Displacement Field Research Articles

Three-dimensional boundary element sensitivity analysis of anisotropic thermoelastic materials

Abstract The fundamental goal of this research is to develop a new three-dimensional boundary element method (BEM) for solving thermal stress sensitivity problems in anisotropic materials with a heat source. The problem at hand is incredibly tough to address analytically. As a result, we devised a novel boundary element technique to address this problem. The use of quadratic isoparametric elements and constant volume heat source to depict displacement and temperature fields is one of the driving forces behind the requirement to quantify thermal stresses in engineering structures. In three-dimensional scenarios, the impacts of isotropic, orthotropic, and anisotropic due to the presence or absence of a heat source on thermal stress sensitivity are investigated. The resulting linear systems were solved using the three-block splitting (TBS) iteration strategy, which reduced both the number of iterations and CPU time. The new TBS iteration method converges quickly and does not require complex calculations. It exceeds the other iterative methods for solving the resulting BEM linear system. To compare with other articles in the literature, we only considered the two-dimensional model as a subset of our three-dimensional model. The numerical data illustrate the accuracy, precision, and effectiveness of our proposed BEM methodology, as the BEM results are highly consistent with the finite difference method (FDM) and finite element method (FEM) results.

GMmorph: dynamic spatial matching registration model for 3D medical image based on gated Mamba.

Deformable registration aims to achieve nonlinear alignment of image space by estimating a dense displacement field. It is commonly used as a preprocessing step in clinical and image analysis applications, such as surgical planning, diagnostic assistance, and surgical navigation. We aim to overcome these challenges: Deep learning-based registration methods often struggle with complex displacements and lack effective interaction between global and local feature information. They also neglect the spatial position matching process, leading to insufficient registration accuracy and reduced robustness when handling abnormal tissues.
Approach: We propose a dual-branch interactive registration model architecture from the perspective of spatial matching. Implicit regularization is achieved through a consistency loss, enabling the network to balance high accuracy with a low folding rate. We introduced the Dynamic Matching Module (DMM) between the two branches of the registration, which generates learnable offsets based on all the tokens across the entire resolution range of the base branch features. Using trilinear interpolation, the model adjusts its feature expression range according to the learned offsets, capturing highly flexible positional differences. To facilitate the spatial matching process, we designed the Gated Mamba Layer (GML) to globally model pixel-level features by associating all voxel information, while the Detail Enhancement Module (DEM), which is based on channel and spatial attention, enhances the richness of local feature details.
Main results: Our study explores the model's performance in single-modal and multi-modal image registration, including normal brain, brain tumor, and lung images. We propose unsupervised and semi-supervised registration modes and conduct extensive validation experiments. The results demonstrate that the model achieves state-of-the-art performance across multiple datasets..
Significance: By introducing a novel perspective of position matching, the model achieves precise registration of various types of medical data, offering significant clinical value in medical applications.&#xD.

Deep 3D-DIC using a coarse-to-fine network for robust and accurate 3D shape and displacement measurements

Deep learning has become an attractive tool for addressing the limitations of traditional digital image correlation (DIC). However, extending learning-based DIC methods to three-dimensional (3D-DIC) measurements is challenging due to the limited displacement estimation range, which cannot handle the large displacements caused by stereo-matching disparities. Besides, most of the existing learning-based DIC architectures lack prior information to guide displacement estimation, resulting in insufficient accuracy. To solve these problems, we proposed a learning-based 3D-DIC (i.e., Deep 3D-DIC) using a coarse-to-fine network called G-RAFT for large and accurate image displacement estimation. Specifically, the large displacement estimation network GMA is adopted to calculate the large coarse displacement field, which is further warped on the deformed image to eliminate the main displacement component. The residual small deformation between the reference image and the warped image is further extracted using the recently proposed RAFT-DIC with high accuracy. By subtracting small displacement from large displacement, the refined displacement field is obtained. In contrast to standard subset-based 3D-DIC, Deep 3D-DIC achieves full-automatic pixel-wise 3D shape and displacement reconstruction without manual parameter input. Experimental results demonstrate that Deep 3D-DIC achieves accuracy comparable to subset-based 3D-DIC, with strong generalization ability and remarkable advantages in scenarios with complex surfaces.

Damage Evolution and Failure Precursor of Rock-like Material Under Uniaxial Compression Based on Strain Rate Field Statistics

In rock engineering, it is crucial to collect and analyze precursor information of rock failure. This paper has attempted to study the strain rate field of rock-like material to obtain the precursor information of its failure. Based on the available laboratory experiments, the intact BPM (bonded-particle model) and other BPMs with a single open prefabricated flaw were simulated by PFC (Particle Flow Code). The volume strain rate field data before the peak stress have been obtained from two hundred measurement circles across each model. The strain rate field data have been firstly statistically analyzed to explore the failure precursor based on the intact model and 45° flaw model and then compared to find the influence of the pre-existing flaw on the damage evolution and precursor signal. The results indicate that (1) all types of statistical data are positively correlated with the increment of microcracks; (2) corresponding to the fluctuation patterns of statistical data, the damage evolution of BPMs in the pre-peak stage can be divided into three parts; (3) the pre-existing flaw would accelerate the damage evolution; (4) the location and evolution rate of damage could be determined by comprehensively analyzing the average deviation curve, the coefficient of variation, and the contour maps of the strain rate field. These analyses of the particle displacement field can be used to distinguish the impacts of the flaw angle and provide some assistance for the failure forecast.

A data-driven framework for developing a unified density-modulus relationship for the human lumbar vertebral body.

Despite the broad agreement that bone stiffness is heavily dependent on the underlying bone density, there is no consensus on a unified relationship that applies to both cancellous and cortical compartments. Bone from the two compartments is generally assessed separately, and few mechanical test data are available for samples from the transitional regions between them. In this study, we present a data-driven framework integrating experimental testing and numerical modeling of the human lumbar vertebra through an energy balance criterion, to develop a unified density-modulus relationship across the entire vertebral body, without the necessity of differentiation between trabecular and cortical regions. A dataset of 25 spinal segments harvested from fresh-frozen human spines consisting of L1 vertebrae with adjacent intervertebral disks and neighboring T12 and L2 endplates was examined through a systematic process. Each specimen was subjected to axial compression using a custom-designed radiolucent device, and the deformation at multiple points during the ramp was quantified using digital volume correlation applied to the time-lapse series of microcomputed tomography images acquired during loading. A finite element model of each specimen was constructed from quantitative computed tomography images, with the experimental displacement fields imposed to replicate the observed deformation. The optimal density-modulus relationship, both in exponential and polynomial forms, was then determined by using data-driven techniques to match the numerical strain energy with the experimental external work. The resulting relationships effectively recovered bone tissue modulus at the microscale. Subsequently, the unified relationships were applied to investigate the vertebral structure-property correlations at the macroscale: as expected, compressive stiffness exhibited a moderate correlation with bone mineral density, whereas bending stiffness was revealed to correlate strongly with bone mineral content. These findings support the accuracy of the developed density-modulus relationships for the vertebral body and indicate the potential of the proposed framework to extend to other properties of interest such as vertebral strength and toughness.

Impact and analysis of corrosion on elastic stress in a composite disk under parabolic temperature distribution using the Rayleigh-Ritz method with trigonometric Ritz functions

This study conducts an in-depth impact and analysis of corrosion on the elastic stresses within a composite disk exposed to a parabolic temperature distribution. The disk, reinforced with steel fibers, is modeled as a thermo-elastic composite material to evaluate its performance under thermal and corrosive conditions. The Rayleigh-Ritz method, a widely recognized numerical approach for solving boundary value problems, is utilized to derive analytical solutions for both radial and tangential stresses. This method applies the principle of minimum potential energy to approximate displacement fields through Trigonometric Ritz Functions, which are subsequently employed to calculate stress components. The parabolic temperature distribution imposes a non-uniform thermal load across the disk, significantly altering the stress distribution. The study explores how the inherent thermal properties of the composite material interact with temperature variations, resulting in intricate stress patterns. By systematically varying temperature parameters, the analysis uncovers the sensitivity of stress components to thermal gradients. Comparative evaluations are performed for different temperature profiles, identifying critical regions of stress concentration. The findings offer essential insights into the behavior of thermo-elastic composites under non-uniform thermal and corrosive conditions, establishing a robust analytical framework for future research and practical engineering applications. This research emphasizes the necessity of integrating both thermal effects and Trigonometric Ritz Functions in the design and analysis of composite structures exposed to varying temperature loads and corrosion.

Analysis of elastic stresses and thermal creep effect for a composite disk under the parabolic distribution of temperature using the Rayleigh-Ritz method with trigonometric Ritz functions

This research provides a detailed examination of the thermal creep effect on elastic stresses in a composite disk exposed to a parabolic temperature distribution. The disk, reinforced with steel fibers, is treated as a thermo-elastic composite material. The Rayleigh-Ritz method, a widely recognized numerical approach for solving boundary value problems, is utilized to derive analytical solutions for the radial and tangential stresses. This method employs the principle of minimum potential energy to approximate displacement fields using Trigonometric Ritz Functions, which are subsequently applied to calculate the stress components. The parabolic temperature distribution imparts a non-uniform thermal load across the disk, significantly affecting the stress distribution. The study explores how the thermal creep effect, intrinsic to the composite material, interacts with thermal variations, resulting in intricate stress patterns. By adjusting temperature parameters, the analysis demonstrates the sensitivity of stress components to thermal gradients. Comparative assessments are performed for various temperature profiles, identifying critical areas of stress concentration. The findings offer significant insights into the behavior of thermo-elastic composites under non-uniform thermal conditions, providing a robust analytical foundation for future research and engineering applications. This research emphasizes the necessity of considering both thermal creep effects and Trigonometric Ritz Functions in the design and analysis of composite structures subjected to varying temperature loads.

Direct View of Gate-Tunable Miniband Dispersion in Graphene Superlattices Near the Magic Twist Angle.

Superlattices from twisted graphene mono- and bilayer systems give rise to on-demand many-body states such as Mott insulators and unconventional superconductors. These phenomena are ascribed to a combination of flat bands and strong Coulomb interactions. However, a comprehensive understanding is lacking because the low-energy band structure strongly changes when an electric field is applied to vary the electron filling. Here, we gain direct access to the filling-dependent low-energy bands of twisted bilayer graphene (TBG) and twisted double bilayer graphene (TDBG) by applying microfocused angle-resolved photoemission spectroscopy to in situ gated devices. Our findings for the two systems are in stark contrast: the doping-dependent dispersion for TBG can be described in a simple model, combining a filling-dependent rigid band shift with a many-body-related bandwidth change. In TDBG, on the other hand, we find a complex behavior of the low-energy bands, combining nonmonotonous bandwidth changes and tunable gap openings, which depend on the gate-induced displacement field. Our work establishes the extent of electric field tunability of the low-energy electronic states in twisted graphene superlattices and can serve to underpin the theoretical understanding of the resulting phenomena.

Shape sensing of composite shell using distributed fibre optic sensing

Shape sensing is critically important throughout the lifecycle of composite shell structures, including the design, manufacturing, service, retirement, and reuse phases. In the service phase, for instance, shape-based structural integrity assessments can inform maintenance strategies, significantly reducing regular maintenance costs. To achieve high-fidelity shape sensing, a novel approach is proposed for strain acquisition and interpolation in carbon fibre reinforced polymer (CFRP) shell structures, utilizing distributed fibre optic sensing. This method is designed to enhance the performance of the inverse finite element method (iFEM). The approach introduces a new strain acquisition strategy based on distributed fibre optic sensors and a strain interpolation technique leveraging single image super-resolution (SISR). In the strain acquisition process, a fundamental sensing block capable of capturing both normal and shear strain is employed for sensor network design, which can be easily implemented using fibre optic sensors. The goal of this acquisition strategy is to standardize sensor network design and provide a digital representation, offering novel insights into shape reconstruction for different composite shells across various applications. Utilizing the obtained strain field, the SISR-based strain interpolation method generates a displacement field with enhanced spatial resolution through iFEM. Experimental evaluation of the SISR-based interpolation demonstrates its efficacy in capturing high-fidelity displacement fields in both smooth and non-smooth strain regions of CFRP shell structures. The introduction of SISR in strain field interpolation, for the first time, offers a potential solution to the challenge of interpolating non-smooth strain fields, providing a reference for addressing complex strain field interpolation in practical applications.

Dilatational disk and finite cylindrical inclusion in elastic nanowire

For the first time, strict analytical solutions for the elastic fields and the strain energies of an infinitely thin dilatational disk (DD) and a dilatational cylindrical inclusion (CyI) of finite length coaxially embedded in an infinite elastically isotropic cylinder with free surface are given and analyzed in detail. The solutions are represented in an integral form that is suitable for further analytical use and numerical study. The screening effect of the cylinder free surface on the elastic fields and the strain energies of the DD and the CyI is discussed. It is shown that this effect is significant for both the axial displacement and stress fields when the DD and CyI radii are comparable with the cylinder radius, however it is rather weak for the DD strain energy (the energy release does not exceed ∼10%). In contrast, for the CyI strain energy, the screening effect can be very strong. It is also shown that the hydrostatic stress is inhomogeneous and exists not only inside the CyI, as is the case with this stress for inclusions in an infinite medium, but also outside it. This stress is concentrated on the free surface at the points that are closest to the CyI boundary. Inside the CyI, the hydrostatic stress is much higher in magnitude than outside it.

Physics-Informed Deep Homogenization Approach for Random Nanoporous Composites with Energetic Interfaces

This contribution presents a new physics-informed deep homogenization neural network model for identifying local displacement and stress fields, as well as homogenized moduli, of nanocomposites with periodic arrays of porosities under general loading conditions. Notably, it accounts for the surface elasticity effect, utilizing the Gurtin-Murdoch interface theory. First of all, a fully connected neural network model is established that maps the spatial coordinates, passing first through several sinusoidal functions, to the microscopic displacements. The loss function is formulated as the weighted sum of residuals of Navier-Cauchy equations in the bulk domains and the Young-Laplace equations on the energetic surfaces, evaluated on separate sets of collocation points. To more effectively predict stress concentrations inside the microstructures, we introduce fully trainable weights to each collocation point. The capacity and effectiveness of the new homogenization technique for capturing the size-dependent local and global response of nanocomposites with distinct pore sizes and shapes are verified upon extensive comparisons with the finite-element benchmark results, under various loading conditions. New results showcase the proposed theory’s ability to model random distributions of nano-porosities with a high degree of accuracy, a task not easily achievable with alternative techniques except for the specialized finite-element method.

Kinematics of abdominal aortic Aneurysms.

A search in Scopus within "Article title, Abstract, Keywords" unveils 2,444 documents focused on the biomechanics of Abdominal Aortic Aneurysm (AAA), mostly on AAA wall stress. Only 24 documents investigated AAA kinematics, an important topic that could potentially offer significant insights into the biomechanics of AAA. In this paper, we present an image-based approach for patient-specific, in vivo, and non-invasive AAA kinematic analysis using patient's time-resolved 3D computed tomography angiography (4D-CTA) images, with an objective to measure wall displacement and strain during the cardiac cycle. Our approach relies on regularized deformable image registration for estimating wall displacement, estimation of the local wall strain as the ratio of its normal displacement to its local radius of curvature, and local surface fitting with non-deterministic outlier detection for estimating the wall radius of curvature. We verified our approach against synthetic ground truth image data created by warping a 3D-CTA image of AAA using a realistic displacement field obtained from a finite element biomechanical model. We applied our approach to assess AAA wall displacements and strains in ten patients. Our kinematic analysis results indicated that the 99th percentile of circumferential wall strain, among all patients, ranged from 2.62% to 5.54%, with an average of 4.45% and a standard deviation of 0.87%. We also observed that AAA wall strains are significantly lower than those of a healthy aorta. Our work demonstrates that the registration-based measurement of AAA wall displacements in the direction normal to the wall is sufficiently accurate to reliably estimate strain from these displacements.

Twist-angle dependent pseudo-magnetic fields in monolayer CrCl2/graphene heterostructures.

The generation of pseudo-magnetic fields in strained graphene leads to quantized Landau levels in the absence of an external magnetic field, providing the potential to achieve a zero-magnetic-field analogue of the quantum Hall effect. Here, we report the realization of a pseudo-magnetic field in epitaxial graphene by building a monolayer CrCl2/graphene heterointerface. The CrCl2 crystal structure exhibits spontaneous breaking of three-fold rotational symmetry, yielding an anisotropic displacement field at the interface. Using scanning tunneling spectroscopy, we have discovered a sequence of pseudo-Landau levels associated with massless Dirac fermions. A control experiment performed on the CrCl2/NbSe2 interface confirms the origin as the pseudo-magnetic field in the graphene layer that strongly interacts with CrCl2. More interestingly, the strength of the pseudo-magnetic fields can be tuned by the twist angle between the monolayer CrCl2 and graphene, with a variation of up to threefold, depending on the twist angle of 0° to 30°. This work presents a rare 2D heterojunction for exploring PMF-related physics, such as the valley Hall effect, with the advantage of easy and flexible implementation.

Self-Powered Sensing and Wireless Communication Synergic Systems Enabled by Triboelectric Nanogenerators

With the rapid advancement of the Internet of Things (IoT) era, the demand for wireless sensing and communication is increasingly prominent. Tens of thousands of sensing and communication nodes have presented new challenges to distributed energy. As a green energy harvesting technology, the triboelectric nanogenerator (TENG), with its outstanding characteristics of simple configuration, low cost, and high compatibility, demonstrates significant advantages in self-powered sensing systems and great application potential in the fields of human–machine interaction and wearable devices in the IoT era. More importantly, the electric displacement field and modulated electromagnetic waves that TENG triggers have opened a new paradigm for self-powered wireless communication, making up for the disadvantages of power supply by traditional distributed power sources. This review comprehensively discusses the latest scientific and technological progress in wireless communication technology prompted by TENG and further discusses its potential applications in various promising fields. Finally, a summary and outlook of TENG-based self-powered sensing and wireless communication synergic systems are presented, aiming to stimulate future innovation in the field and accelerating the paradigm shift to a fully self-powered IoT era.

A new approach to the static bending problem of organic nanoplates

Scientists are growing interested in organic panels because of its effective use in harnessing solar energy for many applications in life and technology. This research used two innovative plate theories to investigate the static bending behavior of organic nanoplates under varying temperature conditions based on analytical solutions, the organic plate consists of five layers of materials including Glass, ITO (indium-doped tin oxide), and PEDOT: PSS (Poly 3,4-ethylenedioxythiophene: poly styrenesulfonate), P3HT: PCBM (Poly 3-hexylthiophene (P3HT) and [6,6]-phenyl-C61-butyric acid methyl ester) and Aluminum. The captivating feature of this study is in the identification of the equilibrium equation for organic nanoplates, which is dependent only on a single unidentified factor. This is possible because the produced displacement field only shows one component of bending displacement. Furthermore, the temperature parameter is also included, demonstrating the influence of the thermal environment on the bending behavior of the organic plate. The innovative approach used in this work has yielded a distinct and accurate formulation for the motion of the plate, leaving just one variable still to be determined. The accuracy and dependability of this formulation are confirmed by comparing it with established analytical and numerical techniques that have been published. The static bending response of organic panels was influenced by various geometric, material, and temperature characteristics, as shown by a series of numerical findings. The calculation results have shown that the two plate theories used in this study provide comparable outcomes for the bending issue of organic naoplates.

Tunable Topological Transitions Probed by the Quantum Hall Effect in Twisted Double Bilayer Graphene.

The moiré system provides a tunable platform for investigating exotic quantum phases. Particularly, the displacement field D is crucial for tuning the electronic structures and topological properties of twisted double bilayer graphene (TDBG). Here, we present a series of D-tunable topological transitions by the evolution of quantum Hall phases (QHPs) in the valence bands of TDBG. As D increases, we observe the alternating emergence of two distinct quantum Hall regions originating from full-filling and half-filling, which we attribute to the D-induced Lifshitz transition. Moreover, we delve into the remote valence bands of TDBG and observe a transition in the sequence of Landau levels upon the application of D, shifting from 8N + 4 to 8N. This observation, combined with theoretical calculations, unveils an alteration in the Berry phase. Our findings highlight the TDBG as an exemplary platform for understanding the origin of the topological transitions in the graphene-based moiré systems.

On the reconstruction of a two-dimensional density of a functionally graded elastic plate

In this article, the in-plane vibrations of a rectangular plate within the framework of a plane stress is formulated based on the general formulation of steady-state vibrations of an inhomogeneous elastic isotropic body. The left side of the plate is rigidly fixed, vibrations are forced by tensile load applied at the right side. The properties of the functionally graded material are described by two-dimensional variation laws (Young’s modulus, Poisson’s ratio and density). A dimensionless problem formulation is given. The direct problem solution of the displacement field determination is obtained using the finite element method. The effect of material characteristics on the displacement field and the value of the first resonance are shown. An analysis of the obtained results is carried out. The inverse problem of density determination from displacement field data for a fixed frequency is considered. To reduce the error in calculating two-variable table functions derivatives, an approach based on spline approximation and a locally weighted regression algorithm is proposed. Reconstruction examples of different laws are presented to demonstrate the possibility of using this approach.

Prestressed and prepolarized piezoelectric material with an elliptical hole

In this paper, the antiplane state problem of an elliptic hole in a prestressed and prepolarized piezoelectric material loaded by constant, uniform remote shear stresses was performed. A compact and elementary form solution of the problem is obtained utilizing the conformal mapping technique and representation of the incremental stress and electrical fields by complex potentials. Using the boundary conditions, the coefficients of complex potentials developed as Laurent series, for the case of a piezoelectric material of class 4¯2m, and implicitly the components of incremental stress and electric displacement fields are obtained in a final compact and closed form.

High-Order Theory Approach for Debonded Sandwich Panels—Part I: Formulation and Displacement Fields

Abstract A high-order theory is developed to model asymmetric sandwich panels with face/core debonds and to provide a solution for the energy release rate and mode mixty. This new theory is a novel re-formulation of the extended high-order sandwich panel theory (EHSAPT), in which faces and core were originally considered to be perfectly bonded. In the new formulation, a sandwich panel with an interfacial debond can be divided into three parts, namely, the debonded part, the substrate part, and the base part. A new high-order displacement pattern is developed to describe the core’s deformation in the substrate part, and it is compatible with the displacement field of the core in the base part. In addition, capturing the high-order shear deformation of the core, this new theory is able to take the transverse compressibility and axial rigidity of the core into account. In this Part I of this two-part research, we focus on the formulation and the displacement field. In Part II, the fracture parameters, namely, the energy release rate and the mode mixity will be addressed. Accordingly, in this paper, results for the deformation of the debonded panel are produced and compared with the ones given by the finite element method with a very fine mesh. The accuracy is proven for a wide range of core materials and for a wide range of debond lengths.

High-Order Theory Approach for Debonded Sandwich Panels—Part II: Energy Release Rate and Mode Mixity

Abstract A novel re-formulation of the extended high-order sandwich panel theory (EHSAPT) for the case of a face/core debond was done in Part I of this two-part series of papers. This high-order theory is capable of including not only the transverse shear but also the transverse compressibility and axial rigidity of the core. In this Part II paper, a closed-form expression for the energy release rate is derived in terms of the equivalent resultant forces and displacements at the two edge sections. Together with the crack surface displacement method, the mode mixity is determined from the displacement field. Benefiting from the accurate displacement field given by the proposed theory, this paper presents a self-contained approach for the mode mixity that is free of parameters that need to be determined via additional numerical simulations (i.e., no extrapolation needed). Results are compared with the ones given by the classical theory in the literature and the ones given by the finite element method with a very fine mesh. The accuracy is proven for a wide range of core materials from the stiffer cores to the very compliant ones, and for a wide range of debond lengths.