are executed on modern graphics processing unit architectures, enabling stress-based modeling of large-scale three-dimensional problems exceeding one billion degrees of freedom. The approach shows promise for ultrasonic simulations in materials with stiffness heterogeneity and uniform mass density, conditions common in polycrystalline metals used in engineering applications. The formulation offers a potential alternative means of modeling wave propagation and scattering in heterogeneous materials, with possible applications in nondestructive evaluation, materials characterization, biomedical ultrasound, and geosciences.

physics.class-ph↗

arXiv2025

Multiple Scattering of Elastic Waves in Polycrystals

Elastic waves that propagate in polycrystalline materials attenuate due to scattering of energy out of the primary propagation direction in addition to becoming dispersive in their group and phase velocities. Attenuation and dispersion are modeled through multiple scattering theory to describe the mean displacement field or the mean elastodynamic Green's function. The Green's function is governed by the Dyson equation and was solved previously (Weaver, 1990) by truncating the multiple scattering series at first-order, which is known as the first-order smoothing approximation (FOSA). FOSA allows for multiple scattering but places a restriction on the scattering events such that a scatterer can only be visited once during a particular multiple scattering process. In other words, recurrent scattering between two scatterers is not permitted. In this article, the Dyson equation is solved using the second-order smoothing approximation (SOSA). The SOSA permits scatterers to be visited twice during the multiple scattering process and, thus, provides a more complete picture of the multiple scattering effects on elastic waves. The derivation is valid at all frequencies spanning the Rayleigh, stochastic, and geometric scattering regimes without additional approximations that limit applicability in strongly scattering cases (like the Born approximation). The importance of SOSA is exemplified through analyzing specific weak and strongly scattering polycrystals. Multiple scattering effects contained in SOSA are shown to be important at the beginning of the stochastic scattering regime and are particularly important for transverse (shear) waves. This step forward opens the door for a deeper fundamental understanding of multiple scattering phenomena in polycrystalline materials.

cond-mat.mtrl-sci↗

arXiv2024

Accurate wave velocity measurement from diffuse wave fields

Directional wave speeds variations in anisotropic elastic solids enables material characterisation capabilities, such as determination of elastic constants and volumetric measurement of crystallographic texture. However, achieving such measurements is challenging especially on samples with complex geometries. Here we propose the use of Green's Function reconstruction from diffuse ultrasonic wave fields for accurate velocity measurements on components with arbitrary geometries. Strategies for accurate reconstruction, including averaging over an increased number of different source locations, using longer window lengths of diffuse fields, and accurately deconvolving a source-dependent factor, were implemented to achieve satisfactory convergence towards Green's Function. Additionally, low signal intensity challenges from laser interferometers were overcome to enable non-contact measurement of the wave speeds, by making use of simultaneous excitation of sources to increase signal-to-noise ratio and signal normalisation to account for energy dissipation of diffuse fields. With successful demonstration using both phased array and laser receivers, this advancement fundamentally broadens acoustic wave velocity measurement capabilities to a wider range of environments and holds promise for future material characterisation of complex-shaped components.

physics.app-ph↗

arXiv2024

High-speed synchrotron X-ray imaging of melt pool dynamics during ultrasonic melt processing of Al6061

Ultrasonic processing of solidifying metals in additive manufacturing can provide grain refinement and advantageous mechanical properties. However, the specific physical mechanisms of microstructural refinement relevant to laser-based additive manufacturing have not been directly observed because of sub-millimeter length scales and rapid solidification rates associated with melt pools. Here, high-speed synchrotron X-ray imaging is used to observe the effect of ultrasonic vibration directly on melt pool dynamics and solidification of Al6061 alloy. The high temporal and spatial resolution enabled direct observation of cavitation effects driven by a 20.2 kHz ultrasonic source. We utilized multiphysics simulations to validate the postulated connection between ultrasonic treatment and solidification. The X-ray results show a decrease in melt pool and keyhole depth fluctuations during melting and promotion of pore migration toward the melt pool surface with applied sonication. Additionally, the simulation results reveal increased localized melt pool flow velocity, cooling rates, and thermal gradients with applied sonication. This work shows how ultrasonic treatment can impact melt pools and its potential for improving part quality.

physics.app-ph↗

arXiv2017

On the harmonic scattering amplitudes from a nonlinear elastic spherical inclusion

In this paper, the interaction of an incident finite amplitude longitudinal wave with a localized region of nonlinearity is considered. This interaction produces a secondary field represented by a superposition of first-, second-, and third-harmonic components. The secondary field is solely a result of the quadratic and cubic elastic nonlinearity present within the region of the inclusion. The second-harmonic scattering amplitude depends on the quadratic nonlinearity parameter $β$, while the first- and third-harmonic amplitudes depend on the cubic nonlinearity parameter $γ$. The special cases of forward and backward scattering amplitudes were analyzed. For each harmonic, the forward-scattering amplitude is always greater than or equal to the backward scattering amplitude in which the equality is only realized in the Rayleigh scattering limit. Lastly, the amplitudes of the scattered harmonic waves are compared to predicted harmonic amplitudes derived from a plane wave model.

physics.app-ph↗

arXiv2017

Monitoring near-surface depth profile of residual stress in weakly anisotropic media by Rayleigh-wave dispersion

Herein we study the inverse problem on inferring depth profile of near-surface residual stress in a weakly anisotropic medium by boundary measurement of Rayleigh-wave dispersion if all other relevant material parameters of the elastic medium are known. Our solution of this inverse problem is based on a recently developed algorithm by which each term of a high-frequency asymptotic formula for dispersion relations can be computed for Rayleigh waves that propagate in various directions along the free surface of a vertically-inhomogeneous, prestressed, and weakly anisotropic half-space. As a prime example of possible applications we focus on a thick-plate sample of AA 7075-T651 aluminum alloy, which has one face treated by low plasticity burnishing (LPB) that induced a depth-dependent prestress at and immediately beneath the treated surface. We model the sample as a prestressed, weakly-textured orthorhombic aggregate of cubic crystallites and assume that by nondestructive and/or destructive measurements we have ascertained everything about the sample, including the LPB-induced prestress, before it is put into service. Under the supposition that the prestress be partially relaxed but other material parameters remain unchanged after the sample undergoes a period of service, we examine the possibility of inferring the depth profile of the partially relaxed stress by boundary measurement of Rayleigh-wave dispersion.

cond-mat.mtrl-sci↗