Nonlinear elastodynamic behavior of intact and fractured rock under in-situ stress and saturation conditions
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Materials Science↗
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Experimental Investigation of Elastodynamic Nonlinear Response of Dry Intact, Fractured and Saturated Rock
Nonlinear elastodynamic response of fractured rocks carries crucial information on fracture features that can be exploited to forecast flow properties, friction constitutive behavior and poromechanical response. Well-controlled laboratory experiments are designed to measure the nonlinear elastodynamic response of Westerly granite in three states: dry intact, dry fractured and saturated fractured. We study the effect of fracturing and saturation in modifying the elastodynamic response of the rock. Each sample is tested at a normal stress level of 15 MPa. We measure the elastodynamic response of an intact L-shaped sample of Westerly Granite subjected to normal stress oscillations of prescribed amplitudes (0.2–1 MPa) and frequencies (0.1, 1, 10 Hz). Ultrasonic waves transmitted across the sample are used to monitor the evolution of wave velocity before, during and after dynamic stressing. Furthermore, the nonlinearity of the elastodynamic response is measured in terms of: (1) the offset in normalized wave velocity; (2) the amplitude of wave velocity fluctuation during the oscillations; and (3) recovery rate of the wave velocity post-oscillation. We observe that the three nonlinearity parameters show a similar trend. Irrespective of the parameter, the nonlinearity measures higher for sample in dry-intact condition than that for dry-fractured and the saturated-fractured sample exhibits smaller nonlinearity than the dry-fractured sample. As expected, the saturated sample exhibits less nonlinearity than the dry intact and fractured samples due to the presence of interstitial fluid and the resulting increased interface stiffness. Conversely, the dry intact rock shows a higher nonlinearity than the dry fractured. We use numerical simulations to show that the presence of fracture significantly alters the strain distribution across the bulk of the sample and only the contacting asperities are highly strained, thus resulting in a decrease in the measured elastodynamic nonlinearity.
58 GEOSCIENCES↗
Relating Hydro–Mechanical and Elastodynamic Properties of Dynamically Stressed Tensile–Fractured Rock in Relation to Applied Normal Stress, Fracture Aperture, and Contact Area
We exploit nonlinear elastodynamic properties of fractured rock to probe the micro-scale mechanics of fractures and understand the relation between fluid transport and fracture aperture under dynamic stressing. Experiments were conducted on rough, tensile-fractured Westerly granite subject to triaxial stresses. We measure fracture permeability for steady-state fluid flow with deionized water. Pore pressure oscillations are applied at amplitudes ranging from 0.2 to 1 MPa at 1 Hz frequency. During dynamic stressing we transmit ultrasonic signals through the fracture using an array of piezoelectric transducers (PZTs) to monitor evolution of interface properties. We examine the influence of fracture aperture and contact area by conducting measurements at effective normal stresses of 10–20 MPa. Additionally, the evolution of contact area with stress is characterized using pressure sensitive film. These experiments are conducted separately with the same fracture and map contact area at stresses from 9 to 21 MPa. The measurements are a proxy for “true” contact area for the fracture surface and we relate them to elastic properties using the calculated PZT sensor footprints via numerical modeling of Fresnel zones. We compare the elastodynamic response of the fracture using the stress-induced changes in ultrasonic wave velocities for transmitter-receiver pairs to image spatial variations in contact properties. We show that nonlinear elasticity and permeability enhancement decrease with increasing normal stress. Additionally, post-oscillation wave velocity and permeability exhibit quick recoveries toward pre-oscillation values. Estimates of fracture contact area (global and local) demonstrate that the elastodynamic and permeability responses are dominated by fracture topology.
58 GEOSCIENCES↗
In‐Operando Spatiotemporal Imaging of Coupled Film‐Substrate Elastodynamics During an Insulator‐to‐Metal Transition
Abstract The drive toward non‐von Neumann device architectures has led to an intense focus on insulator‐to‐metal (IMT) and the converse metal‐to‐insulator (MIT) transitions. Studies of electric field‐driven IMT in the prototypical VO 2 thin‐film channel devices are largely focused on the electrical and elastic responses of the films, but the response of the corresponding TiO 2 substrate is often overlooked, since it is nominally expected to be electrically passive and elastically rigid. Here, in‐operando spatiotemporal imaging of the coupled elastodynamics using X‐ray diffraction microscopy of a VO 2 film channel device on TiO 2 substrate reveals two new surprises. First, the film channel bulges during the IMT, the opposite of the expected shrinking in the film undergoing IMT. Second, a microns thick proximal layer in the substrate also coherently bulges accompanying the IMT in the film, which is completely unexpected. Phase‐field simulations of coupled IMT, oxygen vacancy electronic dynamics, and electronic carrier diffusion incorporating thermal and strain effects suggest that the observed elastodynamics can be explained by the known naturally occurring oxygen vacancies that rapidly ionize (and deionize) in concert with the IMT (MIT). Fast electrical‐triggering of the IMT via ionizing defects and an active “IMT‐like” substrate layer are critical aspects to consider in device applications.
36 MATERIALS SCIENCE↗
Incorporating Full Elastodynamic Effects and Dipping Fault Geometries in Community Code Verification Exercises for Simulations of Earthquake Sequences and Aseismic Slip (SEAS)
ABSTRACT Numerical modeling of earthquake dynamics and derived insight for seismic hazard relies on credible, reproducible model results. The sequences of earthquakes and aseismic slip (SEAS) initiative has set out to facilitate community code comparisons, and verify and advance the next generation of physics-based earthquake models that reproduce all phases of the seismic cycle. With the goal of advancing SEAS models to robustly incorporate physical and geometrical complexities, here we present code comparison results from two new benchmark problems: BP1-FD considers full elastodynamic effects, and BP3-QD considers dipping fault geometries. Seven and eight modeling groups participated in BP1-FD and BP3-QD, respectively, allowing us to explore these physical ingredients across multiple codes and better understand associated numerical considerations. With new comparison metrics, we find that numerical resolution and computational domain size are critical parameters to obtain matching results. Codes for BP1-FD implement different criteria for switching between quasi-static and dynamic solvers, which require tuning to obtain matching results. In BP3-QD, proper remote boundary conditions consistent with specified rigid body translation are required to obtain matching surface displacements. With these numerical and mathematical issues resolved, we obtain excellent quantitative agreements among codes in earthquake interevent times, event moments, and coseismic slip, with reasonable agreements made in peak slip rates and rupture arrival time. We find that including full inertial effects generates events with larger slip rates and rupture speeds compared to the quasi-dynamic counterpart. For BP3-QD, both dip angle and sense of motion (thrust versus normal faulting) alter ground motion on the hanging and foot walls, and influence event patterns, with some sequences exhibiting similar-size characteristic earthquakes, and others exhibiting different-size events. These findings underscore the importance of considering full elastodynamics and nonvertical dip angles in SEAS models, as both influence short- and long-term earthquake behavior and are relevant to seismic hazard.
Geochemistry & Geophysics↗
The effect of a transducer’s spatial averaging on an elastodynamic guided wave’s wavenumber spectrum
Elastodynamic guided waves propagate in an elastic solid which makes it difficult, if not impractical, to place a receiving transducer in the direct path of the propagating wave (as one would for an acoustic wave in a fluid medium). Thus, to account for this, receiving transducers are often placed on the surface of the solid waveguide such that the transducer surface is parallel to the wave propagation direction. This transducer orientation introduces spatial averaging, which causes the received signal to have an altered signal amplitude and mode bias. We investigate both of these effects and present a simple model from which we derive a scaling-ratio expression that describes the effects of spatial averaging. Furthermore, we then test its performance using finite-element simulations that incorporate “real-world” assumptions (e.g., transient waves, piezoelectric effects, etc.). The results from the simulations demonstrate that the scaling-ratio can characterize the effects resulting from spatial averaging. The scaling-ratio expression will be particularly useful when designing experiments involving high frequency (small wavelength) guided waves. Lastly, the proposed scaling-ratio expression could be applied to other sensing methods, like Laser Doppler Vibrometry (LDV) or piezoelectric waveguides with inter-digitated transducers, because of its generality. However, the authors are careful to note that the scaling-ratio expression is not intended as a replacement of multi-physics analysis or good experimental design, and the effects of spatial averaging should be avoided whenever possible.
2DFFT↗
Scale-bridging with the extended/generalized finite element method for linear elastodynamics
This paper presents an extended/generalized finite element method for bridging scales in linear elastodynamics in the absence of scale separation. More precisely, the GFEMgl framework is expanded to enable the numerical solution of multiscale problems through the automated construction of specially-tailored shape functions, thereby enabling high-fidelity finite element modeling on simple, fixed finite element meshes. Furthermore, this introduces time-dependencies in the shape functions in that they are subject to continuous adaptation with time. The temporal aspects of the formulation are investigated by considering the Newmark-β time integration scheme, and the efficacy of mass lumping strategies is explored in an explicit time-stepping scheme. This method is demonstrated on representative wave propagation examples as well as a dynamic fracture problem to assess its accuracy and flexibility.
36 MATERIALS SCIENCE↗
Unified wavefront singularity characterization of three-dimensional elastodynamic time-domain half-space Green's function under impulsive boundary and internal loads
Founded on a novel analytical formulation that led to a rigorous yet compact path-integral representation of the time-domain elastodynamic half-space Green's function, a unified analysis of the possible occurrence of different singular wavefront behaviour in the response under arbitrary impulsive internal or surface point loads at arbitrary source-receiver locations is presented. With the decomposition of the general solution into distinct initiating and reflected wave group integrals that share a common factored format and simple contour definitions, the mathematical framework is shown to allow a straightforward identification of the specific conditions and the particular wave groups that are responsible for the singular wavefront phenomena without resorting to advanced analytic function theories or asymptotic methods. Analytic characterizations of the nature, strength and direction of all intrinsic singular wavefront behaviours of the three-dimensional Green's function in three canonical cases of source-receiver configurations are given in a dual integral-closed form format to facilitate their theoretical understanding as well as computational applications. Graphical illustrations of their variation with the source-receiver configuration and the medium's Poisson's ratio together with relevant comparison and clarifications of some classical treatments are included.
Green’s functions↗
Modeling and characterizing the elastodynamic response of octet-truss lattice structures using resonance techniques
Characterization of additively manufactured materials and structures is an ongoing effort for the advanced manufacturing community. This article will investigate an approach using resonant spectral ultrasound (RUS) to measure the effective elastic constants of an Octet Truss lattice and apply the results to continuum bases models representing the lattice regions in different structures. The study is focused on simple lattices structures fabricated from Ti5553 using a laser powder bed fusion process (LBPF). Solid and lattice samples are measured to determine RUS estimates for the elastic properties of the bulk material and the effective elastic properties of the lattice structure. The estimated elastic properties are then incorporated into 3d finite element models using a continuum approximation of the physical AM parts. Comparisons show good agreement between the experimentally measured eigen frequencies of the Ti5553 LBPF parts and the eigen frequencies calculated using the continuum approximations based on the effective RUS elastic properties. The current results suggest there is additional physics and geometrical effects that are accounted for in the RUS continuum approximation of the lattice that are not captured in the full 3d finite element model of the parts utilizing only the base material properties.
36 MATERIALS SCIENCE↗
The Dirichlet-Neumann Schwarz alternating method for contact problems in elastodynamics: techniques for reducing artificial oscillations
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Koliesnikova, Daria↗
The Dirichlet-Neumann Schwarz alternating method for contact problems in elastodynamics
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Tezaur, Irina Kalashnikova↗
The Dirichlet-Neumann Schwarz alternating method for contact problems in elastodynamics
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Mota, Alejandro [Sandia National Laboratories (SNL↗
Modeling wave propagation in elastic solids via high-order accurate implicit-mesh discontinuous Galerkin methods
Here, a high-order accurate implicit-mesh discontinuous Galerkin framework for wave propagation in single-phase and bi-phase solids is presented. The framework belongs to the embedded-boundary techniques and its novelty regards the spatial discretization, which enables boundary and interface conditions to be enforced with high-order accuracy on curved embedded geometries. High-order accuracy is achieved via high-order quadrature rules for implicitly-defined domains and boundaries, whilst a cell-merging strategy addresses the presence of small cut cells. The framework is used to discretize the governing equations of elastodynamics, written using a first-order hyperbolic momentum-strain formulation, and an exact Riemann solver is employed to compute the numerical flux at the interface between dissimilar materials with general anisotropic properties. The space-discretized equations are then advanced in time using explicit high-order Runge–Kutta algorithms. Several two- and three-dimensional numerical tests including dynamic adaptive mesh refinement are presented to demonstrate the high-order accuracy and the capability of the method in the elastodynamic analysis of single- and bi-phases solids containing complex geometries.
42 ENGINEERING↗
Listening for the Landing: Seismic Detections of Perseverance's Arrival at Mars With InSight
The entry, descent, and landing (EDL) sequence of NASA's Mars 2020 Perseverance Rover will act as a seismic source of known temporal and spatial localization. We evaluate whether the signals produced by this event will be detectable by the InSight lander (3,452 km away), comparing expected signal amplitudes to noise levels at the instrument. Modeling is undertaken to predict the propagation of the acoustic signal (purely in the atmosphere), the seismoacoustic signal (atmosphere-to-ground coupled), and the elastodynamic seismic signal (in the ground only). Our results suggest that the acoustic and seismoacoustic signals, produced by the atmospheric shock wave from the EDL, are unlikely to be detectable due to the pattern of winds in the martian atmosphere and the weak air-to-ground coupling, respectively. However, the elastodynamic seismic signal produced by the impact of the spacecraft's cruise balance masses on the surface may be detected by InSight. The upper and lower bounds on predicted ground velocity at InSight are 2.0 × 10 -14 and 1.3 × 10 -10 m s -1 . The upper value is above the noise floor at the time of landing 40% of the time on average. The large range of possible values reflects uncertainties in the current understanding of impact-generated seismic waves and their subsequent propagation and attenuation through Mars. Uncertainty in the detectability also stems from the indeterminate instrument noise level at the time of this future event. A positive detection would be of enormous value in constraining the seismic properties of Mars, and in improving our understanding of impact-generated seismic waves.
58 GEOSCIENCES↗
Tailored ultrasound propagation in microscale metamaterials via inertia design
The quasi-static properties of micro-architected (meta)materials have been extensively studied over the past decade, but their dynamic responses, especially in acoustic metamaterials with engineered wave propagation behavior, represent a new frontier. However, challenges in miniaturizing and characterizing acoustic metamaterials in high-frequency (megahertz) regimes have hindered progress toward experimentally implementing ultrasonic-wave control. Here, we present an inertia design framework based on positioning microspheres to tune responses of 3D microscale metamaterials. We demonstrate tunable quasi-static stiffness by up to 75% and dynamic longitudinal-wave velocities by up to 25% while maintaining identical material density. Using noncontact laser-based dynamic experiments of tunable elastodynamic properties and numerical demonstrations of spatio-temporal ultrasound wave propagation, we explore the tunable static and elastodynamic property relation. This design framework expands the quasi-static and dynamic metamaterial property space through simple geometric changes, enabling facile design and fabrication of metamaterials for applications in medical ultrasound and analog computing.
42 ENGINEERING↗
A multiscale design method using interpretable machine learning for phononic materials with closely interacting scales
Manipulating the dispersive characteristics of vibrational waves is beneficial for many applications, e.g., high-precision instruments. architected hierarchical phononic materials have sparked promise tunability of elastodynamic waves and vibrations over multiple frequency ranges. In this article, hierarchical unit-cells are obtained, where features at each length scale result in a band gap within a targeted frequency range. Our novel approach, the ‘‘hierarchical unit-cell template method,’’ is an interpretable machine-learning approach that uncovers global unit-cell shape/topology patterns corresponding to predefined band-gap objectives. A scale-separation effect is observed where the coarse-scale band-gap objective is mostly unaffected by the fine-scale features despite the closeness of their length scales, thus enabling an efficient hierarchical algorithm. Moreover, the hierarchical patterns revealed are not predefined or self-similar hierarchies as common in current hierarchical phononic materials. Furthermore, our approach offers a flexible and efficient method for the exploration of new regions in the hierarchical design space, extracting minimal effective patterns for inverse design in applications targeting multiple frequency ranges.
Architected materials↗
Synchronous and Concurrent Multidomain Computing Method for Cloud Computing Platforms
We present a numerical method for synchronous and concurrent solution of transient elastodynamics problem where the computational domain is divided into subdomains that may reside on separate computational platforms. Here, this work employs the variational multiscale discontinuous Galerkin (VMDG) method to develop interdomain transmission conditions for transient problems. The fine-scale modeling concept leads to variationally consistent coupling terms at the common interfaces. The method admits a large class of time discretization schemes, and decoupling of the solution for each subdomain is achieved by selecting any explicit algorithm. Numerical tests with a manufactured solution problem show optimal convergence rates. The energy history in a free vibration problem is in agreement with that of the solution from a monolithic computational domain.
97 MATHEMATICS AND COMPUTING↗