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Elastic metamaterials with double negativity can manipulate the propagation of elastic waves at sub-wavelength scales by inducing multiple resonances to achieve different negative effective parameters. Numerous efforts have been made to control the dynamic behavior by directly tuning the frequency range of double negativity in elastic metamaterials. This study examines the impact of tensile loads on double negativity in relation to ligament inclination angle. The findings will aid in the direct tunability of double negativity in single-phase chiral metamaterials. The study examines a simple single-phase four-ligament chiral unit with low-order double negativity. The presence of double negativity was verified through band structure analysis and calculation of the four effective dynamic parameters. Additionally, the effects of two geometrical factors on the frequency ranges of negative parameters were investigated through parametric scanning. The results indicate that the frequency range of double negativity reaches its maximum at a ligament inclination angle of around 45° and disappears as the angle approaches 65°. Given that the ligament inclination angle of the unit cells can be easily altered by external tension, this intriguing outcome is leveraged to achieve the emergence and vanishing of double negativity. This characteristic is confirmed through the examination of negative refraction phenomena via simulation examples. [ABSTRACT FROM AUTHOR]

Mode coupling and conversion between longitudinal and transverse modes are ubiquitous and universal in elastic waves, presenting a challenge in realistic applications such as nondestructive evaluation and geological exploration, where independent and separate manipulation of each mode is demanded. In this article, we propose a design of elastic metalens that can realize a high-efficiency focusing for the longitudinal wave and a V-shaped converging pattern for the transverse wave at the same time. The metalens is constructed from a metagrating, where each meta-atom has a simple configuration and renders high diffraction efficiency even for large steering angles, enabled by concurrent utilization of grating diffraction theory and advanced optimization algorithms. Interestingly, an arbitrary energy splitting ratio between the reflected longitudinal and transverse waves can be obtained by precisely controlling the coupling strength and conversion efficiency between them, providing improved flexibility and adaptability to various application environments. Two illustrative examples with a sharp focusing effect and tailored conversion efficiency are explicitly demonstrated, with a 50/50 energy splitting ratio between the longitudinal and transverse waves in the first case, and a 70/30 ratio in the second one. [ABSTRACT FROM AUTHOR]

Quasi-isentropic loading and unloading, employing graded density impactors (GDIs) as flyers in gas gun-driven plate impact experiments, can provide novel and valuable insights into the equation of state and strength properties of the loaded material. However, the internal ballistic process may lead to spalling or debonding of the GDI due to the intricate interactions between stress waves and interfaces. In this study, the wave propagation in the GDI was analyzed using the multimaterial Lagrangian elastic-plastic model and elastic wave propagation theory. The impact of gradient direction, power-law constant p, and thickness of the first and last layers on the tensile stress was investigated. The outcomes reveal that the mechanism of generating tensile stress varies for two gradient directions. Moreover, adjusting the constant p and the layer thickness may decrease the maximum tensile stress by 74.1% (forward graded) and 95.8% (reverse graded), respectively. The outcomes of this research provide a theoretical and simulation basis for designing and fabricating GDIs to be utilized in quasi-isentropic experiments. [ABSTRACT FROM AUTHOR]

Crystalline rocks in the subsurface are of interest for geothermal energy extraction, nuclear waste storage, and, when weathered or fractured, as aquifers. Compliant discontinuities such as microcracks, cracks and fractures may nucleate and propagate due to changes in pore pressure, stress and temperature. These discontinuities may provide flow pathways for fluids and, if fracturing extends to surrounding rocks, may allow escape of fluids to neighbouring formations. Monitoring such rocks using sonic logs, passive seismic, borehole seismic and surface seismic requires understanding of the propagation of elastic waves in the presence of such discontinuities. These may have an anisotropic orientation distribution as in situ stress may be anisotropic. As crystalline rock may display intrinsic anisotropy due to foliation and the preferential orientation of anisotropic minerals, quantification of the relative importance of intrinsic and microcrack‐induced anisotropy is important. This may be achieved based on the stress sensitivity of elastic wave velocities. A method that allows both the orientation distribution of microcracks and the stress dependence of their normal and shear compliance to be estimated independently of the elastic anisotropy of the background rock is presented. Results are given for anisotropic samples of gneiss from Bukov in the Czech Republic and granite from Grimsel in Switzerland based on the ultrasonic velocity measurements of Aminzadeh et al. The microcrack orientation distribution is approximately transversely isotropic for both samples with a preferred orientation of microcrack normals perpendicular to foliation. This preferred alignment is stronger in the sample of gneiss than in the granite sample, and the normal and shear compliance of the microcracks decreases with increasing compressive stress. This occurs because the contact between opposing faces of the discontinuities grows with increasing compressive stress, and this results in a decrease in elastic anisotropy with increasing compressive stress. At low stress, the ratio of microcrack normal compliance to shear compliance is approximately 0.25 for the granite sample and 0.7 for the sample of gneiss. The normal compliance ZN for both samples decreases faster with increasing compressive stress than the shear compliance ZT, resulting in a decrease in ZN/ZT with increasing compressive stress. [ABSTRACT FROM AUTHOR]

• Analytic algorithm for SH wave scattering near semi-elliptical crater. • The boundary of the crater is endowed with surface elasticity. • DSCF relative to wave frequency, incident angle and crater's aspect ratio. Cratering occurs inevitably on the surface of materials at all scales due to comprehensive factors. The presence of craters may have a significant influence on the mechanical performance of the surface of an elastic body. In this paper, we study the SH wave propagation in an elastic semi-infinite medium whose surface has a semi-elliptical crater. We explore the scattering of the SH wave by the crater when surface elasticity is incorporated in the model of deformation to account for possible small-scale effects of the crater. We obtain a series solution for the scattered wave function by employing the Mathieu functions in the corresponding elliptical coordinate system. We discuss in some numerical examples the dynamic stress concentration around the crater relative to the wave frequency and few geometric parameters. [ABSTRACT FROM AUTHOR]

AbstractThis research paper investigates the complex dynamics of Love wave propagation on a piezoelectric plate situated atop a micropolar elastic half-space having imperfect interface. The study delves into the multifaceted effects of flexoelectricity, micro-inertia, guiding layer thickness, and interfacial imperfection on the characteristics of Love waves. The electromechanical coupling factor which is significant in analyzing SAW device performances is also studied. Variable separable method is used to solve the governing equations and desired solution is obtained analytically. The findings contribute to a deeper understanding of Love wave propagation in complex elastic structures and development of advanced sensors and communication technologies. [ABSTRACT FROM AUTHOR]

Measurement of the impact process is challenging due to its short duration and high frequency response. Due to the very small strain in low-velocity impacts, the requirements for the temporal and spatial resolution of test methods are extremely high. Traditionally, strain gauges or lasers are commonly used to measure the dynamic response of a single point, or quasi-static loading is used to achieve full-field response. To finely describe the transient full-field deformation process of low-velocity impacts, a high-speed imaging system combined with 3D digital image correlation (DIC) technique is set up to investigate the instantaneous responses of impact on a polyvinyl chloride (PVC) plate at the ms and με level. The full-field deformation of the contact surface and the whole process of elastic wave propagation are measured. The measurement by DIC closely matches the measurement by strain gauges and agrees well with the numerical simulation results. The measurement reveals that the "multi-micro-impacts" phenomenon may happen during a complete impact process due to the complex strain wave propagation. This work provides a benchmark case for low-velocity impact full-field testing, and the results show that 3D DIC can accurately evaluate dynamic behaviors of low-velocity impact between flexible bodies and can accurately describe the spatiotemporal propagation characteristics of strain waves. [ABSTRACT FROM AUTHOR]

Acoustic nonlinearity holds potential as a method for assessing material stress. Analogous to the acoustoelastic effect, where the velocity of elastic waves is influenced by third-order elastic constants, the propagation of nonlinear acoustic waves in pre-stressed materials would be influenced by higher-order elastic constants. Despite this, there has been a notable absence of research exploring this phenomenon. Consequently, this paper aims to establish a theoretical framework for governing the propagation of nonlinear acoustic waves in pre-stressed materials. It delves into the impact of pre-stress on higher-order material parameters, and specifically examines the propagation of one-dimensional acoustic waves within the contexts of the uniaxial stress and the biaxial stress. This paper establishes a theoretical foundation for exploring the application of nonlinear ultrasonic techniques to measure pre-stress in materials. [ABSTRACT FROM AUTHOR]

The suppression of low-frequency vibration and noise has always been an important issue in a wide range of engineering applications. To address this concern, a novel square hierarchical honeycomb metamaterial capable of reducing low-frequency noise has been developed. By combining Bloch's theorem with the finite element method, the band structure is calculated. Numerical results indicate that this metamaterial can produce multiple low-frequency bandgaps within 500 Hz, with a bandgap ratio exceeding 50%. The first bandgap spans from 169.57 Hz to 216.42 Hz. To reveal the formation mechanism of the bandgap, a vibrational mode analysis is performed. Numerical analysis demonstrates that the bandgap is attributed to the suppression of elastic wave propagation by the vibrations of the structure's two protruding corners and overall expansion vibrations. Additionally, detailed parametric analyses are conducted to investigate the effect of θ, i.e., the angle between the protruding corner of the structure and the horizontal direction, on the band structures and the total effective bandgap width. It is found that reducing θ is conducive to obtaining lower frequency bandgaps. The propagation characteristics of elastic waves in the structure are explored by the group velocity, phase velocity, and wave propagation direction. Finally, the transmission characteristics of a finite periodic structure are investigated experimentally. The results indicate significant acceleration amplitude attenuation within the bandgap range, confirming the structure's excellent low-frequency vibration suppression capability. [ABSTRACT FROM AUTHOR]

Curved-beams can be used to design modular multistable metamaterials (MMMs) with reprogrammable material properties, i.e., programmable curved-beam periodic structure (PCBPS), which is promising for controlling the elastic wave propagation. The PCBPS is theoretically equivalent to a spring-oscillator system to investigate the mechanism of bandgap, analyze the wave propagation mechanisms, and further form its geometrical and physical criteria for tuning the elastic wave propagation. With the equivalent model, we calculate the analytical solutions of the dispersion relations to demonstrate its adjustability, and investigate the wave propagation characteristics through the PCBPS. To validate the equivalent system, the finite element method (FEM) is employed. It is revealed that the bandgaps of the PCBPS can be turned on-and-off and shifted by varying its physical and geometrical characteristics. The findings are highly promising for advancing the practical application of periodic structures in wave insulation and propagation control. [ABSTRACT FROM AUTHOR]

Wave propagation in elastic solids is analyzed by a space-time discontinuous Galerkin quadrature element method. First, the space-time quadrature element is conveniently formulated based on the space-time discontinuous Galerkin formulation. This method treats both the spatial and temporal domains in a unified manner, enabling it to handle not only structured space-time meshes but also unstructured ones. It effectively captures discontinuities or sharp gradients in the solution. To transform the formulation into a system of algebraic equations, the Gauss-Lobatto quadrature rule and the differential quadrature analog are utilized. High-order elements are constructed simply by increasing the order of integration and differentiation without the laborious construction of shape functions. Then, dispersion analysis is conducted for one- and two-dimensional elements. The analysis reveals that as the Courant number decreases, the total dispersion error monotonically converges to the spatial dispersion error, which can be reduced by increasing the element order. Additionally, high-order elements nearly eliminate numerical anisotropy in different directions. Finally, several numerical examples of elastic wave propagation validate the method's effectiveness and high accuracy. [ABSTRACT FROM AUTHOR]

The elastic properties and wave propagation of porous rocks are sensitive to the stress variation. The existing theories mainly focus on the impacts of effective stress, confining and pore pressures. The physics of uniaxial stress effect on rock elasticity and wave propagation is seldom well studied, although the uniaxial stress case is frequently encountered in several scenarios, such as the laboratory loading and the subsurface tectonic deformation. Therefore, we propose a new dual‐porosity model to describe the effect of uniaxial effective stress on elastic properties of dry porous rocks, based on the Palmer equation and Shapiro dual‐porosity model. The Gurevich squirt‐flow model is then incorporated to model the dispersion and attenuation of wave velocities of fluid‐saturated porous rocks. Modelling results show that the increase of uniaxial effective stress inflates the P‐ and S‐wave velocities along the stress direction until the velocities asymptotically reach their maximum values within the elastic limit. However, the relevant wave dispersion and attenuation gradually decline with the elevating stress possibly due to the gradual closure of cracks. The effect of viscosity, fluid modulus and crack aspect ratio on wave dispersion is investigated in detail as well. By comparing our model to the published laboratory ultrasonic measurements, we confirm the validity of our model. Furthermore, our dual‐porosity model is used to establish a rock‐physics approach to estimate the wave velocities with the well‐logging data. The well‐logging examples show the reasonable agreement between the predicted results and real data, illustrating the feasibility of our approach. [ABSTRACT FROM AUTHOR]

This paper presents a study of wave propagation through an infinite periodic structure that consists of elastic Timoshenko beams interconnected with rigid bodies. This is a generalized approach in which the beams are not coaxial and the centre of mass of each rigid body is placed away from the intersection of their neutral axes. An analytical approach is used by applying the transfer matrix method (TMM), along with the Floquet–Bloch theorem for elastic wave propagation. Subsequent parametric analysis is performed with visualization of resulting band diagrams of a representative structure. These results are verified through comparison with solutions obtained using the finite-element method (FEM). In this manner, a comprehensive dynamical analysis of tailored metastructures is provided. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'. [ABSTRACT FROM AUTHOR]

An innovative concept of metabarrier is presented for seismic Rayleigh wave attenuation, which consists of a periodic array of cylindrical water tanks acting as resonant units above the soil surface. A pertinent theoretical framework is developed and implemented in COMSOL Multiphysics. The framework treats the dynamics of the water tank by a well-established three-dimensional linear, pressure-based model for fluid-structure interaction under earthquake excitation, accounting for the flexibility of the tank wall; furthermore, the soil is idealized as a homogeneous and isotropic medium. Floquet-Bloch dispersion analysis of the unit cell demonstrates the presence of relevant band gaps in the low-frequency range below 20 Hz and in the higher frequency range as well. The dispersion analysis is validated by comparison with the frequency-domain analysis of a soil domain with a finite array of water tanks. The band gaps are of interest to attenuate seismic Rayleigh waves and, more generally, Rayleigh waves caused by other ground vibration sources such as road or railway traffic. The water-tank resonant units are readily tunable by varying the water level, which allows changing opening frequencies/widths of the wave attenuation zones. This is a remarkable advantage over alternative seismic metamaterials that, in general, are not designed to be tunable. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'. [ABSTRACT FROM AUTHOR]

This paper investigates the propagation of in-plane surface waves in a coated thermoelastic half-space. First, it investigates a special case where the surface layer is described by the Maxwell–Cattaneo thermoelastic approach, while the half-space is filled by a thermoelastic material described by the classical Fourier law for the heat flux. The contact between the layer and the half-space is assumed to be welded, i.e., the displacements and the temperature, as well as the stresses and the heat flux are continuous through the interface of the layer and the half-space. The boundary and continuity conditions of the problem are formulated and then the exact dispersion relation of the surface waves is established. An illustrative numerical simulation is presented for the case of an aluminum thermoelastic layer coating a thermoelastic copper half-space, highlighting important aspects regarding the propagation of Rayleigh waves in such structures. The exact effective boundary conditions at the interface are also established replacing the entire effect of the layer on the half-space. The general case of the problem is also investigated when both the surface layer and the half-space are described by the Maxwell–Cattaneo thermoelasticity theory. This study helps to further understand the propagation characteristics of elastic waves in layered structures with thermal effects described by the Maxwell–Cattaneo approach. [ABSTRACT FROM AUTHOR]

In this work, the Schwarz primitive unit cell is used as the building block of different types of metastructures for steering and focusing elastic vibrations. The emergence of a Bragg-type bandgap when constructing a two-dimensional plate from such unit cells is experimentally validated. It is demonstrated that increasing both mass and porosity of the Schwarz primitive leads to a decrease in the frequency of the out-of-plane propagating wave targeted in this study. By arranging these modified Schwarz primitive unit cells in constant and graded layouts, two-dimensional plates with an embedded metabarrier and a metalens are numerically designed. The metabarrier protects an interior area of the plate from the propagating waves on a wide frequency band (approx. 1.4–3.4 kHz). Equally, the refractive index profile necessary for gradient index lenses is obtained via a progressive variation of the added mass or, alternatively, the porosity of the unit cell over a rectangular area. For the first time, bending of the out-of-plane mode towards the focusing point is practically validated in a challenging mesoscale experiment requiring the assembly of different three-dimensional printed sections of the plate. The increased porosity design is advantageous not only in terms of overall lightweight, but also towards additive manufacturing as it requires less material. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'. [ABSTRACT FROM AUTHOR]

The ever-improving performances of physics-based simulations and the rapid developments of deep learning are offering new perspectives to study earthquake-induced ground motion. Due to the large amount of data required to train deep neural networks, applications have so far been limited to recorded data or two-dimensional (2D) simulations. To bridge the gap between deep learning and high-fidelity numerical simulations, this work introduces a new database of physics-based earthquake simulations. The HEterogeneous Materials and Elastic Waves with Source variability in 3D (HEMEW S -3D) database comprises 30 000 simulations of elastic wave propagation in 3D geological domains. Each domain is parametrized by a different geological model built from a random arrangement of layers augmented by random fields that represent heterogeneities. Elastic waves originate from a randomly located pointwise source parametrized by a random moment tensor. For each simulation, ground motion is synthesized at the surface by a grid of virtual sensors. The high frequency of waveforms (fmax⁡=5 Hz) allows for extensive analyses of surface ground motion. Existing and foreseen applications range from statistical analyses of the ground motion variability and machine learning methods on geological models to deep-learning-based predictions of ground motion that depend on 3D heterogeneous geologies and source properties. Data are available at 10.57745/LAI6YU. [ABSTRACT FROM AUTHOR]

The paper studies the regularities of wave propagation in an inhomogeneous elastic layer with gradient properties varying along the layer thickness. The laws of change in elastic parameters are established at which the waves propagating in the direction of parameter change are harmonic. The waves propagating in the layer with a linear law of change in the elastic parameters are noт-harmonic. Analytical solutions obtained for a monochromatic wave defined on the boundary of a plane layer with a rigidly fixed second boundary are represented by special functions. In the case of gradient variation of the layer density, the solution is determined by a superposition of the Airy functions, in the case of equal relative variations of the density and elastic moduli, they are expressed through the modified Bessel functions, and in the case of arbitrary linear laws of variation in the elastic parameters, they are expressed through the confluent hypergeometric functions. Based on the analytical solution obtained for a layer with inhomogeneous density, the conditions for extreme values of displacements and strains are determined, and their distributions over the layer thickness are calculated and analyzed. [ABSTRACT FROM AUTHOR]

Acoustic waves can be used for wireless telemetry as an alternative to situations where electrical or optical penetrators are unsuitable. However, the response of the ultrasonic transducer can be greatly affected by temperature variations, mechanical deformations, misalignment between transducers, and multiple layers in the propagation zone. Therefore, this work sought to quantify such influences on communication between ultrasonic transducers. The experimental measurements were performed at the frequency where power transfer is maximized. Moreover, there were four experimental models, each with its own performed setup. The ultrasonic transducers are attached to both sides of a 6 mm thick stainless-steel plate for configuring just one barrier. Multiple layers of transducers are attached to the outer side of two plates immersed in an acoustic fluid with a 100 mm thick barrier. In both cases, the S21 parameter was used to quantify the influence of the physical barrier because it correlates with the power flow between ports that return after a given excitation. The results showed that when a maximum deformation of 1250  μ m / m  was applied, the amplitude of the S21 parameter varied around +0.7 dB. Furthermore, increasing the temperature from 30 to 100 °C slightly affected the S21 (+0.8 dB), but the signal decayed quickly for temperatures beyond 100 °C. Additionally, the ultrasonic communication with a multiple layer was found to occur under misalignment with an intersection area of up to 40%. None of the factors evaluated resulted in insufficient power transfer, except for a large misalignment between the transducers. Such results indicate that this type of communication can be a robust alternative, with a minimum alignment of 40% between transducers and electrical penetrators. [ABSTRACT FROM AUTHOR]

Peridynamics describes the material in a non-local form and is very suited for the simulation of dynamic fracture. However, one significant effect regarding dynamic fracture is the correct handling of elastic deformation, like the pressure and tension waves inside a body, due to dynamic boundary conditions like an impact or impulse. Many peridynamic material formulations have been developed with differences in this regard. This study investigates the elastic wave propagation characteristics of bond-based, ordinary state-based, continuum kinematics-inspired peridynamics and a local continuum consistent correspondence formulation. Multiple parameters of a longitudinal pressure wave inside an elastic bar are studied. While all formulations demonstrate adequate wave propagation handling, all except the correspondence formulation are sensitive to incomplete horizons. The local continuum consistent formulation does not suffer from the surface effect and models the wave propagation with perfect accuracy. [ABSTRACT FROM AUTHOR]

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Periodic composite beams play an important role in the bandgap design of phononic crystals. However, for thick beams or high frequencies, conventional theoretical displacement assumptions for beams have limitations. Therefore, it is desirable to improve the accuracy of the vibration frequencies and bandgaps of phononic crystals by using higher-order beam theory. In this work, a modified couple stress theory accounting for the microstructure effect is combined with the third-order shear deformation beam theory to quantitatively study bandgaps in phononic crystal microbeams under different thicknesses and geometric parameters. The elastic wave band structure of the phononic crystal beams is calculated using an improved plane wave expansion method and compared numerically with the finite element model. In addition, compared with the Bernoulli–Euler and Timoshenko beams, the current third-order shear beam has better prediction accuracy for the first bandgap. The numerical results also show that the microstructure effect is significant at the micron scale. Furthermore, at all length scales, the bandgap sizes change significantly with the change in unit cell length and volume ratio. [ABSTRACT FROM AUTHOR]

In this paper, we devise a pentamode metamaterial plate exhibiting topological characteristics. By organizing pentamode metamaterial structural elements, topological boundary states are attained, effectively safeguarding propagation of elastic waves. Moreover, based on the numerical simulation model, we employ a polymer to fabricate a macro-scale specimen via additive manufacturing. Through assessing the vibrational response of the sample, we corroborate its topological attributes in governing elastic wave transmission. This discovery paves the way for a novel approach to manipulating acoustic/elastic waves employing pentamode metamaterials. [ABSTRACT FROM AUTHOR]

The dispersion behaviour of the finite element method, applied to the treatment of stress wave propagation tasks in an elastic solid continuum, is reviewed and complemented with the authorsâ contributions in the field, along with substantial details of finite element technology. It is shown how finite element dispersion disqualifies to a certain extent the stress wave propagation modelling and, as such, cannot be completely eradicated. The paper, however, reveals the ways how the dispersion effect (actually, modelling errors) could be minimized. The effects of spatial and temporal dispersions of the finite element method are treated. 1D and 2D linear and quadratic finite elements and their suitability are analysed for use with implicit and explicit integration methods. Historical as well as new, up-to-date approaches are also reviewed. The paper closes with recommendations for values of mesh size and timestep size, mass matrices and direct time integrations with respect to dispersion errors in finite element modelling of elastic wave propagation problems in solids.

Abstract Since their invention, tissue expanders, which are designed to trigger additional skin growth, have revolutionised many reconstructive surgeries. Currently, however, the sole quantitative method to assess skin growth requires skin excision. Thus, in the context of patient outcomes, a machine learning method which uses non-invasive measurements to predict in vivo skin growth and other skin properties, holds significant value. In this study, the finite element method was used to simulate a typical skin expansion protocol and to perform various simulated wave propagation experiments during the first few days of expansion on 1,000 individual virtual subjects. An artificial neural network trained on this dataset was shown to be capable of predicting the future skin growth at 7 days (avg. $$R^2 = 0.9353$$ R 2 = 0.9353 ) as well as the subject-specific shear modulus ( $$R^2 = 0.9801$$ R 2 = 0.9801 ), growth rate ( $$R^2 = 0.8649$$ R 2 = 0.8649 ), and natural pre-stretch ( $$R^2 = 0.9783$$ R 2 = 0.9783 ) with a very high degree of accuracy. The method presented here has implications for the real-time prediction of patient-specific skin expansion outcomes and could facilitate the development of patient-specific protocols.

The entry and propagation of pores inside an adhesive interface between an elastomer and a rigid sphere were studied experimentally and simulated numerically. It was shown that mutually interacting events involving attachment-detachment of different segments of the elastomer to the indenter resulted in non-trivial patterns of spatially distributed contacts between them, which were additionally influenced by air penetration of the pores. [ABSTRACT FROM AUTHOR]

AbstractThe primary objective of the current work is to establish the impacts of planar boundary and non-planar boundary on the displacement components (DCs) of Rayleigh-type wave propagation in an elastic structure. The elastic structure, precisely, incorporates a pre-stressed nearly incompressible elastic material in the half-space along with the non-planar boundary at the free surface. The methodology applied features variable separable technique and Taylor’s series expansion along with substitution method to establish the expressions for DCs and frequency relation. The frequency relation of Rayleigh-type wave is obtained for the situation considering planar free surface, which is further reduced as a special case of the study and validated with the classical result present in the literature. The DCs of Rayleigh-type wave have been numerically computed, and their reliance on wave number have been exhibited graphically. In addition to this, the influences of affecting parameters viz., hydrostatic stress, principal Cauchy stress and curvature parameter on DCs have been traced out. The computational result also manifests the domain of existence of Rayleigh-type wave propagating in the considered model in the presence of planar free surface. [ABSTRACT FROM AUTHOR]

A set of non-linear optimisation algorithms are combined with a finite element simulation code to analyse the energy absorption and elastic stress wave propagation problem in multilayer/multimaterial armour systems under ballistic impacts. An Abaqus Python script is used to simulate the ballistic event and to generate the variables and post-processing outputs necessary for the integration with the optimisation algorithms. A number of modelling strategies are considered and three optimisation algorithms are used: Particle Swarm Optimisation (PSO), Genetic Algorithm (GA) and Simulated Annealing (SA). The performance and efficiency of each algorithm are assessed through four benchmark tests with different levels of complexity. A multi-objective optimisation procedure is proposed that uses the most efficient algorithm based on every single-objective formulation, variables and constraints from the benchmark tests, resulting in a highly non-linear problem. The proposed optimisation methods successfully achieve the study purposes both in the simulation of generic ballistic impacts and in the quality of the optimised solutions, demonstrating the potential for this type of optimisation method on terminal ballistic applications, serving as a standpoint for further studies into higher energy impacts and material non-linearities. [ABSTRACT FROM AUTHOR]

An editorial focuses on refining Biot elastic coefficients in poroelastic solids by addressing discrepancies between drained and undrained conditions. It proposes new formulas for these coefficients and evaluates their accuracy through numerical analysis of Berea sandstone under different conditions. It highlights theoretical corrections needed for accurate wave propagation modeling in fluid-saturated porous media.

The thermoelastic wave propagation analysis is developed in a Love–Bishop nanorod resonator employing the strain gradient elasticity and Green–Naghdi theories with energy dissipation for the first time. The assumed nanorod resonator is subjected to thermal shock loading. The variational principle is applied to derive the coupled system of partial differential equations for temperature and displacement fields in a Love–Bishop nanorod. An analytical solution is proposed to solve the governing equations in Laplace domain. To obtain the temporal variation of fields' variables, a proper Laplace inversion technique is employed in the problem. The size effects in the nano-sized Love–Bishop rods are taken into account with five small-scale parameters including three higher-order materials length parameters, the micro-length inertia and thermal parameters. Two types of thermal shock loadings such as laser pulse-induced suddenly increasing temperature are utilized in this work, and the laser shock-induced thermoelastic wave propagations in both temperature and displacement fields are illustrated. The effects of the higher-order materials length parameters and the micro-length inertia and thermal parameters on the propagation of thermal and elastic waves are studied in detail. [ABSTRACT FROM AUTHOR]

By employing the strain gradient elasticity theory, we investigate the propagation of in-plane surface waves in a coated half-space with microstructures. We first investigate the general case of the present problem, that is, both the surface layer and the half-space are described by the strain-gradient elasticity theory. We formulate the boundary and continuity conditions of the general case and derive the dispersion relations of the surface waves. Then we investigate two special cases: (1) the surface layer is described by the strain-gradient elasticity theory, while the half-space by the classical elasticity theory; (2) the surface layer is described by the classical elasticity theory while the half-space by the strain-gradient elasticity theory. We examine the effects of strain-gradient characteristic lengths on the dispersion curves of surface waves in all cases. This study helps to further understand the propagation characteristics of elastic waves in materials with microstructures. [ABSTRACT FROM AUTHOR]

The dispersion of elastic shear waves in multilayered bodies is a topic of extensive research due to its significance in contemporary science and engineering. Anti-plane shear motion, a two-dimensional mathematical model in solid mechanics, effectively captures shear wave propagation in elastic bodies with relative mathematical simplicity. This study models the vibration of elastic waves in a multilayered inhomogeneous circular membrane using the Helmholtz equation with fractional-order infusion, effectively leveraging the anti-plane shear motion equation to avoid the computational complexity of universal plane motion equations. The method of the separation of variables and the conformable Bessel equation are utilized for the analytical examination of the model's resulting vibrational displacements, as well as the dispersion relation. Additionally, the influence of various wave phenomena, including the dependencies of the wavenumber on the frequency and the phase speed on the wavenumber, respectively, with the variational effect of the fractional order on wave dispersion is considered. Numerical simulations of prototypical cases validate the formulated model, illustrating its applicability and effectiveness. The study reveals that fractional-order infusion significantly impacts the dispersion of elastic waves in both single- and multilayer membranes. The effects vary depending on the membrane's structure and the wave propagation regime (long-wave vs. short-wave). These findings underscore the potential of fractional-order parameters in tailoring wave behavior for diverse scientific and engineering applications. [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]

This paper studies elastic stress wave propagation generated by an impact in a system consisting of a moving striker rod and an initially stationary semi-infinite rod. This research emphasizes the role of different general impedances in affecting the response during the wave propagation process. The Rayleigh–Love rod theory is used in this research to consider lateral inertia and Poisson's effects on longitudinal waves in rods, as these factors lead to greater stress results compared to the traditional wave equation. To solve the complex wave equations in a Rayleigh–Love rod with different general impedances, the numerical inversion of Laplace transformation is applied and verified using the results of previous research. This study demonstrates that variations in general impedances cause different wave reflection and transmission behaviors at the interface. As the wave interacts with this discontinuity of impedance, it may be amplified or attenuated, and changes in impedance can significantly affect wave propagation behaviors. [ABSTRACT FROM AUTHOR]

Since their invention, tissue expanders, which are designed to trigger additional skin growth, have revolutionised many reconstructive surgeries. Currently, however, the sole quantitative method to assess skin growth requires skin excision. Thus, in the context of patient outcomes, a machine learning method which uses non-invasive measurements to predict in vivo skin growth and other skin properties, holds significant value. In this study, the finite element method was used to simulate a typical skin expansion protocol and to perform various simulated wave propagation experiments during the first few days of expansion on 1,000 individual virtual subjects. An artificial neural network trained on this dataset was shown to be capable of predicting the future skin growth at 7 days (avg. R 2 = 0.9353 ) as well as the subject-specific shear modulus ( R 2 = 0.9801 ), growth rate ( R 2 = 0.8649 ), and natural pre-stretch ( R 2 = 0.9783 ) with a very high degree of accuracy. The method presented here has implications for the real-time prediction of patient-specific skin expansion outcomes and could facilitate the development of patient-specific protocols. [ABSTRACT FROM AUTHOR]

Various engineering equipments and devices use elastic vibrations and acoustic waves extensively for non-destructive testing and technical diagnostics of various materials and products. The propagation characteristics of plane and Rayleigh-type surface waves in an incompressible transversely isotropic diffusive material are investigated in context of nonlocal elasticity theory. The governing equations of motion for the medium are specialized in a plane and solved for time-harmonic solutions. A velocity equation for homogeneous plane wave is obtained which indicates the existence of two plane transverse waves. The two-dimensional equations are also solved for surface wave solutions and a Rayleigh characteristic equation is obtained. A numerical example is taken to illustrate graphically the effects of nonlocality, diffusion and material anisotropy parameters on the speeds of plane and Rayleigh surface waves. [ABSTRACT FROM AUTHOR]

Modelling seismic wavefields in complex 3-D elastic media is the key in many fields of Earth Science: seismology, seismic imaging, seismic hazard assessment and earthquake source mechanism reconstruction. This modelling operation can incur significant computational cost, and its accuracy depends on the ability to take into account the scales of the subsurface heterogeneities varying. The theory of homogenization describes how the small-scale heterogeneities interact with the seismic waves and allows to upscale elastic media consistently with the wave equation. In this study, an efficient and scalable numerical homogenization tool is developed, relying on the similarity between the equations describing the propagation of elastic waves and the homogenization process. By exploiting the optimized implementation of an elastic modelling kernel based on a spectral-element discretization and domain decomposition, a fully scalable homogenization process, working directly on the spectral-element mesh, is presented. Numerical experiments on the entire SEAM II foothill model and a 3-D version of the Marmousi II model illustrate the efficiency and flexibility of this approach. A reduction of two orders of magnitude in terms of absolute computational cost is observed on the elastic wave modelling of the entire SEAM II model at a controlled accuracy. [ABSTRACT FROM AUTHOR]

Quantum computing has attracted considerable attention in recent years because it promises speedups that conventional supercomputers cannot offer, at least for some applications. Though existing quantum computers (QCs) are, in most cases, still too small to solve significant problems, their future impact on domain sciences is already being explored now. Within this context, we present a quantum computing concept for 1-D elastic wave propagation in heterogeneous media with two components: a theoretical formulation and an implementation on a real QC. The method rests on a finite-difference approximation, followed by a sparsity-preserving transformation of the discrete elastic wave equation to a Schrödinger equation, which can be simulated directly on a gate-based QC. An implementation on an error-free quantum simulator verifies our approach and forms the basis of numerical experiments with small problems on the real QC IBM Brisbane. The latter produce simulation results that qualitatively agree with the error-free version but are contaminated by quantum decoherence and noise effects. Complementing the discrete transformation to the Schrödinger equation by a continuous version allows the replacement of finite differences by other spatial discretization schemes, such as the spectral-element method. Anticipating the emergence of error-corrected quantum chips, we analyse the computational complexity of the best quantum simulation algorithms for future QCs. This analysis suggests that our quantum computing approach may lead to wavefield simulations that run exponentially faster than simulations on classical computers. [ABSTRACT FROM AUTHOR]

Film/substrate structures are often seen in nature and engineering and their characteristic mechanical behaviors facilitating widespread application prospects. Surface patterns of film/substrate structures significantly affect the propagation of elastic waves. This paper investigates elastic wave propagation in the thin film/substrate periodic structure with sinusoidal surface patterns through the uniaxial tension. Based on the Bloch wave theory and numerical simulation, diverse bandgaps are triggered and the overall frequency range of the bandgaps shifts upward with the increase of the tensile strain, which demonstrates that tensioning the bilayer is a reliable and robust way for manipulating bandgaps. Band properties and bandgap evolution by various geometric and material parameters are discussed systematically, including various surface sinusoidal amplitudes, thickness of the substrate and various density or modulus ratio. The underlying mechanism of the exciting results in reversal design and regulation of structural geometry is revealed and is explained by using the spring-mass model. This work can provide new thought and insight for controlling wave propagation and promoting potential applications of the film/substrate systems and devices. [ABSTRACT FROM AUTHOR]

Sedimentary strata typically exhibit the characteristics of transverse isotropy (VTI) with a vertical axis of symmetry. However, fractures in sedimentary strata tend to produce anisotropic closure due to horizontal in situ stress, resulting in pronounced orthorhombic anisotropy in VTI media under such stress conditions and influencing the propagation behavior of seismic waves. Previous studies have primarily focused on the elastic wave velocity anisotropy induced by applied stress in isotropic background media, neglecting the impact of VTI background media on the anisotropy induced by horizontal in situ stress and the response characteristics of seismic wave propagation. To address these gaps, we first establish the effective elastic stiffness tensor of VTI media under horizontal in situ stress using nonlinear acoustoelastic theory. Then, we derive the accurate and linearized approximate equations for P-wave seismic reflectivity of VTI media under horizontal in situ stress, based on wave equations and scattering theory, respectively. Finally, we compare and analyze the characteristics of orthorhombic anisotropic seismic response induced by horizontal in situ stress at various types of elastic reflection interfaces. Our results demonstrate that the linearized approximation of the seismic reflection response characteristics closely aligns with the accurate equations under conditions of small stress below 10 MPa, effectively capturing the azimuth-dependent orthorhombic anisotropy induced by horizontal in situ stress in VTI media. The results of this study also provide a novel theoretical approach and valuable insights into the seismic prediction of in situ stress. [ABSTRACT FROM AUTHOR]

The dispersion behaviour of the finite element method, applied to the treatment of stress wave propagation tasks in an elastic solid continuum, is reviewed and complemented with the authors' contributions in the field, along with substantial details of finite element technology. It is shown how finite element dispersion disqualifies to a certain extent the stress wave propagation modelling and, as such, cannot be completely eradicated. The paper, however, reveals the ways how the dispersion effect (actually, modelling errors) could be minimized. The effects of spatial and temporal dispersions of the finite element method are treated. 1D and 2D linear and quadratic finite elements and their suitability are analysed for use with implicit and explicit integration methods. Historical as well as new, up-to-date approaches are also reviewed. The paper closes with recommendations for values of mesh size and timestep size, mass matrices and direct time integrations with respect to dispersion errors in finite element modelling of elastic wave propagation problems in solids. [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]

A novel hollow star-shaped chiral metamaterial (SCM) is proposed by incorporating chiral structural properties into the standard hollow star-shaped metamaterial, exhibiting a wide band gap over 1 500 Hz. To broaden the band gap, solid single-phase and two-phase SCMs are designed and simulated, which produce two ultra-wide band gaps (approximately 5 116 Hz and 6 027 Hz, respectively). The main reason for the formation of the ultra-wide band gap is that the rotational vibration of the concave star of two novel SCMs drains the energy of an elastic wave. The impacts of the concave angle of a single-phase SCM and the resonator radius of a two-phase SCM on the band gaps are studied. Decreasing the concave angle leads to an increase in the width of the widest band gap, and the width of the widest band gap increases as the resonator radius of the two-phase SCM increases. Additionally, the study on elastic wave propagation characteristics involves analyzing frequency dispersion surfaces, wave propagation directions, group velocities, and phase velocities. Ultimately, the analysis focuses on the transmission properties of finite periodic structures. The solid single-phase SCM achieves a maximum vibration attenuation over 800, while the width of the band gap is smaller than that of the two-phase SCM. Both metamaterials exhibit high vibration attenuation capabilities, which can be used in wideband vibration reduction to satisfy the requirement of ultra-wide frequencies. [ABSTRACT FROM AUTHOR]

Multilayered van der Waals (vdW) materials have attracted increasing interest because of the manipulability of their superior optical, electrical, thermal, and mechanical properties. A mass-spring model (MSM) for elastic wave propagation in multilayered vdW metamaterials is reported in this paper. Molecular dynamics (MD) simulations are adopted to simulate the propagation of elastic waves in multilayered vdW metamaterials. The results show that the graphene/MoS2 metamaterials have an elastic wave bandgap in the terahertz range. The MSM for the multilayered vdW metamaterials is proposed, and the numerical simulation results show that this model can well describe the dispersion and transmission characteristics of the multilayered vdW metamaterials. The MSM can predict elastic wave transmission characteristics in multilayered vdW metamaterials stacked with different two-dimensional (2D) materials. The results presented in this paper offer theoretical help for the vibration reduction of multilayered vdW semiconductors. [ABSTRACT FROM AUTHOR]

Phononic crystals as manufactured materials have particular property called bandgap to control elastic wave propagation. The geometric and material parameters have considerable effects on bandgap, but the sensitivities of these parameters to the starting and ending frequencies, and width of bandgap are not yet clear, especially for three-dimensional and three-component PCs. Thus, in this paper, the generation mechanism of bandgap, the influences and sensitivities of geometric and material features on bandgap characteristics are fully investigated according to the improved plane wave expansion method, Sobol's sensitivity method, and artificial neural network. The results demonstrate that the artificial neural network prediction model with multiple hidden layers has good fitness, of which the coefficients of determination for the starting and ending frequencies are 0.9981 and 0.9982, respectively. The radius of the scatterer and the radius of the coating layer have the greatest influence, followed by the elastic modulus and Poisson's ratio of the coating layer on the starting and ending frequencies. The radius of the scatterer and lattice constant have the biggest effect, followed by the elastic modulus and radius of the coating layer on the bandgap width. [ABSTRACT FROM AUTHOR]

This document is a translation of Jerald L. Ericksen's Introduction to the collection "Studies on Mechanics of Continua." Ericksen discusses his interest in the idea of continua with internal structure and the development of a theory for anisotropic fluids. He also explores the application of his theories to liquid crystals and the study of shells. Ericksen emphasizes the importance of considering different perspectives in the field of mechanics and expresses gratitude for the opportunity to publish this collection. [Extracted from the article]

Functionally-graded materials (FGMs) have great potential in many industry areas for the development of novel acoustic devices such as sensors, electromechanical transducers, actuators and filters. The study of the propagation of elastic waves is a primordial step for a number of such applications. In this study, the stiffness matrix method and the Stroh formalism with the formulation of Ingebrigsten and Tonning were used to establish the relationship between the stress and displacement from the top to the bottom of the fictive multilayer. A power-law inhomogeneity distribution is introduced in the mechanical tensor of the magneto-electro-elastic (MEE) composite. The obtained results indicate that the introduction of heterogeneity has a great influence on nondimensional frequency and modal shape. It is also found that the frequency vibration decreases with the increase in gradient coefficient α. Furthermore, the metallization of the free surface (vanishing of electrical and magnetic potential) highly decreases the stress, especially in the median of the plate. [ABSTRACT FROM AUTHOR]

The propagation of coherent longitudinal waves in a viscous liquid containing a random distribution of spherical elastic particles is analysed using a model based on multiple scattering theory. This model, initially developed to describe the propagation of coupled longitudinal and transverse elastic waves in isotropic solid materials, takes into account wave conversions at the particle surface as well as positional correlations between particles via the pair correlation function. By modelling a Newtonian viscous liquid through complex frequency-dependent elastic moduli (i.e. using an imaginary shear modulus), the model is adapted to the case of viscous fluids and we show that conversions of longitudinal waves into transverse waves are important to take into account. We present asymptotic results from the model for case of long wavelength for the longitudinal waves, without assumptions on the shear wavelength. For high concentrations, these wave conversions are reinforced by the contribution of position correlations between the particles. In a subsequent paper, we present numerical validation of the asymptotic approximations and compare them with experimental results for solid particles in water. [ABSTRACT FROM AUTHOR]

We present the results of numerical simulation and experimental studies of the propagation of fle-xural elastic waves in a notched metal bar with a rectangular cross section that approximates the acoustic black hole effect. The sample is a notched bar; the depth of notches increases according to a power law with an exponent of 4/3. The experimental results and the results of numerical simulation confirm that such bars slow the propagation velocity of an elastic wave towards the end of the bar. It is demonstrated that flexural waves in such structures exhibit dispersion and their amplitude at the end of the bar for some eigenfrequencies is higher than that in a solid bar. The eigenmode shapes of a solid and notched bar are compared together with the distribution of the flexural wave amplitude along the bars. The frequency dependence of the flexural wave length is studied during wave propagation towards the end of the notched bar. [ABSTRACT FROM AUTHOR]

The reflection and transmission problems of elastic waves, through a liquid-saturated poroelastic interlayer sandwiched between two elastic solid half-spaces, are investigated. The reflection and transmission coefficients are derived based on the Biot/squirt (BISQ) model, which incorporates both the Biot and squirt-flow mechanisms. Moreover, the viscoelasticity of the solid frame and the pore fluid are also considered. The fractional Zener model and the fractional dashpot model (Abel dashpot) are adopted for the solid frame and the pore fluid, respectively. The numerical results are provided and shown graphically. The dependences of the attenuation, the reflection and transmission coefficients upon the characteristic squirt flow length are numerically discussed. Comparing with that predicted by Biot theory without considering the squirt flow effects, it is observed that the reflection and transmission coefficients and the attenuation due to the sandwiched interlayer are affected noticeably by the effect of the squirt flow. [ABSTRACT FROM AUTHOR]