Modeling Of Elastic Wave Propagation Research Articles

Discrete element method modelling of elastic wave propagation in a meso-scale model of concrete

This paper deals with the accurate modelling of ultrasonic wave propagation in concrete at the mesoscopic level. This was achieved through the development of a discrete element method (DEM) model capable of simulating elastic wave signals comparable to those measured experimentally. The main objective of the work was to propose a novel methodology for constructing a meso-scale model of concrete dedicated to the analysis of elastic wave propagation. All the material parameters necessary to prepare a numerical DEM model of concrete at the mesoscopic level were explored and explained. Calibration of the mechanical parameters of the DEM model to match the experimental values involved linking the local, micro-parameters between particles with the global response of the whole sample. The developed numerical model was further used to simulate the propagation of elastic waves in a cubic concrete sample, in the frequency range of 100–500 kHz. The results of the DEM calculations showed good agreement with the experimental ultrasonic signals.

Study on wave propagation in the modulation structure with gradually changing impedance according to specific waveform based on magneto-rheological fluid

This work proposes a novel hierarchical modulation structure with gradually-changed impedance built by magneto-rheological (MR) fluid and investigates its wave propagation characteristics theoretically and experimentally. Based on the impedance tunable property of the MR fluid, applying multiple magnetic fields to MR fluid realizes the modulation of this proposed structure, and regulating its magnetic field distribution law can effectively change the impedance variation forms in the structure. Establish the elastic wave propagation model of this modulated structure, and analyze the variation trends of its elastic wave propagation characteristics with different impedance distribution patterns, taking the vibration level difference as an indicator. Subsequently, conduct experimental testing for the transmissibility of elastic waves. The results show that the elastic wave transmission characteristics of the proposed modulation structure mainly depend on its impedance variation rate and the frequency of external excitation. On a broader band of the frequency range (20–300 Hz) studied in this paper, the gradual impedance distribution of MR fluid enhances the transmission loss of elastic waves compared to a uniform distribution of its impedance. Moreover, in the lower frequency range (40–125 Hz), the layered modulation structure with a non-monotonic variation of impedance following a wave-like waveform presents more significant attenuation on elastic waves than the structure whose impedance varies monotonously in a gradient waveform. This work contributes to expanding the design thoughts of the structure with gradually changing impedance and providing new ideas and means for the control of elastic waves.

A continuous leakage real-time localization method based on space phase image of elastic wave field with improved CNN

To satisfy the requirement of real-time monitoring and locating of the leakage in large pressure vessels, a method of leakage source location based on improved convolutional neural network (CNN) is proposed in this paper. In this method, the polar coordinate model of elastic wave propagation excited by continues leakage is established, and the improved CNN is constructed according to its spatial field distribution, and the training set of the network is obtained by finite element simulation. The experimental results show that this method can be applied to locate the leak at any time after it occurs, and only a single sensor array is used. In the experiment of 1 m2 stiffened test plate, the absolute distance error was less than 0.1 m and the absolute angle error was less than 0.1 rad in 90.2 % of all samples.

Prediction of elastic wave propagation in composites using 3D CNN

Performing time-dependent finite element simulations for wave propagation in composites is a particularly complex task that consumes a lot of computational energy as it involves modeling the interactions between waves and various constituents that make up the composite material. In this study, we have developed a surrogate model of elastic wave propagation in composites based on three-dimensional conventional neural networks. The input to the model consists of a three-dimensional matrix representing the architecture of the composites and a vector representing the input waves, while the output is a vector representing the output elastic waves. After training the model using 60 000 randomly generated samples, it has shown high accuracy and efficiency in predicting the output elastic waves. This significantly reduces computational resources required to conduct simulation using commercial software, making it a more practical solution for real-world applications, such as composite optimization, nondestructive testing, and material characterization.

Numerical Modeling of Elastic Wave Propagation in Porous Soils with Vertically Inhomogeneous Fluid Contents Due to Infiltration

The structure of soils is often heterogeneous with layered strata having distinct permeabilities. An advanced mathematical and numerical coupled model of elastic wave propagation in poroelastic multi-layered soils subjected to subsoil water infiltration is proposed in this study. The coupled model was based on the introduction of an inhomogeneous functionally graded fluid-saturation of the considered soil depending on the infiltration time, which was evaluated employing Richards’ equation. The time-harmonic solution was formulated in terms of the Fourier transform of Green’s matrix and the surface load that excites the vibration. The convergence and efficiency of the proposed approach are demonstrated. An example of dispersion curves for partially saturated porous strata made of loam, sand, and rock at different infiltration times is provided, and it is shown that the characteristics of the surface acoustic waves change with time, which can be further used for inverse problems’ solution.

Domain decoupling implementation for efficient ultrasonic wave simulations using scaled boundary finite elements and the mortar method

We introduce a novel approach that combines the scaled boundary finite element method (SBFEM) with a mortar coupling to enhance the computational modelling of elastic wave propagation and interaction with local features in the ultrasonic range. The key objective is to achieve decoupling between different regions of interest, enabling independent meshes for the zones where waves either propagate or interact with localised discontinuities in the elastic media. This decoupling allows us to exploit the benefits offered by various SBFEM formulations. Thus, we can select the most suitable solution for each specific region. An important concept we emphasise is the differentiation between the near field and far field regions. The near field encompasses zones where the precise representation of small features compared to the wavelength is crucial. At the same time, the far field comprises homogeneous regions where the waves propagate without interactions, eventually radiating towards infinity if the domain is unbounded. By separating these two zones, we can improve the computational performance by employing finer discretisation only where necessary. Furthermore, this decoupling enables the reuse of far field models in parametric analyses, making it highly valuable for scenarios focused particularly on local elastic wave interactions. This approach offers considerable potential in such cases. The modelling technique is validated, and its potential is demonstrated through practical applications.

Determining the Deformation Characteristics of Railway Ballast by Mathematical Modeling of Elastic Wave Propagation

The article solves the problem of theoretically determining the deformable characteristics of railway ballast, considering its condition through mathematical modeling. Different tasks require mathematical models with different levels of detail of certain elements. After a certain limit, excessive detailing only worsens the quality of the model. Therefore, for many problems of the interaction between the track and the rolling stock, it is sufficient to describe the ballast as a homogeneous isotropic layer with a vertical elastic deformation. The elastic deformation of the ballast is formed by the deviation of individual elements; the ballast may have pollutants, the ballast may have places with different levels of compaction, etc. To be able to determine the general characteristics of the layer, a dynamic model of the stress–strain state of the system based on the dynamic problem of the theory of elasticity is applied. The reaction of the ballast to the dynamic load is modeled through the passage of elastic deformation waves. The given results can be applied in the models of the railway track in the other direction as initial data regarding the ballast layer.

Ordinary state-based peri-ultrasound modeling to study the effects of multiple cracks on the nonlinear response of plate structures

Since it is almost impossible to carry out a comprehensive parametric investigation experimentally for internal cracks with different geometry and orientation, a good numerical modeling and simulation technique is necessary to have a clear understanding of the physics of wave propagation and its interaction with cracks. Such investigation is helpful for structural health monitoring (SHM) with ultrasonic techniques. This work presents a nonlocal peri-ultrasound theory based on ordinary state-based (OSB) peridynamics for modeling elastic wave propagation in three-dimensional (3-D) plate structures containing multiple cracks. A relatively new and promising nonlinear ultrasonic technique called Sideband Peak Count – Index (or SPC-I) is adopted to extract the nonlinearity generated from the interactions between elastic waves and multiple cracks. Effects of three main parameters – the distance between the acoustic source and the crack, the crack spacing and the number of cracks are investigated using the proposed OSB peri-ultrasound theory together with the SPC-I technique. For each of these three parameters investigation, different crack thicknesses were considered − 0 mm (crack-free), 1 mm (thin crack), 2 mm (intermediate thickness) and 4 mm (thick crack); thin and thick cracks are defined after comparing the crack thickness value with the horizon size mentioned in the peri-ultrasound theory. It is found that for obtaining consistent results the acoustic source should be placed at least one wavelength away from the crack and crack spacings also play an important role on the nonlinear response. It is concluded that the nonlinear response diminishes when the cracks become too thick, and thin cracks show higher nonlinearity than that of thick cracks and no cracks. Finally, the proposed method which is combining the peri-ultrasound theory and SPC-I technique is used for monitoring cracks’ evolution process. The numerical modeling results are compared with the experimental findings reported in the literature. Consistent qualitative trends in SPC-I variations predicted numerically and obtained experimentally are observed, thus it gives confidence in the proposed method.

Well-posedness of wave scattering in perturbed elastic waveguides and plates: application to an inverse problem of shape defect detection

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.

3D acoustoelastic FD modeling of elastic wave propagation in prestressed solid media

AbstractSeismic exploration of deep oil/gas reservoirs involves the propagation of seismic waves in high-pressure media. Traditional elastic wave equations are not suitable for describing such media. The theory of acoustoelasticity establishes the dynamic equation of wave propagating in prestressed media through constitutive relation using third-order elastic constants. Many studies have been carried out on numerical simulations for acoustoelastic waves, but are mainly limited to 2D cases. A standard staggered-grid (SSG) finite-difference (FD) approach and the perfectly matched layer (PML) absorbing boundary are combined to solve 3D first-order velocity-stress equations of acoustoelasticity to simulate wave propagating in 3D prestressed solid medium. Our numerical results are partially validated by plane-wave analytical solution through the comparison of calculated and theoretical P-/S-wave velocities as a function of confining prestress. We perform numerical simulations of acoustoelastic waves under confining, uniaxial and pure-shear prestressed conditions. The results show the stress-induced velocity anisotropy in acoustoelastic media, which is closely related to the direction of prestresses. Comparisons to seismic simulations based on the theory of elasticity illustrate the limitation of conventional elastic simulations for prestressed media. Numerical simulations prove the significant effect of prestressed conditions on seismic responses.

A simple model for elastic wave propagation in hard sphere-filled random composites.

A simple model is proposed to study wave propagation in hard sphere-reinforced elastic random composites. Compared to existing related models, the proposed model is featured by a modified form of classical elastodynamic equations in which the inertia term is substituted by the acceleration field of the mass centre of a representative unit cell, supplied with a derived simple differential relation between the displacement field of the composite and the displacement field of the mass centre of a representative unit cell. The present model enjoys conceptual and mathematical simplicity although it is restricted to hard sphere-filled elastic composites in which the elastic moduli of embedded spheres are much (at least 4-5 times) stiffer than those of a softer matrix. Explicit formulas are derived for the attenuation coefficient and the effective phase velocity of plane longitudinal P-waves and transverse S-waves. The efficiency and reasonable accuracy of the present model are demonstrated by reasonably good agreement between the predicted results and some established known data. The proposed model could offer a potential general method to study various three-dimensional dynamic problems of hard sphere-filled elastic random composites.

Ray theory for elastic wave propagation in graded metamaterials

We present a ray theory for modeling elastic wave propagation in spatially graded mechanical metamaterials. Wave propagation in periodic metamaterials has been well studied, motivated by their beneficial wave steering and bandgap properties. By contrast, comparably little work has explored wave propagation in spatially graded metamaterials despite the increased design opportunities, largely due to the lack of efficient modeling techniques. We develop a ray theory to model waves in graded metamaterials based on high-frequency asymptotics and the assumption of local periodicity. This work builds upon the well-developed ray theories that are fundamental in a wide range of fields, from optics to seismology. Our derivations produce a practical framework for computing approximate wave fields in graded metamaterials. Ray trajectories are computed by independently solving a system of ordinary differential equations for each ray, requiring only knowledge of local dispersion relations throughout the metamaterial, which vary smoothly in space due to grading. Equations for the wave amplitude along rays are also derived in the two-dimensional setting. We show that the form of the ray tracing equations are nearly identical to those for smooth solids in seismic ray theory, with the primary difference being the dispersion relations. A numerical framework for computing ray solutions is demonstrated on a mass–spring network with analytical dispersion relations as well as a truss metamaterial that requires the numerical evaluation of dispersion relations. Through these examples, we demonstrate that ray theory provides an efficient means of studying the fascinating behavior of waves in graded metamaterials such as wave guiding along curved trajectories.

A Mechanical Model for Elastic Wave Propagation in Nacre-Like Materials With Brick-and-Mortar Microstructures

Abstract Many biological materials have outstanding properties unparalleled by artificial materials because of their periodic and/or hierarchical structures. In this paper, the longitudinal elastic wave propagation in nacre-like materials with brick-and-mortar microstructures has been studied theoretically by taking the different deformation mechanisms into account. A viscoelastic model in relation to the sacrificial bond behavior for the organic matrix has been developed. The shear-lag model is adopted to simulate the deformation of the brick-mortar structure. Complex band structures have been analyzed and the mechanical model has been validated by finite element method. Results have shown that bandgaps with lower edge close to vanishing frequency may arise in such bio-inspired periodic structures and attenuated propagation of elastic waves may be dominant in the range of higher frequencies. It may cast light on the dynamic strengthening mechanisms in nacre-like materials and provide a scientific basis for the design of bio-inspired metamaterials with low-frequency bandgaps.

Formulation and Stability Analysis of a Multi-Scale Modeling Approach for Simulation of Elastic Wave Propagation

In this work, we report on the formulation and detailed stability analysis of a dynamic multi-scale scheme involving two different local computational strategies for modeling of elastic wave propagation. The coupled model involves the Local Interaction Simulation Approach and Cellular Automata for Elastodynamics, however the presented analysis approach is general and applies to other numerical techniques. This scheme is capable of coupling two numerical models with possibly dissimilar spatial discretization lengths and material properties, hence it is appealing for a multi-scale and/or multi-resolution analysis. The method developed in this paper employs an interface force–displacement coupling to yield the multi-scale model equations. It is shown that the governing equations contain a self-coupling term that affects the stability of the system, as it contributes to additional stiffness at the interface. Stability analysis is presented in terms of rotations of two vectors in [Formula: see text] space, where each vector represents individual model’s stability. Three model configurations of practical interest were investigated, analytical formulae derived and used to analyze stability. These analytical formulae were compared against results from numerical simulations and perfect agreement was observed.

Wave propagation in glass fibre-reinforced polymer (GFRP) bars subjected to progressive damage—Experimental and numerical results

Glass fibre reinforced polymer (GFRP) is a material of increasing interest in civil engineering applications. It is used as internal reinforcement for concrete structures (especially in extremely corrosive environments), as well as structural profiles, plates, and gratings. However, estimating the life of GFRP structures represents a challenge for the construction industry. To address this challenge, a numerical model of elastic wave propagation in GFRP bars is presented in this paper so that it can be used to reduce the number of physical testing required to estimate the degradation of GFRP bars in the field.The proposed numerical model is designed to assist the application of ultrasonic non-destructive testing (NDT) techniques and develop a framework for the evaluation of progressive damage of GFRP bars due to a highly alkaline environment. The proposed methodology consists of: (i) development and calibration of a numerical model of elastic wave propagation in GFRP bars in Abaqus, (ii) simulation of deterioration of the bars, and (iii) comparison of experimental, large and low strain tests (shear test and ultrasonic evaluation) with results of numerical simulations.The results show that the model (low strain properties) correctly captures the deterioration rates seen in the shear strength test (large strains). The model is used to study ultrasonic features and demonstrates that low strain measurements (e.g. wave dispersion, wave amplitude) can be used to estimate the effect of progressive damage on large strain properties in GFRP bars, which can result in a decreased number of required destructive tests.

Investigation of acoustic fields in the arctic zone with uneven ice cover

A mathematical model for elastic wave propagation in an ice cover with uneven relief (hummock) has been developed. The theoretical model is based on the application of “directed” Green’s functions. We obtained numerical results for different distances between radiating and receiving antennas installed inside the ice layer and in water medium. An information-measuring system was created to investigate elastic acoustic waves along ice surface based on electo-hydraulic generator. Experiments of high-frequency acoustic signal propagation from electro-hydraulic generator in water-ice-air system were carried out. We illustrated the model validity for the investigation of hydroacoustic wave propagation in real ice conditions.

Systematic development of upwind numerical fluxes for the space discontinuous Galerkin method applied to elastic wave propagation in anisotropic and heterogeneous media with physical interfaces

This research work presents, within a unified and wave oriented variational framework, systematic development of upwind numerical fluxes for the space discontinuous Galerkin methods to model elastic wave propagation in multidimensional anisotropic media with discontinuous material properties. Both first-order velocity–stress and velocity–strain wave formulations are considered. The proposed approach allows the derivation of upwind numerical fluxes in a well structured and hierarchical way according to the degree of inhomogeneity across a physical interface. The numerical fluxes that are exact solutions of a relevant Riemann problem defined at a physical interface are obtained. The developed explicit and intrinsic tensorial expressions of upwind numerical fluxes in multidimensional case allow a better understanding and analysis of the physical meaning of involved terms. As numerical applications, an example with a physical interface separating two materials, one anisotropic and the other isotropic, and an example of polycrystalline material that presents a particular case with a larger number of physical interfaces, are considered. The proposed numerical fluxes are numerically investigated and validated.

Predicting the response of locally resonant concrete structure under blast load

Abstract Ternary locally resonant metamaterial (LRM) is a manmade material consisting of rigorously designed heavy inclusions with coated soft layer. Such design enables the LRM to possess good wave-filtering characteristics that differ from the matrix materials. Researches of application of this new material for seismic isolation and sound insulation in civil engineering have been reported. In recent decades, there has been an increasing demand to protect civil engineering structures against the effects of blast loading. When blast wave acts on a concrete structure, complex stress waves are generated and propagate in the structure. The wave-filtering characteristics of LRM have brought inspiration to investigate its potential application to reduce the stress wave propagation and hence the damage to cementitious material and enhance the performance of structures under blast wave. By embedding heavy inclusions with soft coating layer into mortar matrix, the product can be named as ternary locally resonant concrete (ternary LRC). Previous studies of the performances of ternary LRC structures are mainly limited to finite element (FE) modeling of elastic wave propagation. The study of the performance of ternary LRC structure subjected to blast loading and the influence of blast loading-induced damage to LRC structure on stress wave propagation is very limited. This paper carries out analytical derivation and numerical modelling to study the mechanism and performance of ternary LRC structure under blast loading. The strain rate effect and material damage of the mortar matrix are considered in numerical simulation. The influence of different material inclusions (natural aggregates and lead), different elastic modulus and thickness of the soft coating on the response of ternary LRC structure are studied. The results show that the ternary LRC can effectively reduce the damage of ternary LRC structure subjected to blast loading.

A high-order multiscale finite-element method for time-domain elastic wave modeling in strongly heterogeneous media

Efficient and accurate numerical methods for elastic wave modeling in complex media have many important applications. However, it is fairly challenging to model elastic wave propagation in strongly heterogeneous media with high computational efficiency and high-order accuracy simultaneously. We develop a novel high-order multiscale finite-element method to model elastic wave propagation in strongly heterogeneous media in the time domain. The most important feature of our method is a generalization of standard multiscale finite element method by using high-order multiscale finite-element basis functions to capture the fine-scale heterogeneities on the coarse mesh, in contrast to conventional finite-element basis functions that are merely determined by the order of polynomials. These multiscale basis functions leads to a system matrix with significantly reduced dimension, thus enable us to solve the elastic wave equation on the coarse mesh with high-order accuracy and very low computational time cost. We use 2D and 3D numerical examples to demonstrate the superior efficiency and accuracy of our new modeling method compared with the conventional spectral-element method.

A stabilized explicit approach to efficiently analyse wave propagation through coupled fluid–structure models

In this paper, a stabilized, locally defined, explicit approach is considered to analyse coupled acoustic–elastic wave propagation models. In this sense, a modified central difference method is applied, which performs adapting itself along the solution process, considering the properties and results of the model, as well as the relations between the adopted temporal and spatial discretizations. The proposed technique enables stabilized decoupled analyses, allowing each subdomain of the coupled model to be handled separately, without considering stability restrictions for the temporal discretization, providing a very versatile and efficient methodology. In addition, the new approach is designed as a single-solve framework based on reduced systems of equations, which further greatly improves the efficiency of the technique. The new method enables adaptive algorithmic dissipation in the higher modes and it is highly accurate, simple to implement and entirely automatized, requiring no decision or expertise from the user. Numerical results are presented at the end of the manuscript, illustrating the performance and effectiveness of the new approach.