Flutter of two parallel flat plates connected by an elastic medium
Flutter boundaries of parallel plates connected by elastic medium
PARALLEL PLATE↗
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Transmission of waves through a pinned elastic medium
We investigate the scattering of elastic waves off a disordered region described by a one-dimensional random-phase sine-Gordon model. The collective pinning results in an effective static disorder potential with universal and non-Gaussian correlations, acting on propagating waves. We find signatures of the correlations in the wave transmission in a wide frequency range, which covers both the weak and strong localization regimes. Our theory elucidates the dynamics of collectively-pinned phases occurring in any natural or synthetic elastic medium. The latter one is exemplified by a one-dimensional array of Josephson junctions, for which we specify our results. Here, the obtained results provide benchmarks for the array-enabled quantum simulations addressing the dynamics in broader and yet-unexplored domains of individual pinning and quantum Bose glass.
1-dimensional systems↗
Interface crack in a nonhomogeneous elastic medium
The linear elasticity problem for an interface crack between two bonded half planes is reconsidered. It is assumed that one of the half planes is homogeneous and the second is nonhomogeneous in such a way that the elastic properties are continuous throughout the plane and have discontinuous derivatives along the interface. The problem is formulated in terms of a system of integral equations and the asymptotic behavior of the stress state near the crack tip is determined. The results lead to the conclusion that the singular behavior of stresses in the nonhomogeneous medium is identical to that in a homogeneous material provided the spacial distribution of material properties is continuous near and at the crack tip. The problem is solved for various values of the nonhomogeneity parameter and for four different sets of crack surface tractions, and the corresponding stress intensity factors are tabulated.
Delale, F.↗
Conservation of angular momentum in an elastic medium with spins
Exact conservation of the angular momentum is worked out for an elastic medium with spins. The intrinsic anharmonicity of the elastic theory is shown to be crucial for conserving the total momentum. As a result, any spin-lattice dynamics inevitably involves multiphonon processes and interaction between phonons. Furthermore, this makes transitions between spin states in a solid fundamentally different from transitions between atomic states in a vacuum governed by linear electrodynamics. Consequences for using solid-state spins as qubits are discussed.
36 MATERIALS SCIENCE↗
Cracking of a layered medium on an elastic foundation under thermal shock
The cladded pressure vessel under thermal shock conditions which is simulated by using two simpler models was studied. The first model (Model 1) assumes that, if the crack size is very small compared to the vessel thickness, the problem can be treated as a semi-infinite elastic medium bonded to a very thin layer of different material. However, if the crack size is of the same order as the vessel thickness, the curvature effects may not be negligible. In this case it is assumed that the relatively thin walled hollow cylinder with cladding can be treated as a composite beam on an elastic foundation (Model 2). In both models, the effect of surface cooling rate is studied by assuming the temperature boundary condition to be a ramp function. The calculated results include the transient temperature, thermal stresses in the uncracked medium and stress intensity factors which are presented as a function of time, and the duration of cooling ramp. The stress intensity factors are also presented as a function of the size and the location of the crack. The problem is solved for two bonded materials of different thermal and mechanical properties. The mathematical formulation results in two singular integral equations which are solved numerically. The results are given for two material pairs, namely an austenitic steel layer welded on a ferritic steel substrate, and a ceramic coating on ferritic steel. In the case of the yielded clad, the stress intensity factors for a crack under the clad are determined by using a plastic strip model and are compared with elastic clad results.
Rizk, Abd El-Fattah A.↗
Void growth in an elastic-plastic medium.
The uniaxial deformation of an elastic-plastic medium containing a doubly periodic square array of circular cylindrical voids is studied under plane-strain conditions. Both the effects of geometrical nonlinearities resulting from large deformation and physical nonlinearities arising from plastic material behavior are included in formulating the problem. A variational principle is used as the basis for implementing a finite-element solution. Results are obtained for the change in void shape and size under increasing overall strain, the overall tensile behavior of the material with voids, and the development of the plastic zone about a void.
Needleman, A.↗
Finite domain solution of a hydraulic fracture in a permeable rock
In this work, we present a domain-based algorithm to simulate the propagation of a plane-strain hydraulic fracture in a zero-toughness permeable elastic medium. The algorithm utilizes a domain-based method to solve the elasticity equation and integrates a multi-scale tip asymptote, which is particular to hydraulic fractures, into this framework. This integration is key to accurately model the energy dissipation and the fluid leak-off in the fracture tip region. The algorithm combines a 2D finite volume method (FVM) for solving the elasticity equation with a 1D FVM for solving the nonlinear lubrication equation. Incorporating the far-field asymptotics and using a moving-mesh scheme reduces the computational burden while improving the accuracy of the scheme. The paper concludes with an analysis of the numerical results. This study demonstrates the potential of this domain-based approach for modeling hydraulic fractures in poroelastic media.
Domain-based method↗
Wave propagation in anisotropic medium due to an oscillatory point source with application to unidirectional composites
The far-field displacements in an infinite transversely isotropic elastic medium subjected to an oscillatory concentrated force are derived. The concepts of velocity surface, slowness surface and wave surface are used to describe the geometry of the wave propagation process. It is shown that the decay of the wave amplitudes depends not only on the distance from the source (as in isotropic media) but also depends on the direction of the point of interest from the source. As an example, the displacement field is computed for a laboratory fabricated unidirectional fiberglass epoxy composite. The solution for the displacements is expressed as an amplitude distribution and is presented in polar diagrams. This analysis has potential usefulness in the acoustic emission (AE) and ultrasonic nondestructive evaluation of composite materials. For example, the transient localized disturbances which are generally associated with AE sources can be modeled via this analysis. In which case, knowledge of the displacement field which arrives at a receiving transducer allows inferences regarding the strength and orientation of the source, and consequently perhaps the degree of damage within the composite.
Williams, J. H., Jr.↗
Finite domain solution of a KGD hydraulic fracture in the viscosity-dominated regime
This paper describes a numerical algorithm for solving the classic problem of a plane strain (KGD) fracture propagating in an impermeable elastic medium with zero toughness. The method, which takes advantage of the self-similar nature of the solution, combines a domain-based scheme to solve the elasticity equations and a finite volume method to solve the nonlinear lubrication equation. This work represents a first step towards developing a model able to account for pore pressure diffusion in the medium and corresponding poroelastic effects, noting that these processes are more efficiently solved using a domain-based rather than a boundary integral method. To enhance the efficiency and accuracy of the numerical scheme, the far-field crack asymptotics is embedded in the discretized elastic relationship between the fluid pressure and the crack opening, while the coupled fluid-solid tip asymptote is enforced in a weak form when solving the nonlinear lubrication equation. The proposed technique yields results that closely match the analytical solution, even with a coarse mesh. This approach offers potential for addressing more complex hydraulic fracturing problems in the future.
Domain-based method↗
New self-consistent homogenization for thermo-elastic polycrystals with imperfect interfaces
Here we present a new thermo-elastic self-consistent formulation to calculate the thermo-mechanical response of polycrystalline aggregates with imperfect interfaces. The new model is based on an improved treatment of the effect of imperfect interfaces on the micromechanical response of the grains compared to pre-existing models. New expressions/algorithms are derived for the effective elastic and thermal properties, localization relations, and calculation of intragranular field fluctuations. In addition, derivation of a novel integral equation for the strain field in a heterogeneous elastic medium subjected to arbitrary thermal strain field and displacement jumps is presented. The new model is applied to study the effective thermo-elastic properties and average field fluctuations as a function of the interface properties for imperfectly-bonded triaminotrinitrobenzene (TATB) polycrystalline granular aggregates. The proposed formulation is general in the sense that it can be extended to other material systems and deformation regimes that require a proper consideration of the effect of imperfect interface properties on the material's thermo-mechanical response.
36 MATERIALS SCIENCE↗
On composites with periodic structure
The overall moduli of a composite with an isotropic elastic matrix containing periodically distributed (anisotropic) inclusions or voids, can be expressed in terms of several infinite series which only depend on the geometry of the inclusions or voids, and hence can be computed once and for all for given geometries. For solids with periodic structures these infinite series play exactly the same role as does Eshelby's tensor for a single inclusion or void in an unbounded elastic medium. For spherical and circular-cylindrical geometries, the required infinite series are calculated and the results are tabulated. These are then used to estimate the overall elastic moduli when either the overall strains or the overall stresses are prescribed, obtaining the same results. These results are compared with other estimates and with experimental data. It is found that the model of composites with periodic structure yields estimates in excellent agreement with the experimental observations.
Nemat-Nasser, S.↗
Interferometric SAR modelling of near surface data to improve geological model in the Surat Basin, Australia
Here we present a study on geophysical inverse modelling for subsurface structural properties of an unconventional hydrocarbon site that was monitored previously by Interferometric Synthetic Aperture Radar (InSAR) technology for surface deformation. A static three-dimensional geomodel along with extracted property maps replicates the depth of each underlying stratigraphic unit and structural feature with the density of each geological layer. We examine the hypothesis that integration of elastic properties of each formation layer with InSAR observations in a stratified elastic medium will lead to a viscoelastic geophysical inverse problem that can be solved to estimate fractional volume change at the reservoir level. Moreover, we examine synthetic scenarios in which the elastic properties of the formations are perturbed before determining the resulting impact on the rate of surface deformation. The results show that although the slope of underlying formations, their density and depth can define the extent and pattern of a deformation signal, their properties have a marginal impact on volumetric change compared to the dense network of shallow depth Coal Seam Gas (CSG) mining wells. Besides, it is also demonstrated that the inversion of InSAR deformation maps can resolve the uncertainties associated with low-resolution seismic interpretation as well as filling the data gaps within seismic acquisitions. A significant contribution of this investigation to the geological basin modelling involves a) introducing a remote and non-invasive technology such as InSAR to improve geophysical mapping of subsurface structures such as faults in areas with sparse or no reflective seismic information, and b) applying a multi-layer viscoelastic geophysical source model for an unconventional hydrocarbon reservoir such as CSG.
58 GEOSCIENCES↗
Seismic Characterization of the Blue Mountain Geothermal Field
Subsurface characterization is crucial for geothermal energy exploration and production. Yet hydrothermal reservoirs usually reside in highly fractured and faulted zones where accurate characterization is very challenging because of low signal-to-noise ratios of land seismic data and lack of coherent reflection signals. We perform an active-source seismic characterization for the Blue Mountain geothermal field in Nevada using active seismic data to reveal the elastic medium property complexity and fault distribution at this field. We first employ an unsupervised machine learning method to attenuate groundroll and near-surface guided-wave noise and enhance coherent reflection and scattering signals from noisy seismic data. We then build a smooth initial P-wave velocity model based on an existing magnetotellurics survey result, and use 3D first-arrival traveltime tomography to refine the initial velocity model. We then derive a set of elastic wave velocities and anisotropic parameters using elastic full-waveform inversion, and obtain PP and PS images using elastic reverse-time migration. We identify major faults by analyzing the variations of seismic velocities and anisotropy parameters, and reveal mid- to small-scale faults by applying a supervised machine learning method to the seismic migration images. Our characterization reveals complex velocity heterogeneities and anisotropies, as well as faults, with a high spatial resolution. These results can provide valuable information for optimal placement of future injection and production wells to increase geothermal energy production at the Blue Mountain geothermal power plant.
58 GEOSCIENCES↗
Phononic Casimir Effect in Planar Materials
The phononic Casimir effect between planar objects is investigated by deriving a formalism from the quantum partition function of the system following multiscattering approach. This fluctuation-induced coupling is mediated by phonons modeled as an effective elastic medium. We find that excitations with three types of polarizations arise from the resolved boundary conditions, however the coupling is dominated by only one of these degrees of freedom due to exponential suppression effects in the other two. Here, the obtained scaling laws and dependence on materials properties and temperature suggest effective pathways of interaction control. Scenarios of materials combinations are envisioned where the phononic Casimir effect is of similar order as the standard Casimir interaction mediated by electromagnetic fluctuations.
Acoustic phonons↗
Modeling the contributions to acoustic nonlinearity from complex dislocation networks using 3D dislocation dynamics
Nonlinear ultrasonic parameters are highly sensitive to microstructural features that affect macroscale material behavior, providing a nondestructive means to characterize their evolution. Although dislocations are known to be a strong source of acoustic nonlinearity, establishing quantitative links between the acoustic nonlinearity parameter (β), measured via Second Harmonic Generation, and dislocation morphology—such as dislocation length and density—remains an open challenge. This work advances the numerical modeling of dislocation–β relationships using 3D dislocation dynamics (DD) simulations in two approaches: a “static” method computing strain and stress fields from dislocation configurations in the absence of external loading, and a “quasi-static” method to estimate β from the curvature of dislocation lines under applied load. First, the static method is combined with finite element analysis to investigate a recent assertion that heterogeneous initial strain fields can induce higher harmonic generation in a linear elastic medium; the present results do not corroborate this outcome. Then, the quasi-static method is applied to multiple-dislocation scenarios through parametric studies, revealing behaviors not predicted by analytical models, such as the competing interactions of edge and screw dislocations and the significant influence of applied stress on β. Finally, the simulations are used to model SHG experimental results and validate the hypothesis that β can decrease during plastic deformation, despite increasing dislocation density. As the DD code used here is open-source, it provides a practical platform for future investigation into microstructure–β relationships important to the interpretation of SHG results.
Materials science↗
Inference of Induced Fracture Geometries Using Fiber-Optic Distributed Strain Sensing in Hydraulic Fracture Test Site 2
Fiber-optic Distributed Strain Sensor observations in a vertical well allow rapid inference of the time evolution of nearby hydraulic fracture heights and their vertical aperture distributions during stimulation and depressurization. We describe a computationally efficient deconvolutional model based on an elastostatic kernel for fracture opening within an isotropic, homogeneous, linear elastic medium. Furthermore, an application of this model to observations from the Hydraulic Fracture Test Site 2 reveals that ultimate fracture heights are typically greater than those indicated by microseismic monitoring, and some hydraulic fractures continue their upward growth for several hours after high-pressure injections ceased.
58 GEOSCIENCES↗
Potential Vorticity Mixing in a Tangled Magnetic Field
A theory of potential vorticity (PV) mixing in a disordered (tangled) magnetic field is introduced. The analysis is in the context of β -plane MHD, with a special focus on the physics of momentum transport in the stably stratified, quasi-2D solar tachocline. A physical picture of mean PV evolution by vorticity advection and tilting of magnetic fields is proposed. In the case of weak field perturbations, quasi-linear theory predicts that the Reynolds and magnetic stresses balance as turbulence Alfvénizes for a larger mean magnetic field. Jet formation is explored quantitatively in the mean field–resistivity parameter space. However, since even a modest mean magnetic field leads to large magnetic perturbations for large magnetic Reynolds number, the physically relevant case is that of a strong but disordered field. We show that numerical calculations indicate that the Reynolds stress is modified well before Alfvénization—i.e., before fluid and magnetic energies balance. To understand these trends, a double-average model of PV mixing in a stochastic magnetic field is developed. Calculations indicate that mean-square fields strongly modify Reynolds stress phase coherence and also induce a magnetic drag on zonal flows. The physics of transport reduction by tangled fields is elucidated and linked to the related quench of turbulent resistivity. We propose here a physical picture of the system as a resisto-elastic medium threaded by a tangled magnetic network. Applications of the theory to momentum transport in the tachocline and other systems are discussed in detail.
79 ASTRONOMY AND ASTROPHYSICS↗
Electromechanical stream-structure instabilities.
Dynamics of conducting fluid stream coupled to elastic medium by transverse electric or parallel magnetic field, considering stability of system
Ketterer, F. D.↗