Displacement Field Research Articles

Displacement field monitoring of tunnel faces using terrestrial laser scanning data

The instability of tunnel faces is a serious geological hazard, thus requiring monitoring and prediction of the stability of tunnel faces. This paper presents a high-accuracy method for estimating the displacement fields of tunnel faces from terrestrial laser scanning data. The proposed method consists of four parts: i) the development of a stable rigid-body reference under planar strain assumption, ii) the fine alignment of the rigid-body references using the developed local deformation constrained rigid-body assumption (LDC-RBA) and local cross-validation iterative closest point (LCV-ICP) algorithm, iii) the segmentation of tunnel faces using a machine learning classifier, and iv) tracking of tunnel face displacement vectors under the LDC-RBA. Qualitative experimental results demonstrate that the estimated displacement fields of the tunnel face using the proposed method conform to the deformation law. Furthermore, quantitative experimental results indicate that the estimation accuracy of tunnel face displacement fields achieves millimeter-level.

Evanescent Acoustic Waves

A theoretical study of “geometric” SP-evanescent (head) waves propagating in an isotropic homogeneous half-space or half-plane with a free boundary shows that these waves can satisfy the condition of absence of effort on the boundary plane if and only if the Lamé parameter λ is vanishingly small, which makes the existence of head waves of this type practically impossible. The analysis is based on the Helmholtz representation for the displacement field in combination with the decomposition of the stress and strain tensor into spherical and deviatoric parts. The obtained result about the non-existence of this type of evanescent waves can find application in theoretical geophysics in the study of seismic wave fields in the vicinity of earthquake epicenters, as well as in non-destructive acoustic diagnostic methods.

Infrared Spectroscopy of Phase Transitions in the Lowest Landau Levels of Bilayer Graphene.

We perform infrared magnetospectroscopy of Landau level (LL) transitions in dual-gated bilayer graphene. At ν=4 when the zeroth LL (octet) is filled, two resonances are observed indicating the opening of a gap. At ν=0 when the octet is half-filled, multiple resonances disperse nonmonotonically with increasing displacement field, D, perpendicular to the sheet, showing a phase transition at modest displacement fields from a canted antiferromagnet (CAFM) to the layer-polarized state, with a gap that opens linearly in D. When D=0 and ν is varied, resonances at ±ν show an electron-hole asymmetry with multiple line splittings as the octet is progressively filled. The ν=4 data show good agreement with predictions from a mean-field Hartree-Fock calculation when accounting for multiple tight-binding terms in a four-band model of bilayer graphene. However, even by incorporating a valley interaction anisotropy tuned to the CAFM ground state, only partial agreement is found at ν=0. Our results suggest additional physics is required to understand bilayer graphene at half-filling.

On the velocity-stress formulation for geometrically nonlinear elastodynamics and its structure-preserving discretization

ABSTRACT We consider the dynamics of an elastic continuum under large deformation but small strain. Such systems can be described by the equations of geometrically nonlinear elastodynamics in combination with the St. Venant-Kirchhoff material law. The velocity-stress formulation of the problem turns out to have a formal port-Hamiltonian structure. In contrast to the linear case, the operators of the problem are modulated by the displacement field which can be handled as a passive variable and integrated along with the velocities. A weak formulation of the problem is derived and essential boundary conditions are incorporated via Lagrange multipliers. This variational formulation explicitly encodes the transfer between kinetic and potential energy in the interior as well as across the boundary, thus leading to a global power balance and ensuring passivity of the system. The particular geometric structure of the weak formulation can be preserved under Galerkin approximation via appropriate mixed finite elements. In addition, a fully discrete power balance can be obtained by appropriate time discretization. The main properties of the system and its discretization are shown theoretically and demonstrated by numerical tests.

Numerical analysis of the stress‐based formulation of linear elasticity

AbstractThe Beltrami–Michell equations of linear elasticity differ from the Navier–Cauchy equations, in that the primary field in former equations is the stress tensor rather than the displacement vector. Consequently, the equations can be used for circumstances where the displacement field is not of interest, for example in design, or when increased smoothness of the solution of the stress tensor is desired. In this work, we explore the stress‐based Beltrami–Michell equations for isotropic linear elastic materials. We introduce the equations in modern tensor notation and investigate their limitations. Further, we demonstrate how to symmetrise and stabilise their weak formulation, complemented by existence and uniqueness proofs. With latter at hand, we construct a conforming finite element discretisation of the equations, avoiding the need for intermediate stress functions. Finally, we present some numerical examples.

Vector field attention for deformable image registration.

Deformable image registration establishes non-linear spatial correspondences between fixed and moving images. Deep learning-based deformable registration methods have been widely studied in recent years due to their speed advantage over traditional algorithms as well as their better accuracy. Most existing deep learning-based methods require neural networks to encode location information in their feature maps and predict displacement or deformation fields through convolutional or fully connected layers from these high-dimensional feature maps. We present vector field attention (VFA), a novel framework that enhances the efficiency of the existing network design by enabling direct retrieval of location correspondences. VFA uses neural networks to extract multi-resolution feature maps from the fixed and moving images and then retrieves pixel-level correspondences based on feature similarity. The retrieval is achieved with a novel attention module without the need for learnable parameters. VFA is trained end-to-end in either a supervised or unsupervised manner. We evaluated VFA for intra- and inter-modality registration and unsupervised and semi-supervised registration using public datasets as well as the Learn2Reg challenge. VFA demonstrated comparable or superior registration accuracy compared with several state-of-the-art methods. VFA offers a novel approach to deformable image registration by directly retrieving spatial correspondences from feature maps, leading to improved performance in registration tasks. It holds potential for broader applications.

An Analytical Approach for the Near‐Tip Field Around V‐Notch in Orthotropic Materials

ABSTRACTThis study introduces a novel theoretical framework for determining the notch stress intensity factors (NSIFs) in composite materials. The approach involves utilizing Irwin's complex stress functions for Mode I and Mode II loading conditions. By investigating displacement and singular stress components around V‐notch tips, the research aims to provide a comprehensive understanding of NSIFs in composite materials. Three different composite materials were considered in the study to explore the relationship between stress and material properties. The stress singularity order, denoted as , is determined through eigenequations. Moreover, explicit solutions for displacement and singular stress fields are derived for a more thorough understanding of the behavior around notches in composite materials. To validate the proposed theoretical framework, a rigorous numerical study is conducted using FEM on finite‐size notches. The results obtained from the numerical simulations are compared with theoretical predictions to assess the accuracy and reliability of the developed approach.

Three-dimensional peridynamic simulation on triaxial compression failure mechanical behavior of cylindrical marble specimen containing pre-existing fissures

A series of triaxial compression experiments and analyses were conducted out by using the three-dimensional bond-based peridynamics (BB-PD) model to investigate the mechanical behavior, deformability, and failure behavior of marble samples under different confining pressures. This study assessed the impact of confining pressure on mechanical performance of the intact marble, calibrated PD model micro-parameters using experimental data, and predicted the fissure behavior of marble specimens with single or parallel fissures. Through detailed analysis of crack evolution, crack pattern, displacement fields, and principal stress fields, the research revealed that the ductility of marble depended on the confining pressure, especially in the presence of fissures. Increasing confining pressure facilitated a transition from splitting failure to conjugate shear failure modes and induced stress concentration at fissure tips, leading to wing cracks and secondary cracks initiation. The presence and number of fissures were found to directly influence the mechanical behavior and failure process complexity of marble. A higher number of fissures reduced brittleness and strength while enhancing ductility and variety of failure modes. Seven distinct failure patterns of marble were identified under triaxial compression, illustrating the combined effect of confining pressure and fissures on marble specimen failure modes. This work can provide a theoretical and numerical basis for fissured rocks fracture in deep engineering.

Modeling via peridynamics for damage and failure of hyperelastic composites

Modeling damage and failure behaviors of hyperelastic composites under large deformations is pivotal for advancing the design of cutting-edge elastomers used in biomedical engineering and soft robotics. However, existing methods struggle with capturing the non-linearities and singularities in the displacement field under such conditions. To address these difficulties, we propose a novel bond-based peridynamics (PD) framework with multiple advancements. First, we develop a PD bond strain model grounded in the nonlinear Piola-Kirchhoff stress-stretch relationship, precisely capturing hyperelasticity and ensuring full compliance with thermodynamic laws and kinematics in large deformation scenarios. Second, our framework employs a particle discretization technique that not only sidesteps the mesh distortion issues commonly encountered in grid-based methods subjected to large deformation but also significantly lowers the computational complexity due to the ease of numerical implementation of random inclusion distributions. Third, we propose, for the first time, a refined 3D hyperelastic model within the PD framework that enables a more comprehensive and accurate prediction of material responses to external loads, surpassing the limitations of conventional 2D simulations. Validation against experimental data demonstrates that our model accurately captures key physical phenomena in hyperelastic composites, such as spontaneous crack initiation and propagation, interface debonding, crack coalescence, and the formation of non-smooth crack surfaces. Crucially, this framework is versatile and adaptable to a wide range of engineered composite systems with different inclusions and matrices, making it a powerful tool for predicting and analyzing large deformation behaviors in various advanced applications.

Analysis of the influence of bottom flow holes in control rod guide tubes on flow field and control rod displacement

During the operation of pressurized water reactors, flow-induced vibration issues are commonly encountered, where control rod components vibrate due to the impact of coolant flow, leading to wear, thereby posing a threat to the safe operation of the reactor. This paper conducts a detailed numerical simulation of the flow field and force distribution inside a full-scale lower control rod guide tube based on the CFD method. The fluid–structure interaction analysis is performed to reveal the influence of cross-flow under various operating conditions on the vibration and displacement of control rods. The research subject consists of 24 control rods, one continuous guide section, and six control rod guide cards. The lower part of the guide tube has two flow holes on each surface, with one assumed to be a cross-flow inlet and the others as outlets. The results indicate that when considering the cross-flow effect at the flow holes, 90 % of the coolant flows out from other flow holes at the bottom of the guide tube, resulting in increased transverse velocity at the bottom and the presence of numerous vortices. The magnitude and location of the force exerted on the control rod by coolant impact are correlated. The control rod closest to the inlet of the flow hole experiences the greatest force, approximately 5.35 times the average at other positions. At a cross-flow velocity of 0.4 m/s and a low frequency of 10 Hz, the maximum displacement of the control rod is 0.3355 mm.

Combining artificial intelligence with different plasticity induced crack closure criteria to determine opening and closing loads on a three-dimensional centre cracked specimen

Fracture due to fatigue crack growth remains a significant failure mode in both brittle and ductile materials. When dealing with crack tip plasticity induced phenomena, characterized by high strain and stress field gradients, only highly refined meshes around the crack tip can produce accurate results. Therefore, optimized mesh parameters must be used, in order to achieve high quality models with low computational costs. In this study, artificial intelligence models and a numerical three-dimensional model for a middle tension specimen were combined to enhance crack closure and opening loads assessment. The numerical accuracy was analysed based on the estimated stress and strain fields, plastic zone shape and size and crack closure and opening load values. Two artificial neural networks were trained using four different crack lengths, mesh sizes and simulated plastic wakes. The networks were capable of stress and strain field predictions and crack opening and closure load determination. It was verified that the crack stress criterion is strongly correlated with the principal strain field and the displacement field around the crack tip, providing a viable way to analyse plasticity induced crack closure.

Modeling Challenges and Limitation Principles of Reissner’s Mixed Approaches to Laminates

Displacement-based formulations for composite structures are directly linked to the functional called the Principle of Virtual Displacements and present the minimum number of independent modeled fields, which are the displacements. However, these models usually provide an inadequate approximation of the transverse stress fields and suffer from pathological numerical problems. These issues have been addressed with the introduction of mixed variational formulations where independent stress fields are included in the definition of the corresponding functionals. Particularly effective and widely used are Reissner’s mixed variational theorem and Hellinger–Reissner Principle. Both Reissner’s mixed variational theorem and Hellinger–Reissner principle allow the a priori enforcing of the interlaminar equilibrium because of the axiomatic modeling of the transverse stresses. However, these functionals are different and present their own challenges. Under certain circumstances, Reissner’s Mixed Variational Theorem was shown to produce thickness oscillations of the displacements and transverse stresses. It was not clear if Hellinger-Reissner Principle had similar properties. It is shown that both functionals may present numerical oscillations. Moreover, the reconstructed displacement and stress fields are actually identical between Reissner’s Mixed Variational Theorem and Hellinger-Reissner Principle if the orders of the in-plane stresses of the Hellinger–Reissner Prinicple case are sufficiently large. In other words, a Hellinger–Reissner Principle/Reissner’s Mixed Variational Theorem Limitation Principle is shown to exist in addition to the well-studied limitation principle between Hellinger–Reissner principle and principle of virtual displacements.

Constructing Surrogate Lung Ventilation Maps from 4DCT-derived Subregional Respiratory Dynamics

PurposeTo present a two-stage framework that robustly extracts and maps reliable lung ventilation surrogates based on subregional respiratory dynamics (SRD) measured from four-dimensional computed tomography (4DCT) images, with comprehensive consideration of spatial and temporal heterogeneity in the ventilation process over the respiratory cycle. Materials and MethodsWe retrospectively analyzed three subject cohorts from the VAMPIRE challenge containing 4DCT and reference ventilation imaging (RefVI) scans. Lung subregions were partitioned on the 4DCT end-of-exhale base phase using anatomically constrained simple linear iterative clustering, while sliding-preserved interphase image registrations were performed between the base and other phases. SRDs of breathing-induced volume and intensity changes were tracked across phases utilizing the displacement fields. Voxel-level representations integrating mechanical collapsibility and physiological tissue density (VSRD) were accordingly constructed from SRDs. Imaging performance of VSRD as the proposed surrogate ventilation map was studied against RefVI scans and compared to classical biphasic Jacobian maps. The dosimetric performance evaluation was also conducted to assess the clinical benefits of incorporating VSRD maps into functional lung avoidance radiotherapy (FLA-RT) planning. ResultsThe extracted SRD highlighted temporally varying subregional volume and CT intensity changes related to underlying functional physiology and pathologies. For imaging performance, the median Spearman correlation coefficients between VSRD and RefVI scans were 0.600, 0.582, and 0.561 for the three cohorts, while median Dice similarity coefficients against RefVI scans showing the high(low)-functioning lung regions’ concordances, were 0.611(0.626), 0.592(0.620), and 0.601(0.611), superior to biphasic Jacobian maps for both metrics. For dosimetric performance, VSRD-guided FLA-RT plans achieved significantly better dose sparing of high-functioning lung regions compared to FLA-RT plans based on biphasic Jacobian maps. ConclusionsVSRD maps captured spatial and temporal heterogeneity in the ventilation process, providing improved ventilation representations compared to classical algorithms. The capability to extract multidimensional ventilation-correlated image information from widely available 4DCT images showed promise in enhancing personalized FLA-RT implementations.

Electrostatic-elastic coupling in colloidal crystals

Electrostatic-elastic coupling in colloidal crystals, composed of a mobile Coulomb gas permeating a fixed background crystalline lattice of charged colloids, is studied on the continuum level in order to analyze the lattice-mediated interactions between mobile charges. The linearized, Debye-Hückel–like mean-field equations incorporating a minimal coupling between electrostatic and displacement fields imply an additional effective attractive interaction between mobile charges. For small screening lengths, the interactions between like mobile charges exhibit colloid-lattice–mediated effective interaction, ranging from weak to strong attraction, while for large screening lengths the lattice-mediated interaction is purely repulsive. Continuum theory incorporating the standard lattice elasticity and electrostatics of mobile charges, augmented by the minimal electrostatic-elastic coupling terms, can serve as a baseline for more detailed microscopic models.

The Influence of Using a Seismically Inferred Magma Reservoir Geometry in a Volcano Deformation Model for Soufrière Hills Volcano, Montserrat

AbstractVolcano deformation models contribute to hazard assessment by simulating magma system dynamics. Traditional magma reservoir pressure source shape assumptions often fail to replicate irregular, geophysically identified geometries. Uncertainties regarding the influence of reservoir geometry can limit the effectiveness of using deformation models to decipher unrest signals. Here, we aim to determine the feasibility of using a magma reservoir geometry directly derived from a seismic tomography survey in a volcano deformation model for Soufrière Hills Volcano, Montserrat. Three‐dimensional deformation models are created to simulate displacement using a pressure source geometry constrained from a low seismic velocity anomaly, inferred to be a region of partial melt, and contrasted against a traditional ellipsoid reservoir geometry. We also test a “hybrid” model combining a seismically inferred reservoir upper geometry and ellipsoidal base. Results of each model are evaluated against ground displacement observed on Montserrat from 2010 to 2022. Our results show that different reservoir geometries change the horizontal and vertical displacement fields across the island: the ellipsoid reservoir best reproduces vertical displacement magnitude, while the hybrid reservoirs best simulate horizontal displacement vectors and the region of maximum uplift. Overall, the ellipsoid‐shaped reservoir provides our best‐fit to the observed data, but we note this result could be biased due to prior years of optimization helping constrain the ellipsoid shape, size, and location. Our results show the potential for further use of geophysically constrained reservoir geometries in deformation modeling, and our methods could be applied to other deforming volcanoes worldwide.

GMDIC: a digital image correlation measurement method based on global matching for large deformation displacement fields

The digital image correlation method is a non-contact optical measurement method, which has the advantages of full-field measurement, simple operation, and high measurement accuracy. The traditional DIC method can accurately measure displacement and strain fields, but there are still many limitations. (i) In the measurement of large displacement deformations, the calculation accuracy of the displacement field and strain field needs to be improved due to the unreasonable setting of parameters such as subset size and step size. (ii) It is difficult to avoid under-matching or over-matching when reconstructing smooth displacement or strain fields. (iii) When processing large-scale image data, the computational complexity will be very high, resulting in slow processing speeds. In recent years, deep-learning-based DIC has shown promising capabilities in addressing the aforementioned issues. We propose a new, to the best of our knowledge, DIC method based on deep learning, which is designed for measuring displacement fields of speckle images in complex large deformations. The network combines the multi-head attention Swin-Transformer and the high-efficient channel attention module ECA and adds positional information to the features to enhance feature representation capabilities. To train the model, we constructed a displacement field dataset that conformed to the real situation and contained various types of speckle images and complex deformations. The measurement results indicate that our model achieves consistent displacement prediction accuracy with traditional DIC methods in practical experiments. Moreover, our model outperforms traditional DIC methods in cases of large displacement scenarios.

Superconductivity in twisted bilayer WSe2.

Moiré materials have enabled the realization of flat electron bands and quantum phases that are driven by the strong correlations associated with flat bands1-4. Superconductivity has been observed, but only in graphene moiré materials5-9. The absence of robust superconductivity in moiré materials beyond graphene, such as semiconductor moiré materials4, has remained a mystery and challenged our current understanding of superconductivity in flat bands. Here we report the observation of robust superconductivity in both 3.5° and 3.65° twisted bilayer tungsten diselenide (WSe2), which hosts a hexagonal moiré lattice10,11. Superconductivity emerges near half-band filling and zero external displacement fields. The optimal superconducting transition temperature is about 200 mK in both cases and constitutes about 1-2% of the effective Fermi temperature; the latter is comparable to the value in high-temperature cuprate superconductors12 and suggests strong pairing. The superconductor borders on two distinct metals below and above half-band filling; it undergoes a continuous transition to a correlated insulator by tuning the external displacement field. The observed superconductivity on the verge of Coulomb-induced charge localization suggests roots in strong electron correlations12,13.

Activation of Ms 6.9 Milin Earthquake on Sedongpu Disaster Chain, China with Multi-Temporal Optical Images

In recent years, disaster chains caused by glacier movements have occurred frequently in the lower Yarlung Tsangpo River in southwest China. However, it is still unclear whether earthquakes significantly contribute to glacier movements and disaster chains. In addition, it is difficult to measure the high-frequency and large gradient displacement time series with optical remote sensing images due to cloud coverage. To this end, we take the Sedongpu disaster chain as an example, where the Milin earthquake, with an epicenter 11 km away, occurred on 18 November 2017. Firstly, to deal with the cloud coverage problem for single optical remote sensing analysis, we employed multiple platform optical images and conducted a cross-platform correlation technique to invert the two-dimensional displacement rate and the cumulative displacement time series of the Sedongpu glacier. To reveal the correlation between earthquakes and disaster chains, we divided the optical images into three classes according to the Milin earthquake event. Lastly, to increase the accuracy and reliability, we propose two strategies for displacement monitoring, that is, a four-quadrant block registration strategy and a multi-window fusion strategy. Results show that the RMSE reduction percentage of the proposed registration method reaches 80%, and the fusion method can retrieve the large magnitude displacements and complete displacement field. Secondly, the Milin earthquake accelerated the Sedongpu glacier movement, where the pre-seismic velocities were less than 0.5 m/day, the co-seismic velocities increased to 1 to 6 m/day, and the post-seismic velocities decreased to 0.5 to 3 m/day. Lastly, the earthquake had a triggering effect around 33 days on the Sedongpu disaster chain event on 21 December 2017. The failure pattern can be summarized as ice and rock collapse in the source area, large magnitude glacier displacement in the moraine area, and a large volume of sediment in the deposition area, causing a river blockage.

Spin-orbit proximity in MoS2/bilayer graphene heterostructures

Van der Waals heterostructures provide a versatile platform for tailoring electronic properties through the integration of two-dimensional materials. Among these combinations, the interaction between bilayer graphene and transition metal dichalcogenides (TMDs) stands out due to its potential for inducing spin–orbit coupling (SOC) in graphene. Future devices concepts require the understanding of the precise nature of SOC in TMD/bilayer graphene heterostructures and its influence on electronic transport phenomena. Here, we experimentally confirm the presence of two distinct types of SOC – Ising (ΔI = 1.55 meV) and Rashba (ΔR = 2.5 meV) – in bilayer graphene when interfaced with molybdenum disulfide. Furthermore, we reveal a non-monotonic trend in conductivity with respect to the electric displacement field at charge neutrality. This phenomenon is ascribed to the existence of single-particle gaps induced by the Ising SOC, which can be closed by a critical displacement field. Our findings also unveil sharp peaks in the magnetoconductivity around the critical displacement field, challenging existing theoretical models.

Mesh topology-based spurious pressure stabilization in 3D finite elasticity using Voronoi tessellations

AbstractIn this paper, we present a mesh topology-based stabilization approach to suppress spurious pressure modes in 3D nearly-incompressible finite elasticity. The focus lies on a mixed formulation with lowest-order approximation for the displacement and pressure fields. Motivated by the fact that the popular H1/P0 element does not fulfill the inf-sup condition, all possible local spurious pressure modes are derived on a patch of elements. The nullspace method is used to determine all spurious pressure solutions. From this, the topological requirements of the finite element mesh are established. We conclude that no more than four elements are allowed to intersect in the same vertex to overcome local checkerboarding. To fulfill this requirement, we employ non-degenerate 3D Voronoi diagrams with several different site distributions. These result in random, centroidal, and honeycomb Voronoi meshes. The resulting convex polyhedral elements are discretized by a polyhedral mixed finite element based on the lowest possible interpolation pair. The numerical examples illustrate that spurious pressure modes do not occur for any degree of mesh refinement as long as the topological mesh requirements are met. Furthermore, it is shown that the numerical inf-sup test is passed. By violating the topological requirements, it is shown that a stable pressure field cannot be guaranteed and the checkerboard phenomenon is provoked.