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Characterisation of soft tissue mechanical properties is a topic of increasing interest in translational and clinical research. Magnetic resonance elastography (MRE) has been used in this context to assess the mechanical properties of tissues in vivo noninvasively. Typically, these analyses rely on linear viscoelastic wave equations to assess material properties from measured wave dynamics. However, deformations that occur in some tissues (e.g. liver during respiration, heart during the cardiac cycle, or external compression during a breast exam) can yield loading bias, complicating the interpretation of tissue stiffness from MRE measurements. In this paper, it is shown how combined knowledge of a material's rheology and loading state can be used to eliminate loading bias and enable interpretation of intrinsic (unloaded) stiffness properties. Equations are derived utilising perturbation theory and Cauchy's equations of motion to demonstrate the impact of loading state on periodic steady-state wave behaviour in nonlinear viscoelastic materials. These equations demonstrate how loading bias yields apparent material stiffening, softening and anisotropy. MRE sensitivity to deformation is demonstrated in an experimental phantom, showing a loading bias of up to twofold. From an unbiased stiffness of [Formula: see text] Pa in unloaded state, the biased stiffness increases to 9767.5 [Formula: see text]1949.9 Pa under a load of [Formula: see text] 34% uniaxial compression. Integrating knowledge of phantom loading and rheology into a novel MRE reconstruction, it is shown that it is possible to characterise intrinsic material characteristics, eliminating the loading bias from MRE data. The framework introduced and demonstrated in phantoms illustrates a pathway that can be translated and applied to MRE in complex deforming tissues. This would contribute to a better assessment of material properties in soft tissues employing elastography.

Wave propagation in slender beams is addressed in the framework of nonlocal continuum mechanics. The elastodynamic problem is formulated exploiting consistent methodologies of pure integral, mixture and nonlocal strain gradient elasticity. Relevant wave solutions are analytically provided, with peculiar attention to reflection and near field phenomena occurring in presence of boundaries. Notably, the solution field is got as superimposition of incident, reflected, primary near field and secondary near field waves. The latter contribution represents a further effect due to the size dependent mechanical behaviour. Limit responses for vanishing nonlocal parameter are analytically evaluated, consistently showing a zero amplitude of the secondary near field wave. Parametric analyses are carried out to show how length scale parameter, amplitude of incident wave and geometric and elastic properties of the beam affect the amplitudes of reflected, primary near field and secondary near field waves. The results obtained exploiting different nonlocal integral elasticity approaches are compared and discussed. [ABSTRACT FROM AUTHOR]

Successful management of chalk reservoirs for various subsurface applications as well as construction in chalk/limestone formations rely on descriptions of compaction behaviour commonly predicted from laboratory experiments. This study aims to understand and describe better the compaction behaviour that oil and water-saturated chalk undergo. Seven North Sea Lower Cretaceous chalk samples with initial porosity ranging from 31 to 45% were compacted hydrostatically in the laboratory. The traditionally named elastic, transitional, elastoplastic and strain hardening phases were identified from stress–strain curves. The observed compaction behaviour is described in phenomenological terms based on the interpretation of Biot's coefficient as a measure of grain-to-grain contact area within the chalk frame. Biot's coefficient was derived from elastic wave velocities and bulk density via Gassmann fluid substitution by first approximations assuming a simple calcite-bearing rock frame. Biot's coefficient identifies both elastoplastic and elastic phases in the initial compaction phase traditionally denoted as the elastic phase. The plastic component of the elastoplastic phase presumably originates from closure of micro-crack introduced by unloading and equilibration from core recovery. Biot's coefficient is a reliable indicator of pore collapse, and a specific constant magnitude of purely elastic strain controls the onset of pore collapse. In situ reservoirs presumably only experience the elastic strain during effective stress changes, not the elastoplastic behaviour seen in experiments. Yet, as laboratory experiments often form a calibration background for large-scale models, quantifying the plastic component of elastoplastic phases and pore collapse from pure elastic strain provides new insight to improve models and avoid the unphysical use of porosity as a controlling physical parameter. Highlights: During initial compaction, both elastoplastic and elastic phases exit and are identified from Biot's coefficient. During compaction, a local minimum Biot's coefficient derive from ultrasonic velocities is a reliable indicator of pore collapse. A critical and purely elastic strain derived from applied stress and dynamic moduli is the controlling mechanism of pore collapse. Identification of subphases and a critical pore collapse elastic strain provides new insight into calibration of reservoir model from experiments. [ABSTRACT FROM AUTHOR]

A comprehensive examination of the crystal structure, as well as elastic and thermal properties, of the recently created Zintl phase CsGaSb2 has been carried out using ab initio density functional theory pseudo-potential plane-wave calculations. All the provided facts presented are newly forecasted, with the exception of the structural properties under normal conditions. The calculated lattice parameters and interatomic bond lengths of the investigated material closely correspond to the actual values, indicating a high level of accuracy. Forecasts have been generated for the elastic parameters and related characteristics of both single-crystal and polycrystalline phases of CsGaSb2. The parameters encompassed in this list are elastic constants, shear modulus, bulk modulus, Poisson's ratio, Young's modulus, anisotropy indices, elastic wave velocities, Pugh's criterion, and Debye temperature. The mechanical and dynamic stability of CsGaSb2 as well as its elastic anisotropy have been established. The temperature dependence of various macroscopic properties, including bulk modulus, unit cell volume, volumetric thermal expansion coefficient, isochoric and isobaric thermal capacities, Debye temperature, Grüneisen parameter, and entropy function, was evaluated at specific pressures using Debye's quasi-harmonic approach in combination with ab initio calculations. [ABSTRACT FROM AUTHOR]

The article concerns the modeling of the transverse impact of an impactor (test sample) on the surface of an infinite elastic layer. The Laplace transform with respect to time and the Hankel transform with respect to the radius for the axisymmetric case were applied. The propagation of elastic waves in the layer and local deformations in the contact zone are taken into account. Impact force, impact time and the coefficient of restitution were examined. The results are compared with the elastic half-space. The calculations carried out showed that for layer thicknesses of more than five impactor diameters, the layer can be considered as a half-space. [ABSTRACT FROM AUTHOR]

The introduction of metamaterials has provided new possibilities to manipulate the propagation of waves in different fields of physics, ranging from electromagnetism to acoustics. However, despite the variety of configurations proposed so far, most solutions lack dynamic tunability, i.e. their functionality cannot be altered post-fabrication. Our work overcomes this limitation by employing a photo-responsive polymer to fabricate a simple metamaterial structure and enable tuning of its elastic properties using visible light. The structure of the metamaterial consists of graded resonators in the form of an array of pillars, each giving rise to different resonances and transmission band gaps. Selective laser illumination can then tune the resonances and their frequencies individually or collectively, thus yielding many degrees of freedom in the tunability of the filtered or transmitted wave frequencies, similar to playing a keyboard, where illuminating each pillar corresponds to playing a different note. This concept can be used to realize low-power active devices for elastic wave control, including beam splitters, switches and filters. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'. [ABSTRACT FROM AUTHOR]

Wave equation forward modeling is a useful method to study the propagation regulation of seismic wavefields. Finite difference (FD) is one of the most extensively employed numerical approaches for computing wavefields in earthquake and exploration seismology. However, the FD approach relying on regular grids often struggles to calculate wavefields in regions featuring surface topographies. The elastic wave equation can more accurately describe the propagation of seismic wavefields in elastic media compared to the acoustic wave equation. We introduce a new FD scheme to calculate the elastic wavefields in an isotropic model with a surface topography. The novel approach can use a conventional staggered grid FD (SGFD) approach based on regular grids. A new elastic model with a horizontal surface is first obtained from the nearby surface's elastic properties and the undulating terrain elevation. We subsequently employ a topography-related strategy to eliminate the effects of surface topographies on the seismic wavefields in models with irregular surface topographies. The merits of our proposed scheme lie in its ability to stable numerically compute wavefields in models with irregular surface topographies without altering the conventional SGFD relying on regular grids. To validate the effectiveness and practicality of our method, we utilize elastic models featuring complex surface topographies. Numerical experiments demonstrate that our approach efficiently calculates elastic wavefields in isotropic media with irregular topographies based on conventional SGFD. [ABSTRACT FROM AUTHOR]

Unconsolidated, undrained triaxial deformation tests were performed on sandy facies Opalinus Clay at 50 MPa confining pressure to characterize the effect of water and microfabric orientation on the deformation behavior, mechanical properties, and P-wave velocity evolution. Dry and wet (≈ 8 and > 95% initial water saturation, respectively) samples with 12.6 ± 0.4 vol% porosity were deformed parallel and perpendicular to the bedding direction at a constant strain rate of 5 × 10–6 s−1. Dry samples revealed semi-brittle behavior and exhibited strain localization at failure, while deformation was more ductile at saturated conditions, promoting stable, slow faulting. Peak strength, Young's modulus, and number of cumulative acoustic emissions decreased significantly for wet samples compared to dry samples; the opposite was observed for Poisson's ratio. P-wave velocity anisotropy was significantly altered by differential stress, primarily due to the interplay between pore and fracture closure and stress-induced microcrack formation. For samples that were deformed perpendicular to bedding, we observed a reduction and reversal of P-wave velocity anisotropy with increasing differential stress, whereas anisotropy of parallel samples increased. The results suggest that water saturation reduces the pressure at the brittle-ductile transition and that the elastic properties and anisotropy of sandy facies Opalinus Clay can be significantly altered in an anisotropic stress field, e.g., adjacent to fault zones or tunnel excavations. Changes in elastic anisotropy are primarily controlled by the orientation between the pre-existing microfabric and the maximum principal stress direction, stress magnitude, and the degree of water saturation. Highlights: The presence of water reduces compressive strength, stiffness and P-wave velocity anisotropy of sandy facies Opalinus Clay, accompanied by increasing strain delocalization, promoting stable, slow faulting during triaxial deformation Triaxial deformation alters the elastic wave velocity anisotropy and symmetry of sandy facies Opalinus Clay, depending on water content and on the orientation of bedding relative to loading direction Changes in elastic anisotropy are mainly controlled by the closure of pores and microcracks and the formation of stress-induced fractures [ABSTRACT FROM AUTHOR]

Elastic metamaterials with unusual elastic properties offer unprecedented ways to modulate the polarization and propagation of elastic waves. However, most of them rely on the resonant structural components, and thus are frequency-dependent and unchangeable. Here, we present a reconfigurable 2D mechanism-based metamaterial which possesses transformable and frequency-independent elastic properties. Based on the proposed mechanism-based metamaterial, interesting functionalities, such as ternary-coded elastic wave polarizer and programmable refraction, are demonstrated. Particularly, unique ternary-coded polarizers, with 1-trit polarization filtering and 2-trit polarization separating of longitudinal and transverse waves, are first achieved. Then, the strong anisotropy of the proposed metamaterial is harnessed to realize positive-negative bi-refraction, only-positive refraction, and only-negative refraction. Finally, the wave functions with detailed microstructures are numerically verified. [ABSTRACT FROM AUTHOR]

In this study, phonon crystal structures embedded in acoustic black holes are discussed. The low-frequency band gap is widened by exploiting the low-frequency, broadband and multimode properties of the acoustic black hole. The energy band properties of the acoustic crystal structure embedded in an acoustic black hole are calculated by means of a finite element method. The mechanism of band gap generation is investigated. The vibration transfer characteristics of finite period structures are analyzed. The influence of the structural parameters of the acoustic black hole is analyzed. The results show that the acoustic crystal structure embedded in an acoustic black hole has multiple band gaps in the 500 Hz band and the band gap coverage is increased to 45.18%. The starting bandgap is 16.10% lower than before embedding in the acoustic black hole and the width of the first bandgap expands to 173.03% of that before embedding in the acoustic black hole. The onset and termination frequencies of the first band gap are mainly determined by the vibrational modes of the scatterer and the acoustic black hole structure. The vibrational transfer of the finite period structure is analyzed and shows good damping characteristics in the bandgap interval. Finally, vibration experiments verify the vibration damping effect of the proposed coupled acoustic black hole phononic crystal, and the relevant findings of this paper can be used in the vibration damping design of plate structures, enriching the experience of research related to acoustic black holes. [ABSTRACT FROM AUTHOR]

The utilization of a reverberant shear-wave field in shear-wave elastography has emerged as a promising technique for achieving robust shear-wave speed (SWS) estimation. However, many types of estimators cannot accurately measure SWS within such a complicated 3D wave field. This study introduces an advanced autocorrelation estimator based on angular integration known as the angular integral autocorrelation (AIA) approach to address this issue. The AIA approach incorporates all the autocorrelation data from various angles during measurements, resulting in enhanced robustness to both noise and imperfect distributions in SWS estimation. The effectiveness of the AIA estimator for SWS estimation is first validated using a k-Wave simulation of a stiff branching tube in a uniform background. Furthermore, the AIA estimator is applied to ultrasound elastography experiments, magnetic resonance imaging (MRI) experiments, and optical coherence tomography (OCT) studies across a range of different excitation frequencies on tissues and phantoms, including in vivo scans. The results verify the capacity of the AIA approach to enhance the accuracy of SWS estimation and the signal-to-noise ratio (SNR), even within an imperfect reverberant shear-wave field. Compared to simple autocorrelation approaches, the AIA approach can also successfully visualize and define lesions while significantly improving the estimated SWS and SNR in homogeneous background materials and providing improved elastic contrast between structures within the scans. These findings demonstrate the robustness and effectiveness of the AIA approach across a wide range of applications, including ultrasound elastography, magnetic resonance elastography (MRE), and optical coherence elastography (OCE), for accurately identifying the elastic properties of biological tissues in diverse excitation scenarios. [ABSTRACT FROM AUTHOR]

When an impactor strikes a layered target, both the impactor and the target experience waves. The waves produced travel and engage in interactions with other waves as well as the interfaces in the impactor-target system. For the impact problems on a layered mediumwith periodic properties and layered elastic media of Goupillaud-type (each layer has the same wave travel time), researchers have presented an analytical solution for stress variation with position and time within the target. However, the solution for an elastic media not satisfying the above conditions is not available in the literature. The present study fills this gap and finds the behaviour of a generalized layered medium to an impact problem. The response of the material at any position inside the layered medium is found by solving the interaction between waves, interfaces, and boundaries. The mass, momentum balance and constitutive relationship are solved to get the exact analytical expressions for particle velocity and stress for each possible wave interaction happening in the impactor and the layered medium. The expressions are utilized in a computer program to study the impact behaviour of a layered media. The code tracks each wave as it travels through the system and identifies those interactions that occur in the shortest time, uses the stress and velocity expression for that interaction, and updates the state of the material. When stress produced at the impact surface is tensile in nature, the impactor and target can be separated. The work can be applied to both finite and semi-infinite impactors and targets, and the layered medium does not necessarily have to be a periodic layered media or a Goupillaud-type medium. [ABSTRACT FROM AUTHOR]

In this article, we analyzed the response of elastic waves after striking the interface between two elastic mediums. The upper-medium is isotropic while the lower medium is semiconductor nanostructure in nature. Both the mediums are set on rotation with some fix angular frequency $ {\bf \Omega } $ Ω . A fractional ordered heat conduction model of three-phase lag along with the nonlocal theory of elasticity is adopted to formulate the problem. The incident wave after striking the interface results in five coupled quasireflected waves and three elastic transmitted waves. The ratios of the amplitude of reflection and transmitted waves with incident wave are calculated. Variations in obtained amplitude ratios with respect to incident angle have been shown graphically for silicon (Si) semiconductor. The effects of nonlocal parameter, rotational frequency and fractional order parameter on the reflection and transmitted coefficients in the presence of voids parameters are studied. The results obtained through the current analysis may be applicable in the field of seismology and semiconductors nanostructure appliances. [ABSTRACT FROM AUTHOR]

We consider the problem of elastic diffraction tomography, which consists in reconstructing elastic properties (i.e., mass density and elastic Lam\'e parameters) of a weakly scattering medium from full-field data of scattered waves outside the medium. Elastic diffraction tomography refers to the elastic inverse scattering problem after linearization using a first-order Born approximation. In this paper, we prove the Fourier diffraction theorem, which relates the twodimensional Fourier transform of scattered waves with the Fourier transform of the scatterer in the three-dimensional spatial Fourier domain. Elastic wave mode separation is performed, which decomposes a wave into five modes. A new two-step inversion process is developed, providing information on the modes first and second on the elastic parameters. Finally, we discuss reconstructions with plane wave excitation experiments for different tomographic setups and with different plane wave excitation frequencies, respectively. [ABSTRACT FROM AUTHOR]

Water infiltration into fractures is ubiquitous in crustal rocks. However, little is known about how such a progressive wetting process affects fracture stiffness and seismic wave propagation, which are highly relevant for characterizing fracture systems in situ. We study the acousto‐mechanical behavior of a free‐standing fractured granite subjected to gradual water infiltration with a downward‐moving wetting front over 12 days. We observe significant differences (i.e., by an order of magnitude) in wave amplitudes across the fractured granite compared to an intact granite, with both cases showing a strong correlation between wave amplitudes and wetting front movement. Effects of water infiltration into the fracture and surrounding matrix on seismic attenuation are captured by a numerical model with parameters constrained by experimental data. Back‐calculated fracture stiffness decreases exponentially with the wetting front migration along the fracture. We propose that moisture‐induced matrix expansion around the fracture increases asperity mismatch, leading to reduced fracture stiffness. Plain Language Summary: In the shallow layers of the Earth, hydrological cycles such as snowmelt, fog, dew, and rain have been shown to change the moisture content of crustal rocks, which can alter the elastic properties of natural fractures and affect the propagation of seismic waves. Understanding how seismic waves propagate in the near‐surface environment is crucial for the assessment of earthquake hazards and the characterization of geologic heterogeneities. In this work, we perform well‐controlled laboratory experiments to study the acousto‐mechanical behavior of a single fracture in granitic rock subjected to progressive wetting over 12 days. We report that the fracture stiffness decreases exponentially as the wetting front advances along the fracture. Our research sheds light on an important question in fracture characterization: how elastic waves propagate across a fracture undergoing moisture‐induced expansion. Key Points: A laboratory study establishes a relationship among water imbibition, seismic attenuation, and stiffness evolution in a wetted fractureWave amplitudes across a fracture correlate strongly with the wetting front movement of infiltrated water within the fractureFracture stiffness exponentially decreases with the advance of the wetting front along the fracture [ABSTRACT FROM AUTHOR]

The orientation of S Hmax is commonly estimated from in situ borehole breakouts and earthquake focal mechanisms. Borehole measurements are expensive, and therefore sparse, and earthquake measurements can only be made in regions with many well-characterized earthquakes. Here, we derive the stress-field orientation using stress-induced anisotropy in nonlinear elasticity. In this method, we measure the strain derivative of velocity as a function of azimuth. We use a natural pump-probe (NPP) approach which consists of measuring elastic wave speed using empirical Green's functions (probe) at different points of the earth tidal strain cycle (pump). The approach is validated using a larger data set in the Northern Alpine Foreland region where the orientation of maximum horizontal compressive stress is known from borehole breakouts and drilling-induced fractures. The technique resolves NNW-SSW to N-S directed S Hmax which is in good agreement with conventional methods and the recent crustal stress model. We confirm that the NPP method can be applied to dense large-scale seismic arrays. The technique is then applied to the Southern Alps to understand the contemporary stress pattern associated with the ongoing deformation due to counterclockwise rotation of the Adriatic plate with respect to the European plate. Our results explain why the two major faults in Northeastern Italy, the Giudicarie Fault and the Periadriatic Line (Pustertal–Gailtal Fault) are currently inactive, while the currently acting stress field allows faults in Slovenia to deform actively. We have demonstrated that the pump-probe method has the potential to fill in the measurement gap left by conventional approaches, both in terms of regional coverage and in depth. [ABSTRACT FROM AUTHOR]

The Moore–Gibson–Thompson (MGT) generalized thermoelasticity theory together with the Eringen's nonlocal elasticity model is used to study the propagation of harmonic plane waves in an infinite elastic medium that conducts heat. Two sets of coupled longitudinal thermoelastic waves have been initiated. These waves are dispersive in nature and experience attenuation. In conjunction with the coupled waves, there also exists one uncoupled vertically shear–type (SV-type) wave. The SV-type wave is dispersive in nature but without any attenuation. The elastic nonlocality parameter influences all these waves. Furthermore, the SV-type wave faces critical frequency, while the coupled longitudinal waves may face critical frequencies conditionally. We also explore the problem of reflection of thermoelastic waves at a stress-free insulated and isothermal plane boundary of the medium considered here. The reflection coefficients and their respective energy ratios of the reflected waves to that of incident wave are determined analytically and numerically by considering an appropriate material. The numerical results are presented graphically to highlight the effects of various parameters of interest. Some important observations about the prediction of the MGT model in comparison to the other existing models (Lord–Shulman (LS) and the Green–Nagdhi theory of type III (GN-III) models) are highlighted. [ABSTRACT FROM AUTHOR]

We demonstrate that strong elastic pump wave pulses soften sandstone more in humidified conditions than they do in dry conditions and that this effect is repeatable and reversible. We assess these changes via the non-linear interactions of a strong pump wave with a weaker probe wave. We find that there is an exponential time constant (τ ≈ 13 days) associated with this process that is independent of the amplitudes of the pump and the probe, the phase delay between the two waves (the time between transmission of the pump and probe waves), the sampling rate, and whether the sample is being dried or humidified. We demonstrate that the humidity-dependent differences in the amount of softening are induced by only a very small amount of absorbed water vapor and argue that this water is intercalated within clay particles. We also show that our pump–probe experiments detect these humidity-dependent differences in the amount of softening easily and repeatably using an experimental design that does not rely on resonance conditions. This means that, in principle, our experiments could be more easily generalized to other experimental geometries to investigate non-linear elastic properties in complex or irregular sample geometries. Our method and findings have potential relevance in oil and gas exploration, civil engineering, and understanding of the mechanism of earthquakes. [ABSTRACT FROM AUTHOR]

Artificial construction of a weakening zone over the roadway is an essential method for preventing coal bursts and rock bursts caused by strong mining tremors. However, concerning the seismic absorption and load reduction capabilities of an artificial structural weakening zone, the degree of rock mass damage to the roadway under weakening zone protection remains unclear. This study employed principles of elasticity and UDEC (Universal Distinct Element Code) to explore the seismic attenuation and load reduction capabilities of the weakening zone. The results indicate that the absorbing ability of the weakening zone increases exponentially with its weakening coefficient. Under the same dynamic load disturbance, when the weakening coefficient rises from 0.00 to 0.99, the sidewall displacement from the elastic wave source side changes from 0.400 m to 0.228 m. The total number of cracks in the roadway-surrounding rock, and the ranges of overstressed zones decreased linearly. The critical threshold of the roadway resisting the mining tremor disturbance increased. In particular, when the mining tremor is located directly above the roadway, the initial deformation of the roof is the largest, and the cumulative deformation of the rib is greater than the roof. By creating a weakening zone with a coefficient exceeding 0.95, the roadway remains unaffected by the 20 MPa dynamic loading. The study provides a theoretical basis for controlling coal burst that is triggered by mining tremors. [ABSTRACT FROM AUTHOR]

The article presents the results of experimental studies of how 3D printing with 100% filling influences the elastic properties of PLA filament polymer samples. The static and Thurston–Brugger methods simultaneously measure the dependence of strain and the relative change in the velocity of elastic waves on the applied mechanical stress (up to failure) for the initial and 3D-printed samples of the PLA polymer. Based on the measurement results, the linear and nonlinear Young's moduli and second-order acoustic nonlinear parameter are calculated. It has been established that 3D printing leads to a deterioration in the strength and plastic characteristics of PLA. A different behavior of the nonlinear parameters of the initial and 3D-printed PLA samples in the loading and unloading region was revealed, associated with a change in the internal structure of the sample caused by 3D printing. [ABSTRACT FROM AUTHOR]

Geophysical properties of oceanic crust are strongly influenced by the presence of cracks. We studied the effects of cracks on the physical properties of oceanic crustal rocks collected from the ICDP Oman Drilling Project Hole GT3A. Electrical resistivity and P‐ and S‐wave velocities were measured under dry and brine‐water‐saturated conditions for each sample. The experimental results reveal that electrical resistivity and elastic wave velocities are differently correlated with porosity. We performed joint inversion of the measured electrical and elastic properties combining an effective medium model by Kachanov and a statistical crack fluid flow model by Guéguen and Dienes with percolation theory. As a result, the variations in electrical and elastic properties can be related to the crack microstructural parameters: crack density and aspect ratio, as well as connectivity of cracks evaluated from crack density. To understand the influence of in situ conditions of oceanic crust, the joint inversion using the proposed cross‐property relationship was performed for geophysical properties obtained by logging measurements at IODP Hole 1256D. Results show the depth variations of resistivity and sonic velocities can be successfully interpreted by decreasing crack porosity and connectivity. Our data and analysis can provide new insights into the interpretation of geophysical data from the oceanic crust at which pore‐fluid plays key roles in various geodynamic activities. Plain Language Summary: Cracks in the oceanic crust play key roles in subsurface processes, including fluid transportation, heat and chemical exchange, and microbial activity. Therefore, it is important to understand how cracks are distributed in the oceanic crust. Given that cracks exert an important influence on the physical properties of rocks, electrical and seismological surveys have been conducted at various locations in the oceanic plates. However, to quantitatively interpret the geophysical data obtained from these surveys, laboratory investigations are essential. In this study, we measured the electrical resistivity and elastic wave velocity of oceanic crustal rocks collected from drillcores of the Oman ophiolite, in which tectonic fragments of ancient oceanic plate are preserved on land. Our experimental data show that electrical resistivity and elastic wave velocity are differently correlated with porosity. Analysis of these data indicates that the variations in the electrical and elastic properties can be related to crack density, aspect ratio, and crack connectivity. The cross‐property relationship established is applied successfully to in situ geophysical data obtained by borehole logging in oceanic crust. Our data and proposed cross‐property relationship provide new insights into the interpretation of geophysical data from the oceanic crust. Key Points: We measured the electrical resistivity and elastic wave velocity of the sheeted dike–gabbro transition zone of the Oman Drilling ProjectVariation in the electrical and elastic properties of Hole GT3A was interpreted by combining effective medium model and percolation modelApplying the cross‐property relationship to logging data at IODP Hole 1256D, we estimated the crack parameters of in situ oceanic crust [ABSTRACT FROM AUTHOR]

The reflection and transmission of elastic waves are of great significance for predicting reservoir physical properties, interpreting seismic data and detecting crustal structures. Most studies only consider the initial vertical stress state when studying the reflection and transmission of elastic waves at imperfectly bonded interfaces, but few studies consider the influence of initial stress on boundary conditions. Moreover, the effect of initial stress on the energy distribution of elastic waves at imperfectly bonded interfaces has rarely been investigated. We propose a unified method to calculate the energy reflection and transmission coefficients for different incident waves at welded or imperfectly bonded interfaces in stressed media. The effects of initial stress on the equation of motion, the elastic properties of the medium and the boundary conditions at the interface are considered. The elastic properties of rocks under initial stress are described by acoustoelasticity theory. In addition, we define a new stress tensor to modify the linear-slip model for describing boundary conditions at the imperfectly bonded interface in the presence of initial stress. Numerical results show that the energy reflection and transmission coefficients at the non-welded interface in stressed media depend on the elastic properties of the incident and transmitted media, the initial stress, the type and magnitude of the interfacial compliance and the frequency and propagation direction of the incident wave. The initial vertical and horizontal stresses dominate the reflection and transmission coefficients at small and large angles, respectively. The discontinuity in displacement across the imperfectly bonded boundary results in the frequency dependence of the reflection and transmission coefficients. Imperfect bonding enhances P-wave and SV-wave energy reflection and weakens P-wave energy transmission. However, imperfect bonding can enhance the energy transmission of the SV wave for the imperfectly bonded interface with high contrast between tangential and normal compliance and a resonance peak appears at a specific frequency. We also notice that imperfectly bonded interfaces with interfacial compliance less than |$1.0 \times {10}^{ - 11}$| m Pa−1 can be regarded as welded interfaces in the seismic frequency band (lower than 100 Hz). In addition, the initial stress greatly influences the reflection coefficients at high frequencies and the transmission coefficients at low frequencies. The initial vertical stress can reduce the energy transmission of SV waves at imperfectly bonded interfaces. In contrast, the initial horizontal stress can significantly increase the energy transmission of low-frequency SV waves and may lead to the disappearance of the resonant peak in the transmission coefficients. [ABSTRACT FROM AUTHOR]

Spectral anomalies in the seismic ambient noise are commonly observed above hydrocarbon reservoirs at frequencies of several Hertz. If properly understood, these anomalies could be a potential indicator for hydrocarbon reservoir exploration or monitoring. Under the assumption that ambient noise mainly consists of surface waves, previous studies showed that the geological structure, rather than the hydrocarbon content, could be the major cause of the observed anomalies for purely elastic waves. This work further explores how Rayleigh waves interact with an anticline structure, a typical geological trap for a hydrocarbon reservoir. We propose an approximate semi-analytical surface wave approach for modelling the spectral anomalies. It is based on the contribution of 1-D local solutions from two different models. The results are compared with those obtained via 3-D numerical simulations using the spectral-element approach in the case of a wavefield dominated by Rayleigh waves. Analysis of the anomalies generated by an anticline structure is performed for different source configurations. It shows that the semi-analytical method provides reasonable spectrum predictions for smooth layered models and under some restrictions on the source distribution. Such a tool allows us to run a larger number of simulations to explore the parameter space and finally provide a general law linking the anticline geometrical parameters and the elastic properties of the medium to the anticline-induced spectral anomaly for the case of fundamental mode Rayleigh waves. [ABSTRACT FROM AUTHOR]

Multiple elastic shock waves carry the information on elastic properties under dynamic extreme conditions, but may complicate the interpretation of wave structure including the elastic–plastic transition. On the basis of the acoustic wave-equation analysis, we predict the absence or presence of multiple elastic shock waves in a single crystal subjected to shock loading along a specific crystallographic orientation. Typical FCC and BCC single crystals are taken as validation and application cases. Large-scale molecular dynamics simulations are performed for Cu and Ta; double-wave or triple-wave structures of elastic shock waves (quasilongitudinal and quasitransverse) are observed in the simulations, and the multi-wave structures are in excellent agreement with the wave-equation analysis. Also, the acoustic wave-equation analysis is used to analyze MD calculations, as well as the complex structure of the shock wave during plastic deformation. Free-surface velocity history, transverse velocity history of free surface, and ultrafast X-ray diffraction are explored as experimental means to resolve multiple elastic shock waves. [ABSTRACT FROM AUTHOR]

Based upon the Green–Lindsay (GL) theory of thermoelasticity and the Eringen non-local elasticity theory, we describe the new constitutive relations and the field equations for generalized non-local thermoelastic model. The propagation of harmonically time-dependent thermoelastic plane waves of assigned frequency is studied in a homogeneous, isotropic, non-local infinite elastic solid by employing these equations. Reflection phenomenon of thermoelastic waves at a stress-free thermally insulated or isothermal flat boundary of a non-local thermoelastic solid half-space is also studied in case of incident coupled longitudinal wave. The amplitude ratios of the reflected waves to that of incident wave are determined analytically and numerically by considering an appropriate material. The numerical results are presented graphically to highlight the effects of various parameters of interest. [ABSTRACT FROM AUTHOR]

The aim of this work is to present theoretical tools to study wave propagation in elastic waveguides and perform multi-frequency scattering inversion to reconstruct small shape defects in elastic waveguides and plates. Given surface multi-frequency wavefield measurements, we use a Born approximation to reconstruct localized defect in the geometry of the plate. To justify this approximation, we introduce a rigorous framework to study the propagation of elastic wavefield generated by arbitrary sources. By studying the decreasing rate of the series of inhomogeneous Lamb mode, we prove the well-posedness of the PDE that model elastic wave propagation in two- and three-dimensional planar waveguides. We also characterize the critical frequencies for which the Lamb decomposition is not valid. By using these results, we generalize the shape reconstruction method already developed for acoustic waveguide to two-dimensional elastic waveguides and provide a stable reconstruction method based on a mode-by-mode spacial Fourier inversion given by the scattered field. [ABSTRACT FROM AUTHOR]

The problem of determining the shape of an object from knowledge of the far-field of a single incident wave in two-dimensional elasticity was considered. We applied an iterative hybrid method to tackle this problem. An advantage of this method is that it does not need a forward solver, and therefore, the exact boundary condition is not essential. By deriving the Fréchet derivatives of two boundary operators, we established reconstruction algorithms for objects with Dirichlet, Neumann, and Robin boundary conditions; by introducing a general boundary condition, we also established the reconstruction algorithm for objects with unknown physical properties. Numerical experiments showed the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this study, elastic waves generated from a SKD11 (HV670) steel specimen under various corrosive solutions were investigated. The frequency characteristics of the waves, as well as how hydrogen aggregation and crack propagation affected these characteristics, were studied using time-frequency analysis conducted in LabVIEW. The waves detected were either in a low frequency band, below 40 kHz, or in a high frequency band, above 60 kHz. The low frequency waves below 40 kHz were caused by hydrogen aggregation and corrosion, while the high frequency waves above 60 kHz were caused by crack initiation and propagation due to HAC. Inspection by SEM confirmed that the grains and cracks were caused by HAC via hydrogen embrittlement. [ABSTRACT FROM AUTHOR]

Elastic properties of the solid-state CdTe1−xSex (x= 0-0.5, with Δx= 0.125) solutions within the framework of density functional theory calculations were investigated. The structures of the CdTe1−xSex samples are obtained by the substitution of tellurium with selenium atoms in cubic CdTe. Young's modulus, shear modulus, bulk modulus, and the Poisson ratio of CdTe1−xSex crystals were calculated from the first principles. The dependences of the elastic properties of the CdTe1−xSex solid solution on the content index x within the interval 0 ≤ x ≤ 0.5 are analyzed. According to the Frantsevich rule and the value of the Poisson ratio, the materials have been classified as ductile. The Zener anisotropy factor and the Kleimann parameter are calculated on the basis of the elastic constants Cij. Also, the concentration dependence of longitudinal elastic wave velocity, transverse elastic wave velocity, and average sound velocity, are calculated. Based on the average sound velocity the concentration behavior of the Debye temperature was calculated. The correlation analysis shows a good agreement between the calculation results (elastic modulus and Debye temperature) and known experimental data. [ABSTRACT FROM AUTHOR]

Under compressive stress, rock 'damage' in the form of tensile microcracks is coupled to internal slip on microscopic interfaces, such as pre-existing cracks and grain boundaries. In order to characterize the contribution of slip to the overall damage process, we conduct triaxial cyclic loading experiments on Westerly granite, and monitor volumetric strain and elastic wave velocity and anisotropy. Cyclic loading tests show large hysteresis in axial stress–strain behaviour that can be explained entirely by slip. Elastic wave velocity variations are observed only past a yield point, and show hysteresis with incomplete reversibility upon unloading. Irrecoverable volumetric strain and elastic wave velocity drop and anisotropy increase with increasing maximum stress, are amplified during hydrostatic decompression, and decrease logarithmically with time during hydrostatic hold periods after deformation cycles. The mechanical data and change in elastic properties are used to determine the proportion of mechanical work required to generate tensile cracks, which increases as the rock approaches failure but remains small, up to around 10 per cent of the net dissipated work per cycle. The pre-rupture deformation behaviour of rocks is qualitatively compatible with the mechanics of wing cracks. While tensile cracks are the source of large changes in rock physical properties, they are not systematically associated with significant energy dissipation and their aperture and growth is primarily controlled by friction, which exerts a dominant control on rock rheology in the brittle regime. Time-dependent friction along pre-existing shear interfaces explains how tensile cracks can close under static conditions and produce recovery of elastic wave velocities over time. [ABSTRACT FROM AUTHOR]

What makes elastic waves different from other waves is the existence of various wave modes and coupling between these modes. Accordingly, the manipulation of elastic waves suffers from many limitations due to mode coupling, which is an inherent complex physical property of elastic waves. In this study, we propose fluid-like elastic metasurfaces that act as an acoustic (fluid) surface to perfectly eliminate mode coupling. Because longitudinal and shear waves are decoupled, only reflected longitudinal (or shear) waves exist when longitudinal (or shear) waves are incident. Using a strip-type unit cell, elastic metasurfaces mimicking acoustic hard-wall and soft-wall were designed and realized. In addition, numerical analysis and experiments were conducted to prove the validity of the designed unit cells. This study presents a more versatile metasurface by solving the mode coupling of solid elastic waves. In addition, two types of designed fluid-like metasurfaces are expected to be utilized in further studies considering the opposite phase shift characteristic. [ABSTRACT FROM AUTHOR]

Modeling elastic waves in complex media, with varying physical properties, require very accurate algorithms and a great computational effort to avoid nonphysical effects. Among the numerical methods the spectral elements (SEM) have a high precision and ease in modeling such problems and the physical domains can be discretized using very coarse meshes with elements of constant properties. In many cases, models with very complex geometries and small heterogeneities, shorter than the minimum wavelength, require grid resolution down to the thinnest scales, resulting in an extremely large problem size and greatly reducing accuracy and computational efficiency. In this paper, a poly-grid method (PG-CSEM) is presented that can overcome this limitation. To accurately deal with continuous variations or even small-scale fluctuations in elastic properties, temporary auxiliary grids are introduced that prevent the need to use large meshes, while at the macroscopic level wave propagation is solved maintaining the SEM accuracy and computational efficiency as confirmed by the numerical results. [ABSTRACT FROM AUTHOR]

High‐porosity sandstones are important for hydrocarbon production, underground CO2 storage, extraction of geothermal energy and freshwater aquifers. Porosity of sandstones may be estimated using elastic wave velocities, but these depend also on fluid saturation, clay content, pore shape and contacts between sand grains. An understanding of how elastic properties of sandstones depend on these factors is important for characterizing their storage potential and for geomechanical issues, such as sanding, borehole stability, reservoir compaction and fracturing. Ultrasonic velocity measurements in clay‐bearing sandstones indicate that much of the clay in shaly sandstones is non‐load‐bearing. This enables a simple approach for modelling the elastic properties of shaly sandstones that includes the effect of pore concavity and agrees with ultrasonic P‐ and S‐velocities measured in the laboratory. Despite this agreement, some clay may reside within the contacts and may act to inhibit the development of quartz cement, thus reducing porosity loss and helping to preserve storage volume. This appears to be the case for the Lower Mt. Simon Sandstone, a target formation for underground storage of CO2 in the Illinois Basin, for which the bulk moduli agree with the predicted bulk moduli, but the shear moduli are lower than predicted. This appears to result from an increase in a shear compliance of the grain contacts that may enable sliding along the grain contacts and increase the tendency to shear failure. [ABSTRACT FROM AUTHOR]

Bar impact instruments, such as the (split) Hopkinson bars and direct impact Hopkinson bars, measure blast/impact waves or mechanical properties of materials at high strain rates. To effectively use such instruments, it is essential to know (i) the elastic properties of the bar, (ii) the correction factor of the measured strain, and (iii) information on impact velocity. This paper presents a graphic-user-interface (GUI) program prepared for solving these fundamental issues. We describe the directory structure of the program, roles and relations of associated files, GUI panels, algorithm, and execution procedure of the program. This program employs a separately measured bar density value and governs the ABAQUS simulations (explicit finite element analyses) of the bar impact test at a given impact velocity for a range of bar properties (elastic modulus and Poisson's ratio) and two correction factors (in compression and tension) of the measured strain. The simulation is repeated until the predicted elastic wave profile in the bar is reasonably consistent with the experimental counterpart. The bar properties and correction factors are determined as the calibrated values when the two wave profiles are reasonably consistent. The program is also capable of impact velocity calibration with reference to a reliably measured bar strain wave. The quantities of a 19.1 mm diameter bar (maraging steel) were successfully calibrated using the presented GUI program. The GUI program, auxiliary programs, pre-processing files, and an example ABAQUS input file are available in a publicly accessible data repository. Dataset: Available online in a publicly accessible repository (https://doi.org/10.5281/zenodo.7652652). Dataset License: CC BY 4.0 [ABSTRACT FROM AUTHOR]

The article discusses the importance of understanding and manipulating mechanical vibrations in solid materials. It explains that elastic waves, which propagate as mechanical vibrations, can be transverse or longitudinal in character and are difficult to manipulate. The article highlights recent research that explores the potential of topological concepts in manipulating elastic waves. The researchers designed a plate-type elastic-wave crystal and found that by using a chiral inter-plate coupling design, they could create a topological bandgap and chiral topological states. The findings have implications for various fields, including nanophononics, robotics, and civil engineering. [Extracted from the article]

We propose a unified approach to the investigation of the processes of dynamic interaction of thin elastic inhomogeneities with an elastic medium. It is based on the methods of the theory of singular perturbations in constructing mathematical models of contact of the components of elastic systems with subsequent application of the null-field method for the analysis of the wave fields in composites. This approach proves to be efficient in studying the phenomenon of interaction of elastic waves with local or multiple thin elastic inhomogeneities, as well as in solving the corresponding inverse problems. [ABSTRACT FROM AUTHOR]

Supported by laboratory experimental results, the reduction in elastic thickness (Te ${T}_{e}$) and flexural rigidity (D $D$) at trench outer rise, which enables bending, is attributed to damage. A series of laboratory experiments were performed on intact and thermally treated diabase and peridotite (400°C–800°C) under increasing confining pressures (3–200 MPa) at room temperature. Simultaneous porosity and elastic wave velocity (P and S) measurements were obtained under dry and fluid saturated conditions. The velocity and porosity inversions indicated a significant variation in crack properties (crack density, aspect ratio) and reduction in Young's modulus, of thermally treated samples in comparison to the intact samples. Hence the experimental results suggested weakening in elastic properties of a damaged oceanic lithosphere. Subsequently created lithospheric strength profiles showed a strength reduction in wet models in comparison to dry models. Under the assumption of different cooling models, the aging of the plate resulted in an increase in strength with deeper neutral zones. The outcome of the strength profiles was utilized to estimate Te ${T}_{e}$ and D $D$, which are also dependent on the elasticity of the lithosphere. The results showed a reduction in D $D$ with increasing damage and suggest that the bending at the subduction zone is facilitated by weakened elastic properties of a damaged lithosphere. While most of the geophysical observations of Te ${T}_{e}$ were able to be constrained by the proposed damaged models, some shallow observations indicated enhanced damage triggered either by increased depth to brittle‐ductile transition or by large bending related faulting events. Plain Language Summary: In this investigation, we propose that the bending of the plate at the subduction zone is facilitated by cracks that are present in the rocks. To test this idea, we conducted several experiments in the laboratory on rocks which represent the oceanic plate (diabase and peridotite). By increasing the temperature inside a furnace, we induced cracks (damage) in the samples before the experiments and compared the results with the undamaged samples. During the experiment, we measured the wave velocity and porosity. From the comparison, it was understood that the damaged rocks have weak elastic properties. Following the results of the experiments, we calculated the lithospheric strength profiles, for both dry and wet models for different ages of the oceanic plate and found that the strength decrease markedly when water is present. From this strength estimations, we calculated the thickness of the elastic layer which can transmit bending stress and the flexural rigidity which is the resistance to bending. The results showed that with more damage present in the plate, the elastic thickness and flexural rigidity decrease. Finally, we compared these results with the actual geophysical data and have shown the validity of our model. Key Points: Hydrostatic experiments were conducted on thermally treated diabase and peridotite with simultaneous velocity and porosity measurementsDamaged models showed significant weakening in the elastic properties of the rocks due to the development of cracksSupported by the experimental results, elastic thickness, and rigidity of dry and wet oceanic lithospheres were estimated [ABSTRACT FROM AUTHOR]

We study the one-dimensional problem for the linear strain gradient porous elasticity. Our aim is to analyze the behavior of the solutions with respect to the time variable when a dissipative structural mechanism is introduced in the system. We consider five different scenarios: hyperviscosity and viscosity for the displacement component and hyperviscoporosity, viscoporosity and weak viscoporosity for the porous component. We only apply one of these mechanisms at a time. We obtain the exponential decay of the solutions in the case of viscosity and a similar result for the viscoporosity. Nevertheless, in the hyperviscosity case (respectively hyperviscoporosity) the decay is slow and it can be controlled at least by t - 1 / 2 . Slow decay is also expected for the weak viscoporosity in the generic case, although a particular combination of the constitutive parameters leads to the exponential decay. We want to emphasize the fact that the hyperviscosity (respectively hyperviscoporosity) is a stronger dissipative mechanism than the viscosity (respectively viscoporosity); however, in this situation, the second mechanism seems to be more "efficient" than the first one in order to pull along the solutions rapidly to zero. This is a striking fact that we have not seen previously at any other linear coupling system. Finally, we also present some numerical simulations by using the finite element method and the Newmark- β scheme to show the behavior of the energy decay of the solutions to the above problems, including a comparison between the hyperviscosity and the viscosity cases. [ABSTRACT FROM AUTHOR]

We investigate the effect of temperature on the elastic properties of rocks by combining the thermal-damage factor (TDF) with the Gassmann equation. The resulting model is tested in carbonate samples by analyzing the ultrasonic wave velocity. A comparison between the estimated and measured TDF shows that the model quantitatively describes the behavior of carbonates at relatively low temperatures, while the high-temperature one is underestimated. The dry- and wet-rock TDF difference increases significantly with increasing temperature, and the TDF is highly affected by the rock permeability and microcrack aspect ratio. [ABSTRACT FROM AUTHOR]

Guided elastic wave (GEW) transducers for structural health monitoring (SHM) can act as transmitters (senders) and receivers (sensors). Their performance in both cases depends on the structure to which they are coupled. Therefore, they must be characterized as system transducer- structure. The characterization of the transducer-structure as transmitter using a Scanning Laser Doppler Vibrometer (SLDV) is straightforward, whereas its characterization as receiver is non-trivial. We propose to exploit electromechanical reciprocity, which is an identity between the transfer functions of electrical-to-mechanical and mechanical-to-electrical conversions. For this purpose, the well-known electromechanical reciprocity theorem was adapted to the following situation: The two reciprocal states are "electrical excitation and detection of the surface velocity at point P" and "mechanical excitation at P and measurement of the electrical quantities". According to the derived formulas, the quantities on the mechanical and electrical sides must be chosen appropriately to ensure reciprocity as well as that the corresponding transfer functions are equal. We demonstrate the reciprocity with experimental data for correctly chosen transfer functions and show the deviation in reciprocity for a different choice. Furthermore, we propose further applications of electromechanical reciprocity. [ABSTRACT FROM AUTHOR]

The dynamic elasticity modulus (Ed) is the most commonly usEd indexes for nondestructive testing to represent the internal damage of hydraulic concrete. Samples with a specific size is requirEd when the transverse resonance method was usEd to detect the Ed, resulting in a limitation for field tests. The impact-echo method can make up defects of traditional detection methods for frost-resistance testing, such as the evaluation via the loss of mass or strength. The feasibility of the impact-echo method to obtain the relative Ed is explorEd to detect the frost-resistance property of large-volume hydraulic concretes on site. Results show that the impact-echo method can replace the traditional resonance frequency method to evaluate the frost resistance of concrete, and has advantages of high accuracy, easy to operate, and not affecting by the aggregate size and size effect of samples. The dynamic elastic modulus of concrete detectEd by the impact-echo method has little difference with that obtainEd by the traditional resonance method. The one-dimensional elastic wave velocity of concrete has a good linear correlation with the transverse resonance frequency. The freeze-thaw damage occurrEd from the surface to the inner layer, and the surface is expectEd to be the most vulnerable part for the freeze-thaw damage. It is expectEd to monitor and track the degradation of the frost resistance of an actual structure by frequently detecting the P-wave velocity on site, which avoids coring again. [ABSTRACT FROM AUTHOR]

We consider the propagation of flexural and torsional waves in a square lattice of Euler–Bernoulli beams. The refraction and reflection of waves across interfaces between two dissimilar lattices is investigated. By carefully controlling the inertial and elastic properties of the lattice elements, we demonstrate that it is possible to induce negative refraction and other associated phenomena. These effects are shown to be broadband and are facilitated by the unprecedented control over wave propagation afforded by the interaction between torsional and flexural waves and the additional freedom associated with the applied forcing. Closed-form analytical findings are accompanied by numerical simulations, which demonstrate negative refraction, unidirectional reflection and mode trapping. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'. [ABSTRACT FROM AUTHOR]

The stiffnesses and microstructures of interfaces may have significant influence on the propagation of elastic waves. In this paper, we investigate the reflection and refraction of SH waves at a non-ideal interface between two elastic half-spaces. First, we use the surface elasticity theory (Gurtin and Murdoch in Arch. Ration. Mech. Anal. 57: 291–323, 1975) to describe the mechanical behaviour of the interface. We derive the reflection and transmission coefficients, as well as the phase angles of the reflected and transmitted waves. Then we treat the non-ideal interface between two elastic bodies as a thin membrane with microstructures. By employing the second-order strain-gradient model (Aifantis in Int. J. Eng. Sci. 30: 1279–1299, 1992) to describe the mechanical behaviour of the thin membrane, we establish the strain-gradient thin membrane model for the present problem. Finally, by selecting combinations of non-dimensional parameters, we demonstrate the effects of interfacial material constants on the reflection and refraction of SH waves. [ABSTRACT FROM AUTHOR]

The Rayleigh-type wave solution within a widely used differential formulation in non-local elasticity is revisited. It is demonstrated that this wave solution does not satisfy the equations of motion for non-local stresses. A modified differential model taking into account a non-local boundary layer is developed. Correspondence of the latter model to the original integral theory with the kernel in the form of the zero-order modified Bessel function of the second kind is addressed. Asymptotic behaviour of the model is investigated, resulting in a leading-order non-local correction to the classical Rayleigh wave speed due to the effect of the boundary layer. The suitability of a continuous set-up for modelling boundary layers in the framework of non-local elasticity is analysed starting from a toy problem for a semi-infinite chain. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'. [ABSTRACT FROM AUTHOR]

A one-dimensional phononic crystal model based on Galois structure is proposed. The transmission coefficients of the elastic waves are numerically calculated and compared with those of the periodical structure. Band gaps are found and the results show that if the number of medium layers is small, the frequency range of the band gap in the Galois structure and periodic structure is basically the same. However, with the increase of the number of medium layers, the frequency range of the band gap in the Galois structure increases, and the localized resonant modes appear in the band gap. The study of transmission properties of Galois structures is helpful to understand the propagation properties of classical elastic waves in aperiodic composite structures. [ABSTRACT FROM AUTHOR]

Once the structure of a metamaterial is fixed, it has the property of controlling elastic waves in a fixed frequency range. To obtain a metamaterial with an optimal structure, a co-simulation optimization method is proposed in this paper to optimize the acoustic properties of metamaterials. The method combines the advantages of COMSOL, MATLAB, and ISIGHT to obtain optimal results. Due to the application of the algorithms in ISIGHT, different design requirements can be met, such as designing the bandgap frequency of the acoustic metamaterial in a specific range, reducing the frequency of the bandgap, and improving the overall performance of the STL (sound transmission loss) without manual tuning. To test the feasibility of the method, a new double-panel acoustic metamaterial is also proposed, where the bandgap interval of the metamaterial can be designed to nearly 240 Hz by using the thickness of the support columns and the structural parameters of the open split-ring resonance as bandgap optimization parameters. The bandgap interval can also be lowered from 174 to 193 Hz when different optimization targets are chosen. In addition, the overall performance of the STL can be optimized, showing better absorption of low-frequency noise. Therefore, this co-simulation method can achieve multi-parameter optimization for different optimization targets and ensure that the results obtained by the applied algorithm are optimal. Furthermore, this method has great potential in further development as it avoids complex algorithm programming. [ABSTRACT FROM AUTHOR]

Soft materials such as gels, elastomers, and biological tissues have diverse applications in nature and technology due to their viscoelastic nature. These soft materials often exhibit complex rheology and display elastic and viscous characteristics when undergoing deformation. In recent years, fractional calculus has emerged as a promising tool to explain the viscoelastic behavior of soft materials. Scalar constants are primarily used to quantify viscoelastic elements such as springs and dashpots. However, in three-dimensional (3D) space, not all materials show the same elastic or viscoelastic properties in all directions, especially under elastic/viscoelastic wave propagation (or anisotropy). Though previously reported studies on viscoelastic models have explained a power-law decay of the memory functions, none of them explicitly explained the 3D complex modulus through a matrix notation. In this paper, we present a mathematical formulation that employs tensor algebra and fractional calculus to derive the 3D complex modulus of Kelvin–Voigt, Maxwell, and other arrangements of viscoelastic models. The 3D complex modulus provides information about the elastic wave propagation in a media and can be used to explain anisotropy in different viscoelastic materials. Additionally, an advanced formulation of the moduli can improve the modeling in finite element analysis of 3D viscoelastic materials where discretization is vital for studying media of asymmetric shapes. Finally, we demonstrated a polar decomposition method to visualize viscoelastic tensors using the Green–Christoffel tensor and surface plots to represent the degrees of anisotropy and viscoelasticity in the Fourier domain when the medium is probed by a time-harmonic homogeneous plane wave. [ABSTRACT FROM AUTHOR]

The classical problem of reflection of Lamb waves from a free edge perpendicular to the centre line of an elastodynamic plate is studied. It is known that Lamb wave expansions for the displacement and stress fields poorly represent the irregular behaviour near corners, leading to the slow convergence of a series of such waves. The form of the irregularity for an elastodynamic corner is derived asymptotically, and a new solution method, which incorporates this corner behaviour analytically, is then implemented. Results are presented showing that this new approach represents the near-field and far-field behaviour very accurately, requiring very modest numbers of Lamb wave and corner modes. Further, it is revealed that the method can recover the trapped-mode phenomenon encountered in this configuration at the Lamé frequency and a specific Poisson's ratio that we find to be approximately 0.224798 . [ABSTRACT FROM AUTHOR]

A process of calibrating a one-dimensional sound speed (co) and Poisson's ratio (ν) of a (split) Hopkinson bar is presented. This process consists of Fourier synthesis and iterative dispersion correction (time-domain phase shift) of the elastic pulse generated by the striker impact on a circular bar. At each iteration, a set of co and ν is assumed, and the sound speed versus frequency (cdc versus fdc) relationship under the assumed set is obtained using the Pochhammer-Chree equation solver developed herein for ground state excitation. Subsequently, each constituting wave of the overall elastic pulse is phase shifted (dispersion corrected) using the cdc-fdc relationship. The co and ν values of the bar are determined in the iteration process when the dispersion-corrected overall pulse profiles are reasonably consistent with the measured profiles at two travel distances in the bar. The observed consistency of the predicted (dispersion-corrected) wave profiles with the measured profiles is a mutually self-consistent verification of (i) the calibrated values of co and ν, and (ii) the combined theories of Fourier and Pochhammer-Chree. The contributions of the calibrated values of co and ν to contemporary bar technology are discussed, together with the physical significance of the tail part of a traveling wave according to the combined theories. A preprocessing template (in Excel®) and calibration platform (in matlab®) for the presented calibration process are openly available online in a public repository. [ABSTRACT FROM AUTHOR]