Displacement Field Research Articles

Force and Energy Transmission at the Brain-Skull Interface of the Minipig In Vivo and Post-Mortem

The brain-skull interface plays an important role in the mechano-pathology of traumatic brain injury (TBI). A comprehensive understanding of the mechanical behavior of the brain-skull interface in vivo is significant for understanding the mechanisms of TBI and creating accurate computational models. Here we investigate the force and energy transmission at the minipig brain-skull interface by non-invasive methods in the live (in vivo) and dead animal (in situ). Displacement fields in the brain and skull were measured in four female minipigs by magnetic resonance elastography (MRE), and the relative displacements between the brain and skull were estimated. Surface maps of deviatoric stress, the apparent mechanical properties of the brain-skull interface, and the net energy flux were generated for each animal when alive and at specific times post-mortem. After death, these maps reveal increases in relative motion between brain and skull, brain surface stress, stiffness of brain-skull interface, and net energy flux from skull to brain. These results illustrate the ability to study both skull and brain mechanics by MRE; the observed post-mortem decrease in the protective capability of the brain-skull interface emphasizes the importance of measuring its behavior in vivo.

Sub‐Pixel Displacement Estimation With Deep Learning: Application to Optical Satellite Images Containing Sharp Displacements

AbstractOptical image correlation is a powerful method for remotely constraining ground movement from optical satellite imagery related to natural disasters (e.g., earthquakes, volcanoes, landslides). This approach enables the characterization, and identification of the causal factors and mechanisms underlying such processes. By employing sub‐pixel correlation algorithms, one can obtain highly accurate (m‐to‐cm level) displacement fields at high spatial resolution (dm‐to‐cm) by comparing satellite images acquired before and after a period of movement. However, this method generally assumes a homogeneous translation of all pixels within a given correlation window, which will lead to biased estimates of ground displacement if the real case is not well represented by such a simplification, especially when resolving ground displacements next to sharp gradients in displacement, such as those found in the near‐field of earthquake surface ruptures. In this paper, we present an innovative deep learning method estimating sub‐pixel displacement maps from optical satellite images for the retrieval of ground displacement. From the generation of a realistic simulated database, comprising Landsat‐8 satellite image pairs containing simulated sub‐pixel shifts and sharp discontinuities, we develop a Convolutional Neural Network able to retrieve sub‐pixel displacements. The comparison to state‐of‐the‐art correlation methods shows that our pipeline significantly reduces by 32% the estimation bias around fault ruptures, leading to more accurate characterization of the near‐field strain in surface rupturing earthquakes. Application of our model to the 2019 Ridgecrest earthquake demonstrates the ability of our model to accurately and quickly resolve ground displacement using real satellite images. Code is made available at https://gricad‐gitlab.univ‐grenoble‐alpes.fr/montagtr/cnn4l‐discontinuities.

Enhanced strain mapping Unveils internal deformation dynamics in Silicon-based lithium-ion batteries during electrochemical cycling

Silicon-based anodes have emerged as a promising advancement in lithium-ion battery technology, offering significantly higher lithium storage capacities than traditional graphite. However, the volumetric expansion of silicon—anodes can swell by up to 300 % during lithiation—presents serious challenges to their structural integrity and electrochemical stability. This study investigates the internal structural dynamics of silicon anodes during lithiation and delithiation cycles. A novel cell design for a 18,650 cylindrical cell featuring micro-sized internal speckles within the silicon anode is presented. This design improves the simulation of electrochemical conditions and allows for precise displacement tracking, mitigating impacts on capacity and cycle performance while enhancing Digital Volume Correlation (DVC) analysis. The research prioritizes reducing scan time and radiation exposure in micro-CT assessments of Li-ion cells, and improves the accuracy of internal strain mapping via DVC. Displacement fields over three charging and discharging cycles are documented. Notably, uneven volumetric changes are observed, with local displacements reaching up to 35 µm in areas smaller than 2.5 mm in radius, which contracted during charging and expanded during discharging. This protocol offers insights into the relationship between electrode mechanics and cell performance, promoting non-destructive evaluations of internal structures in commercial cells.

Bootstrapping Lagrangian perturbation theory for the large scale structure

We develop a model-independent approach to Lagrangian perturbation theory for the large scale structure of the universe. We focus on the displacement field for dark matter particles, and derive its most general structure without assuming a specific form for the equations of motion, but implementing a set of general requirements based on symmetry principles and consistency with the perturbative approach. We present explicit results up to sixth order, and provide an algorithmic procedure for arbitrarily higher orders. The resulting displacement field is expressed as an expansion in operators built up from the linear density field, with time-dependent coefficients that can be obtained, in a specific model, by solving ordinary differential equations. The derived structure is general enough to cover a wide spectrum of models beyond ΛCDM, including modified gravity scenarios of the Horndeski type and models with multiple dark matter species. This work is a first step towards a complete model-independent Lagrangian forward model, to be employed in cosmological analyses with power spectrum and bispectrum, other summary statistics, and field-level inference.

A multiscale Gaussian expansion method for low-frequency multimodal damping analysis of variable stiffness acoustic black hole beams

To address the issues of slow convergence and poor accuracy in existing dynamics methods caused by non-uniform variable cross-sections and layered material stiffness variations in variable stiffness acoustic black hole structure (VSABH). A multiscale Gaussian expansion method (MSGEM) is proposed in this paper. The structural dimensions are taken into account, and the structural parameters of multiple shape functions are adaptively selected based on stiffness and cross-sectional variation parameters. This results in the formation of shape function groups of various scales, which in turn creates the matrix of multi-scale Gaussian function groups. The feature information of the displacement field is realized to be extracted from multiple scales, and the fitting error of MSGEM to the displacement field of VSABH beam is within 2.02%. The missing solution of eigenfrequency of Gaussian expansion method is avoided, and the modal vibration patterns are basically matched, which verifies the validity of MSGEM. Meanwhile, the advantages of low-frequency multimodal vibration reduction of VSABH beams are highlighted from several aspects, and the trend of the adjustment of the vibration reduction characteristics of VSABH beams by different parameters is clarified, which provides valuable design guidance for ABH metamaterials oriented to low-frequency vibration reduction.

The field-enriched finite element method with gravity effects for simulating the cracking behaviors of large-scale engineering rock masses

The field-enriched finite element method uses a scalar field defined as a field variable to describe cracks and characterize their impact on the displacement field and stress field of the solution model. It is capable of avoiding remeshing and employing level set functions to describe cracks when simulating the propagation of cracks. In this work, a field-enriched finite element model with gravity effects is proposed to simulate the large-scale failure process of engineering rock masses, and several numerical cases of geotechnical engineering are successfully analyzed. First, by introducing the unified tensile fracture criterion into the numerical model, the large-scale failure process of the intact slope is simulated. Second, the sliding process of rock slopes containing en echelon joints is numerically investigated. Third, the cracking process of the concrete dam is analyzed. Finally, the effects of joint and bedding plane inclination angles on the stability of tunnel chamber in transversely isotropic rock mass are studied. The numerical results indicate that the numerical method proposed in this work can accurately solve the large-scale failure process of rock masses.

Learning-Based Slip Detection for Dexterous Manipulation Using GelStereo Sensing.

Endowing the robot with tactile perception can effectively improve manipulation dexterity, along with various benefits of human-like touch. Using GelStereo (GS) tactile sensing, which gives high-resolution contact geometry information, including 2-D displacement field, and 3-D point cloud of the contact surface, we present a learning-based slip detection system in this study. The results reveal that the well-trained network achieves 95.79% accuracy on the never-seen testing dataset, which surpasses the current model-based and learning-based methods using visuotactile sensing. We also propose a general framework for slip feedback adaptive control for dexterous robot manipulation tasks. The experimental results show the effectiveness and efficiency of the proposed control framework using GS tactile feedback when deployed on real-world grasping and screwing manipulation tasks on various robot setups.

Effects of the excavation of deep foundation pits on an adjacent double-curved arch bridge

The excavation of deep foundation pits can cause variations in the displacement and stress fields of surrounding soils, which hence induces adverse effects on adjacent structures. This study presents a two-stage method to quantify the impact of the excavation of a deep foundation pit on the adjacent double-curved arch bridge in the historical city of Nanjing, Southeastern China. The entire process of the foundation pit excavation was simulated and the induced deformation of the arch foot was obtained in the first stage by hardening soil model with small-strain stiffness. Then, the obtained deformation of the arch foot was applied to the bridge structure as a displacement boundary in the second stage to calculate the internal forces and deformations of the double-curved arch bridge structure. The tensile strength of concrete is taken as the limit value of the tensile stress of the double-curved arch bridge. The limit values of arch foot displacement under four evaluation conditions are obtained by step loading calculation. The present results provide construction guidance and safety warning for the process of foundation pit excavation adjacent to double-curved arch bridges for historical preservation.

Experimental study on fracture properties of heat-treated granite in I-II mixed mode suffered from water and liquid nitrogen cooling methods

Hot dry rock (HDR) development is significant for solving energy problems and realizing energy conservation and emission reduction. Liquid nitrogen (LN2) fracturing and hydraulic fracturing can form cracks in the HDR and improve the efficiency of geothermal energy mining. Therefore, it is necessary to study the fracture characteristics of high-temperature granite under different cooling methods. In this study, the deterioration of the physical and mechanical properties of granite subjected to high-temperature treatment under water cooling and LN2 cooling was studied. Two I/II mixed modes (tensile orientation mode and shear orientation mode) and a pure II mode fracture characteristics of cracked straight-through Brazilian disc (CSTBD) specimens made of granite were explored. The displacement and strain fields of cracked granite specimens were measured by using a digital image correlation (DIC) method. The results show that when the temperature is 25℃, 200℃, and 400℃, the loading angle and cooling method have a great influence on the fracture mechanical characteristics of the granite. In general, the increase of loading angle and LN2 cooling will lead to the decrease of peak load. For example, at 200℃, β = 15°, the deterioration degree of water-cooled and LN2-cooled specimens is 13.77 % and 16.69 %, respectively. When β = 23°, it increases to 14.62 % and 19.91 %, respectively. At the same time, an interesting phenomenon was found in the study. At 400℃, due to the Leidenfrost effect, the peak load of LN2-cooled specimens was higher than that of water-cooled specimens, and the further increase of temperature weakened the effect. When the temperature is 600℃, the difference between the loading angle and the cooling method is weakened.

Dynamic digital image correlation method for rolling convective contact

Digital image correlation (DIC) is an increasingly popular and effective non-contact method for measuring full-field displacements and strains of deformable bodies under load. Current DIC methods applied to bodies undergoing large displacements and rotations require a large measurement area for both the reference (i.e., undeformed) image and the deformed images. This can limit the resulting resolution of the displacement and strain fields. To address this issue, we propose a two-stage dynamic DIC method capable of measuring displacements and strains under material convection with high resolution. During the first stage, the reference image is assembled from smaller, high-resolution images of the undeformed object obtained using a spatially-fixed or moving frame. Following capture, each sub-image is rigidly translated and rotated into its appropriate place, thereby producing a full, high-resolution image of the reference body. In stage two, images of the loaded and deformed body, again obtained using a small camera frame with high resolution, are aligned with matching regions of the undeformed composite image using BRISK feature detection before performing DIC. We demonstrate the method on a contact problem whereby an elastomeric roller travels along a rigid surface. In doing so, we obtain fine-resolution measurements of the state of strain of the region of the roller sidewall in contact with the substrate, even as new material convects through the region of interest. We present these measurements as a series of images and videos capturing strain evolution as the roller transitions from static loads to a fully dynamic steady-state, documenting the effectiveness of the method.

Simulating the Universe from the cosmological horizon to halo scales

Ultra-large scales close to the cosmological horizon will be probed by the upcoming observational campaigns. They hold the promise to constrain single-field inflation as well as general relativity, but in order to include them in the forthcoming analyses, their modelling has to be robust. In particular, general relativistic effects may be mistaken for primordial signals, and no consensus has emerged either from analytical modelling nor from the numerical route, obstructed by the large dynamical range to be simulated. In this work, we present a numerical technique to overcome the latter limitation: we compute the general relativistic displacement field with the N-body relativistic code gevolution and combine it with the accurate Newtonian simulation Gadget-4. This combination leads to an effective simulation reproducing the desired behaviour at the level of the matter power spectrum and bispectrum. We then measure, for the first time in a simulation, the relativistic scale-dependent bias in Poisson gauge; at redshift z = 0, we find b 1 GR = -8.1 ± 2.8. Our results at the field level are only valid in the Poisson gauge and need to be complemented with a relativistic ray tracing algorithm to compute the number count observable.

Level-set topology optimization with PDE generated conformal meshes

This paper presents a level-set topology optimization approach that uses conformal meshes for the analysis of the displacement field. The structure’s boundary is represented by the iso-contour of a level-set field discretized on a fixed background design mesh. The conformal mesh is updated for each design iteration via a PDE based mesh morphing process that identifies the set of facets in the background mesh that are homeomorphic to the boundary and relaxes the homeomorphic mesh to conform to the structure’s boundary and ensure high element quality. The conformal mesh allows for a more accurate computation of the response versus density and some level-set based methods which interpolate material properties using the volume fraction. Numerical examples illustrate the proposed approach by optimizing linear-elastic two- and three-dimensional structures, wherein insight into the performance of the mesh morphing process is provided. The examples also highlight the scalability of the approach.

Impact of breathing signal-guided dose modulation on step-and-shoot 4DCT image reconstruction.

Breathing signal-guided 4DCT sequence scanning such as the intelligent 4DCT (i4DCT) approach reduces imaging artifacts compared to conventional 4DCT. By design, i4DCT captures entire breathing cycles during beam-on periods, leading to redundant projection data and increased radiation exposure to patients exhibiting prolonged exhalation phases. A recently proposed breathing-guided dose modulation (DM) algorithm promises to lower the imaging dose by temporarily reducing the CT tube current, but the impact on image reconstruction and the resulting images have not beeninvestigated. We evaluate the impact of breathing signal-guided DM on 4DCT image reconstruction and correspondingimages. This study is designed as a comparative and retrospective analysis based on 104 4DCT datasets. Each dataset underwent retrospective reconstruction twice: (a) utilizing the acquired clinical projection data for reconstruction, which yields reference image data, and (b) excluding projections acquired during potential DM phases from image reconstruction, resulting in DM-affected image data. Resulting images underwent automatic organ segmentation (lung/liver). (Dis)Similarity of reference and DM-affected images were quantified by the Dice coefficient of the entire organ masks and the organ overlaps within the DM-affected slices. Further, for lung cases, (a) and (b) were deformably registered and median magnitudes of the obtained displacement field were computed. Eventually, for 17 lung cases, gross tumor volumes (GTV) were recontoured on both (a) and (b). Target volume similarity was quantified by the Hausdorffdistance. DM resulted in a median imaging dose reduction of 15.4% (interquartile range [IQR]: 11.3%-19.9%) for the present patient cohort. Dice coefficients for lung ( ) and liver ( ) patients were consistently high for both the entire organs and the DM-affected slices (IQR lung: [entire lung/DM-affected slices only] to ; IQR liver: to ), demonstrating that DM did not cause organ distortions or alterations. Median displacements for DM-affected to reference image registration varied; however, only two out of 73 cases exhibited a median displacement larger than one isotropic 1 voxel size. The impact on GTV definition for the end-exhalation phase was also minor (median Hausdorff distance: 0.38mm, IQR: 0.15-0.46mm). This study demonstrates that breathing signal-guided DM has a minimal impact on image reconstruction and image appearance while improving patient safety by reducing doseexposure.

A new mesh deformation method using quaternion and displacement normal propagation for high quality and high efficiency

Mesh deformation technology is widely used in aerodynamic applications like unsteady flow, aeroelasticity, and aerodynamic shape optimization because of its low computational costs and consistent mesh connectivity. In order to raise deformed mesh quality and improve efficiency, a new mesh deformation method based on quaternion and displacement normal propagation (named QN method) is introduced in this paper. The boundary points propagate their displacements composed of translational vectors and quaternions to corresponding volume points along the normal direction under the control of the damping function, which preserves the mesh shape and guarantees the quality near boundaries, including orthogonality and normal size. It can also prevent the volume points from being interfered by other less relevant boundary points, so dealing with complex displacement fields effectively. In addition, it avoids complicated matrix and interpolation operations, thus saving lots of computational costs. For mesh with complex topology, a hybrid method combining the QN method and the radial basis function method (RBF method) is investigated to broaden application scenarios, which are applied to the mesh with normal correspondence inside the boundary layer and the mesh outside, respectively. Benefitting from effective handling for the near-wall elements by the QN method, the RBF interpolation part in the hybrid method requires minor support points to carry out valid large deformation, improving the deformation efficiency greatly compared to the individual RBF method. Five typical test cases with different deformation modes and mesh characteristics are implemented, showing better performance of the proposed method in deformed mesh quality and deformation efficiency.

Phase stability of convergence zone propagation at mid-frequency.

Mid-frequency transmissions (1.5 to 7.5 kHz) from a towed source to a drifting array one convergence zone away demonstrate smoothly varying phase. Calculations of the strength and diffraction parameters Φ and Λ for a representative background environment predict partially saturated propagation. For a single convergence zone path, the evolving phase rate due to the changing internal wave field corresponds to a narrowband coherent integration time, defined by the length of a discrete Fourier transform that likely captures the signal, from ∼370 s at 10 kHz to ∼1370 s at 1 kHz in the absence of source motion. Simulated propagation with a split-step parabolic equation solver through a sound speed field with thermocline fine structure and a Garrett-Munk internal wave displacement field provides a full wave picture that is consistent with the statistical predictions. Experimental data from the Philippine Sea demonstrates signal phase that is highly correlated with source tow body vertical excursions, measured by a pressure sensor, that couple into horizontal motion. The received signal can be integrated for up to 128 s at 5.5 kHz, with the upper limit thought to be due to non-uniform source motion rather than ocean dynamics.

Piezoelectric Interaction Analysis and Load‐Deflection Prediction for Nonlinear Bending and Snap‐Through of Post‐Buckled FG Piezoelectric Beams

Revealing the interaction effect in the nonlinear bending of post‐buckled functionally graded (FG) piezoelectric beams promotes the intelligent development of structural design. The nonlinear bending behavior of post‐buckled piezoelectric beams is studied. Based on the displacement field constructed by the refined beam model, the post‐buckling configuration is considered. The nonlinear geometric relationship and the constitutive relationship in the multi‐physical field are modeled. In the framework of the principle of minimum potential energy, the nonlinear static models of post‐buckled FG piezoelectric beams are established. The post‐buckling configuration is obtained by the extended two‐step perturbation method. To obtain the approximate solution for the static problems of the post‐buckled FG piezoelectric beam, the perturbation scheme of electric potential and generalized displacement is proposed. The detailed parametric analysis indicates the interaction mechanism in the nonlinear bending of the post‐buckled FG piezoelectric beam. The snap‐through process and its sensitive interval are further captured. The back propagation neural network (BPNN) technique developed for the nonlinear bending problem of post‐buckled FG piezoelectric beams achieves accurate prediction.

Frequency studies of nonlinear TSDT FGM plates in the linear shear corrections and thermal environment temperature

The effects of third-order shear deformation theory (TSDT) and varied linear shear correction coefficient on the vibration frequency of thick functionally graded material (FGM) plates with fully homogeneous equations under thermal environment and power law are investigated. The nonlinear coefficient c_1 term of displacement field of TSDT is included in the fully homogeneous equation under vibration of FGM plates. The determinant of the coefficient matrix in dynamic equilibrium differential equations under vibration can be represented in the fully fifth-order polynomial equation, thus the natural frequency can be found. The natural frequency with/without the nonlinear c_1 term of displacement fields is investigated. It is a significant novelty with the consideration of the nonlinear c_1 term in the frequency computation.

Antiscreening and Nonequilibrium Layer Electric Phases in Graphene Multilayers.

Screening is a ubiquitous phenomenon through which the polarization of bound or mobile charges tends to reduce the strengths of electric fields inside materials. Here, we show how photoexcitation can be used as a knob to transform conventional out-of-plane screening into antiscreening-the amplification of electric fields-in multilayer graphene. We find that, by varying the photoexcitation intensity, multiple nonequilibrium screening regimes can be accessed, including near-zero screening, antiscreening, and overscreening (reversing electric fields). Strikingly, at modest continuous wave photoexcitation intensities, the nonequilibrium polarization states become multistable, hosting light-induced ferroelectriclike steady states with nonvanishing out-of-plane polarization (and band gaps) even in the absence of an externally applied displacement field in nominally inversion symmetric stacks. This rich phenomenology reveals a novel paradigm of dynamical quantum matter that we expect will enable a variety of nonequilibrium broken symmetry phases.

An isogeometric approach to dynamic structures for integrating topology optimization and optimal control at macro and micro scales

In the context of active vibration suppression, an integrated topology optimization framework is proposed for the optimal control of dynamic structures. This article formulates a new composite objective function by considering the external harmonic excitations with different excitation frequencies and the complex-valued displacement field. Within the proposed optimal control performance function, the symmetric weighting matrix, the magnitudes of which are related to the importance of the control forces, is integrated into dynamic compliance to serve the state displacement. Utilizing the non-uniform rational B-splines (NURBS) basis functions, the material interpolation model defined at control points is described by the NURBS surface, which is incorporated into the optimization formulation for optimal structural and vibration control design. The sensitivity results are deduced in terms of the pseudo-densities and the corresponding weights at control points from both macro and micro perspectives of structural dynamics. To demonstrate the effectiveness of the integrated topology optimization of dynamic structures at macro and micro scales, several numerical examples, including the topology optimization of solid beams in plane stress and Mindlin plates with 3D microstructures, are provided and discussed in terms of structural shape and topology, frequency response curve, and modal displacement.

Sprain energy consequences for damage localization and fracture mechanics

The 2023 smooth Lagrangian Crack-Band Model (slCBM), inspired by the 2020 invention of the gap test, prevented spurious damage localization during fracture growth by introducing the second gradient of the displacement field vector, named the "sprain," as the localization limiter. The key idea was that, in the finite element implementation, the displacement vector and its gradient should be treated as independent fields with the lowest ([Formula: see text]) continuity, constrained by a second-order Lagrange multiplier tensor. Coupled with a realistic constitutive law for triaxial softening damage, such as microplane model M7, the known limitations of the classical Crack Band Model were eliminated. Here, we show that the slCBM closely reproduces the size effect revealed by the gap test at various crack-parallel stresses. To describe it, we present an approximate corrective formula, although a strong loading-path dependence limits its applicability. Except for the rare case of zero crack-parallel stresses, the fracture predictions of the line crack models (linear elastic fracture mechanics, phase-field, extended finite element method (XFEM), cohesive crack models) can be as much as 100% in error. We argue that the localization limiter concept must be extended by including the resistance to material rotation gradients. We also show that, without this resistance, the existing strain-gradient damage theories may predict a wrong fracture pattern and have, for Mode II and III fractures, a load capacity error as much as 55%. Finally, we argue that the crack-parallel stress effect must occur in all materials, ranging from concrete to atomistically sharp cracks in crystals.