Model-Assisted Guided-Wave-Based Approach for Disbond Detection and Size Estimation in Honeycomb Sandwich Composites.

One of the axioms of structural health monitoring states that the severity of damage assessment can only be done in a learning mode under the supervision of an expert. Therefore, a numerical analysis was conducted to gain knowledge regarding the influence of the damage size on the propagation of elastic waves in a honeycomb sandwich composite panel. Core-skin debonding was considered as damage. For this purpose, a panel was modelled taking into account the real geometry of the honeycomb core using the time-domain spectral element method and two-dimensional elements. The presented model was compared with the homogenized model of the honeycomb core and validated in the experimental investigation. The result of the parametric study is a function of the influence of damage on the amplitude and energy of propagating waves.

Influence of different factors on coseismic deformation of the 2015 Mw7.8 earthquake in Nepal.

In Geophysics, topographic factors are observations that can be directly measured, but they are often ignored to simplify the model. Studying the coseismic deformation caused by earthquakes helps accurately determine the epicenter's parameterization. It provides a reference for the reasonable layout of coseismic observation stations and GNSS observation stations. After the Mw7.8 earthquake in Nepal in 2015, GCMT, USGS, GFZ, CPPT, and other institutions released their epicenter parameter. However, according to their parameters, the coseismic displacements simulated by the spectral-element method are quite different from the GNSS observations. Firstly, this paper inverts the geometric parameters of the seismogenic fault with Nepal's coseismic GNSS displacement. The spectral-element method determines the source's location and depth under the heterogeneous terrain and outputs the source parameters. Among the results of many studies, the surface source is more consistent with the generation mechanism of large earthquakes. Secondly, this paper calculates the fault slip distribution of this earthquake using SDM (Steepest Descent Method) based on GNSS and InSAR data, which is divided into 1500 subfaults, and the moment tensor of each subfault is calculated. This paper investigates the distribution characteristics of the coseismic deformation field of the 2015 Mw 7.8 earthquake in Nepal under three different models. The results show that the influence of topographic factors is ~ 20%, and the influence of heterogeneous factors is ~ 10%. This paper concludes that the influence of topographic factors is much more significant than that of heterogeneous factors, and the influence of both should be addressed in coseismic deformation calculations.

Convolutional neural network and level-set spectral element method for ultrasonic imaging of delamination cavities in an anisotropic composite structure.

We present a computational approach that incorporates a convolutional neural network (CNN) for detecting internal delamination in a layered 2D plane-strain anisotropic composite structure of transient elastodynamic fields. The two-dimensional spectral element method (SEM) is utilized to simulate the propagation of elastic waves in an orthotropic solid sandwiched by isotropic solids and their interaction with the internal delamination cavity. This work generates training data consisting of input-layer features (i.e., measured wave signals) and output-layer features (i.e., element types, such as void or regular, of all elements in a domain). To accelerate training data generation, we utilize explicit time integration (e.g., the Runge-Kutta scheme) coupled with an SEM wave solver. Applying the level-set method additionally avoids having to perform an expensive re-meshing process for every possible configuration of the delamination cavities during the data-generation phase. The CNN is trained to classify each element as a non-void or void element from the measured wave signals. Clusters of identified void elements reconstruct targeted cavities. Once our neural network is trained using synthetic data, we analyze how effectively the CNN performs on synthetic measurement data. To this end, we use blind test data from a third-party simulator that explicitly models the traction-free boundary of cavities for anisotropic materials without the application of the level-set method. Our numerical examples show that our approach can effectively detect the internal cavities in an anisotropic structure made of aluminum and carbon fiber-reinforced epoxy using the measured elastic waves without any prior information about the cavities' locations, shapes, and numbers. The presented method can be extended into a more realistic 3D setting and utilized for the nondestructive test of various anisotropic composite structures.

Towards quantifying the effect of pump wave amplitude on cracks in the Nonlinear Coda Wave Interferometry method.

In Non-Destructive Testing and Evaluation (NDT&E), an ultrasonic method called Nonlinear Coda Wave Interferometry (NCWI) has recently been developed to detect cracks in heterogeneous materials such as concrete. The underlying principle of NCWI is that a pump wave is used to activate the crack breathing which interact with the source probe signal. The resulting signal is then measured at receiver probes. In this work, a static finite element model (FEM) is used to simulate the pump wave/crack interaction in order to quantifies the average effect of the pump waves on a crack. By considering both crack opening and closure phases during the dynamic pump wave excitation, this static model aims to determine the pump stress amplitude for a given relative crack length variation due to the dynamic pump wave excitation at different amplitudes. Numerical results show, after reaching certain stress amplitude, a linear relationship between the relative crack length variation and the equivalent static load when considering a partially closed crack at its tips. Then, numerical NCWI outputs, e.g., the relative velocity change θ and the decorrelation coefficient Kd, have been calculated using a spectral element model (SEM). These results agree with previously published experimental NCWI results derived for a slightly damaged 2D glass plate.

A Finite/Spectral Element Hybrid Method for Modeling and Band-Gap Characterization of Metamaterial Sandwich Plates.

In this study, elastic metamaterial sandwich plates with axially deformed Timoshenko beam cores, considering both the out-of-plane and in-plane deformations of the face plates, are designed and the vibration band-gap properties are explored. The beam cores act as local resonators that can bear axial force, bending moment and shearing force. The finite element method (FEM) and the spectral element method (SEM) are combined to create the finite/spectral element hybrid method (FE-SEHM) for establishing the dynamic model and calculating the frequency response functions (FRFs) of the elastic metamaterial sandwich plate with axially deformed beam cores. It is observed that the metamaterial sandwich plate possesses both the axial and transverse vibration band-gaps of the beams, and the two kinds of band-gaps are independent. Compared with the metamaterial sandwich plates with rod cores, those with axially deformed beam cores have more extensive application ranges for vibration reduction.

Spectral element modeling of ultrasonic guided wave propagation in optical fibers.

Recent advancements in fiber optic methods have enabled their use for guided wave sensing. It opens up new possibilities for Structural Health Monitoring. The aim of this paper is to provide insight for the physics related to guided wave propagation and coupling between the optical fiber and solid structure. For this purpose, a new approach for non-matching interface based on Lagrange multipliers and the time domain spectral element method was developed. A parallelized code has been implemented in order to simulate the guided wave propagation in the structure, its coupling into the optical fiber and the propagation in the fiber in a computationally efficient way. The paper presents four studies showing the efficacy of the modeling approach. The paper first shows the improvement in the computation speed through the use of parallelization and a more efficient implementation. Then the results of the simulation of wave propagation in the fiber are compared with results from previous simulation studies using commercially available software. The third study shows that the spectral element method is able to capture the directional sensitivity of optical fiber based sensors. Lastly, the simulation is used for detection of simulated damage using the spectral element method based simulation. The results indicate that indeed the spectral element implementation is able to recreate the wave coupling phenomena, capture the physics of the system including directional sensitivity and reflections from damage.

Conservation of Forces and Total Work at the Interface Using the Internodes Method.

The Internodes method is a general purpose method to deal with non-conforming discretizations of partial differential equations on 2D and 3D regions partitioned into disjoint subdomains. In this paper we are interested in measuring how much the Internodes method is conservative across the interface. If hp-fem discretizations are employed, we prove that both the total force and total work generated by the numerical solution at the interface of the decomposition vanish in an optimal way when the mesh size tends to zero, i.e., like O ( h p ) , where p is the local polynomial degree and h the mesh-size. This is the same as the error decay in the H 1-broken norm. We observe that the conservation properties of a method are intrinsic to the method itself because they depend on the way the interface conditions are enforced rather then on the problem we are called to approximate. For this reason, in this paper, we focus on second-order elliptic PDEs, although we use the terminology (of forces and works) proper of linear elasticity. Two and three dimensional numerical experiments corroborate the theoretical findings, also by comparing Internodes with Mortar and WACA methods.

Numerical parametric study of Nonlinear Coda Wave Interferometry sensitivity to microcrack size in a multiple scattering medium.

This paper reports a numerical study of the sensitivity and applicability of the Nonlinear Coda Wave Interferometry (NCWI) method in a heterogeneous material with a localized microcracked zone. We model the influence of a strong pump wave on the localized microcracked zone as a small average increase in the length of each crack. Further probing of this microcracked zone with a multiply scattered ultrasonic wave induces small changes to the coda-type signal, which are quantified with coda wave interferometry. A parametric sensitivity study of the CWI observables with respect to the changes in crack length is established via numerical simulations of the problem using a 2D spectral element method (SEM2D). The stretching of the signal, proportional to the relative variation in effective velocity, is found to be linearly proportional to the global change in crack length, while the other CWI parameter, the remnant decorrelation coefficient, is found to be quadratically proportional to the crack length change. The NCWI method is shown to be relevant for the detection of different damaged material states in complex solids. The reported numerical results are especially significant in the context of quantitative nondestructive evaluation of micro-damage level of a heterogeneous materials using nonlinear ultrasound signals.

Vibration Analysis of Fluid Conveying Carbon Nanotubes Based on Nonlocal Timoshenko Beam Theory by Spectral Element Method.

In this work, we applied the spectral element method (SEM) to analyze the dynamic characteristics of fluid conveying single-walled carbon nanotubes (SWCNTs). First, the dynamic equations for fluid conveying SWCNTs were deduced based on the nonlocal Timoshenko beam theory. Then, the spectral element formulation was established for a free/forced vibration analysis of fluid conveying SWCNTs by introducing discrete Fourier transform. Furthermore, the proposed method was validated using several comparison examples. Finally, the natural frequencies and dynamic responses of a simply-supported fluid conveying SWCNTs were calculated by the SEM, considering different internal fluid velocities and small-scale parameters (SSPs). The effects of fluid velocity and SSPs on the dynamic characteristics of SWCNTs conveying fluid were revealed by the numerical results. Compared with other methods, the SEM shows high accuracy and efficiency.

Transmission of Lamb waves across a partially closed crack: Numerical analysis and experiment.

The transmission characteristics of Lamb waves across a partially closed through-thickness crack in a plate are investigated numerically and experimentally. In the numerical analysis, the spectral element method is used to simulate the transmission of the lowest-order symmetric (S0) and antisymmetric (A0) Lamb modes across a crack in a low-frequency range. The analysis is carried out for an open crack with traction-free surfaces as well as for a partially closed crack modeled as a spring-type interface characterized by normal and tangential stiffnesses. The transmission ratios of both modes are obtained from the spectral amplitude of the simulated transmission waveforms for different crack lengths and interfacial stiffnesses. The numerical results show that the transmission ratio of the S0 mode increases monotonically with the interfacial stiffness, but that of the A0 mode depends on the interfacial stiffness in a non-monotonic manner depending on the frequency. The Lamb wave transmission measurements are carried out for aluminum alloy plates with artificial slits or a fatigue crack. The experimental results for the plates with slits show reasonable agreement with the numerical results for open cracks. The measured transmission ratio of the S0 mode is shown to decrease with the tensile load applied to the plate, but that of the A0 mode shows different load dependence for different frequencies. The qualitative features of the experimental results for the fatigue crack are discussed based on the numerical simulation for closed cracks.

Nonlinear Coda Wave Interferometry: Sensitivity to wave-induced material property changes analyzed via numerical simulations in 2D.

The numerical studies conducted in this paper are based on our previous research (Chen et al., 2017); through use of the spectral element method, parametric sensitivity studies of Nonlinear Coda Wave Interferometry (NCWI) are established here and divided into two parts. In the first part, CWI observables are found to be proportional to the product of the changes in elastic modulus within the Effective Damaged Zone (EDZ) and the EDZ surface area. The modifications to intrinsic properties are quantified via an overall wave velocity variation, as probed by a reverberated coda wave. However, for high-level changes, CWI may fail due to meaningless decorrelation values. In this context, parametric studies are conducted to yield a maximum range for EDZ contrast and area. To further validate these observations using a more realistic numerical model, instead of introducing a homogeneous EDZ model, the second part of this paper adds random cracks with random orientations into the EDZ of a material sample. The influence of a strong pump wave on localized nonlinear damage is reestablished; results show that the cracks added into the EDZ reduce the property changes required to match the previous experimental dataset.

Fractional modeling of viscoelasticity in 3D cerebral arteries and aneurysms.

We develop efficient numerical methods for fractional order PDEs, and employ them to investigate viscoelastic constitutive laws for arterial wall mechanics. Recent simulations using one-dimensional models [1] have indicated that fractional order models may offer a more powerful alternative for modeling the arterial wall response, exhibiting reduced sensitivity to parametric uncertainties compared with the integer-calculus-based models. Here, we study three-dimensional (3D) fractional PDEs that naturally model the continuous relaxation properties of soft tissue, and for the first time employ them to simulate flow structure interactions for patient-specific brain aneurysms. To deal with the high memory requirements and in order to accelerate the numerical evaluation of hereditary integrals, we employ a fast convolution method [2] that reduces the memory cost to O(log(N)) and the computational complexity to O(N log(N)). Furthermore, we combine the fast convolution with high-order backward differentiation to achieve third-order time integration accuracy. We confirm that in 3D viscoelastic simulations, the integer order models strongly depends on the relaxation parameters, while the fractional order models are less sensitive. As an application to long-time simulations in complex geometries, we also apply the method to modeling fluid-structure interaction of a 3D patient-specific compliant cerebral artery with an aneurysm. Taken together, our findings demonstrate that fractional calculus can be employed effectively in modeling complex behavior of materials in realistic 3D time-dependent problems if properly designed efficient algorithms are employed to overcome the extra memory requirements and computational complexity associated with the non-local character of fractional derivatives.

High-order space-time finite element schemes for acoustic and viscodynamic wave equations with temporal decoupling.

We revisit a method originally introduced by Werder et al. (in Comput. Methods Appl. Mech. Engrg., 190:6685-6708, 2001) for temporally discontinuous Galerkin FEMs applied to a parabolic partial differential equation. In that approach, block systems arise because of the coupling of the spatial systems through inner products of the temporal basis functions. If the spatial finite element space is of dimension D and polynomials of degree r are used in time, the block system has dimension (r + 1)D and is usually regarded as being too large when r > 1. Werder et al. found that the space-time coupling matrices are diagonalizable over [Formula: see text] for r ⩽100, and this means that the time-coupled computations within a time step can actually be decoupled. By using either continuous Galerkin or spectral element methods in space, we apply this DG-in-time methodology, for the first time, to second-order wave equations including elastodynamics with and without Kelvin-Voigt and Maxwell-Zener viscoelasticity. An example set of numerical results is given to demonstrate the favourable effect on error and computational work of the moderately high-order (up to degree 7) temporal and spatio-temporal approximations, and we also touch on an application of this method to an ambitious problem related to the diagnosis of coronary artery disease. Copyright © 2014 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.