Displacement Field Research Articles

Metamaterial design enabling simultaneous manipulation of Rayleigh and Love waves

Studies on elastic metamaterials have expanded from manipulating bulk waves to surface waves, aiming to control the propagation of in-plane Rayleigh waves or anti-plane Love waves. Considering the coexistence of Rayleigh and Love waves in various scenarios, the objective of this study is to develop a metamaterial capable of simultaneously manipulating both types of waves. The proposed metamaterial consists of horizontal resonators with an oblique mounting angle relative to the wave propagation direction, as well as vertical resonators. Initially, analytical solutions for the dispersion of surface waves are derived, followed by Finite Element (FE) simulations to validate the analytically predicted dispersion and illustrate the corresponding wave modes, as well as the in-plane and out-of-plane displacement fields at specified frequencies. The present study reveals that the mounting angle of the horizontal resonators plays a crucial role in surface wave manipulation. By adjusting the mounting angle, three distinct objectives can be achieved: (i) the attenuation of Rayleigh waves alone; (ii) the independent attenuation of Rayleigh and Love waves, targeting different frequency ranges; and (iii) the simultaneous attenuation of both Rayleigh and Love waves.

Study on the influence of temperature on the damage evolution of hot dry rock in the development of geothermal resources

In order to more accurately understand the rock mechanics properties of hot dry rock (HDR) reservoirs under high-temperature conditions and further guide the drilling and construction of HDR wells, conducting research on rock damage evolution under high-temperature conditions plays a guiding role in the efficient development of geothermal resources. To reveal the evolution law of fracture damage of HDR under temperature influence, taking marble as an example, the thermo-mechanical damage and failure mechanism under the conditions of 30 °C, 60 °C, 90 °C, 120 °C and 150 °C were studied using a rock high-temperature rheometer and an acoustic emission (AE) testing system. The numerical simulation results were compared with the indoor experimental results by combining the particulate flow program Particle Flow Code 3D (PFC3D) to verify the effectiveness of the simulation analysis model of thermo-coupled particulate flow at the micro scale. The results show that under high temperature, the marble three-axis compression failure passes through the compaction and elastic deformation stage, plastic deformation stage, ductile failure stage and instability failure stage, and the peak strength and elastic modulus of the marble decrease with the increase of temperature, and the acoustic emission b-value of the sample can judge the damage evolution process of the marble. At the micro scale, high temperature accelerates the force chain transmission between particles, the contact force between marble particles gradually decreases during the heating process, and the number of particle bonding failures increases steadily; the bearing capacity and elastic modulus attenuation of the rock are the result of microcrack evolution, and the force chain void zone and particle displacement field inside the sample are consistent with its macroscopic failure form. The development of microcracks in marble under different test loading conditions is different, and with the increase of test temperature, the total number of cracks inside the sample increases, but the proportion of shear cracks decreases, the activity of particle displacement increases, and the “plastic extension” characteristic of marble becomes more significant. The thermal damage evolution of marble was quantitatively analyzed based on the elastic modulus method and the peak stress method, and the damage evolution law of marble under different temperatures was obtained.

Experimental analysis of the piezomagnetic behavior of double-shear bolted connections of wire and arc additively manufactured steel

ABSTRACT In this paper, the piezomagnetic behaviour of WAAM double-shear connection specimens were investigated. It aims to develop a damage monitoring method based on piezomagnetic effect for WAAM steel bolted connections. Eight WAAM steel coupons with two different print layer orientations were fabricated to measure the mechanical properties of WAAM materials. A total of 32 WAAM double-shear bolted connection specimens with two print layer orientations were designed to analyse the structural properties of WAAM members. A magnetic probe was used to monitor the variations of the piezomagnetic field. The evolutions of piezomagnetic field of transversal and longitudinal WAAM coupons were compared and analysed. Notably, it is found that piezomagnetic field manifests anisotropy consistent with the mechanical properties. The characteristics of five failure modes including net section tension, end-splitting, shear-out, bearing, block shear were discussed. The correlation between the magnetic field–displacement curve and the load-displacement curve was systematically examined. The characteristics of magnetic field of specimens failing by bearing were emphatically explored. The results show that bearing failure can be distinguished from other failure modes by monitoring the magnetic field. In addition, the evolution of magnetic field serves as a predictor of the ultimate capacity and failure of double-shear bolted connections.

Tunable even- and odd-denominator fractional quantum Hall states in trilayer graphene

Fractional quantum Hall (FQH) states are exotic quantum many-body phases whose elementary charged excitations are anyons obeying fractional braiding statistics. While most FQH states are believed to have Abelian anyons, the Moore–Read type states with even denominators – appearing at half filling of a Landau level (LL) – are predicted to possess non-Abelian excitations with appealing potential in topological quantum computation. These states, however, depend sensitively on the orbital contents of the single-particle LL wavefunctions and the LL mixing. Here we report magnetotransport measurements on Bernal-stacked trilayer graphene, whose multiband structure facilitates interlaced LL mixing, which can be controlled by external magnetic and displacement fields. We observe robust FQH states including even-denominator ones at filling factors ν = − 9/2, − 3/2, 3/2 and 9/2. In addition, we fine-tune the LL mixing and crossings to drive quantum phase transitions of these half-filling states and neighbouring odd-denominator ones, exhibiting related emerging and waning behaviour.

Dimensional tolerance optimization of SAR antennas with uncertainty quantification and reliability analysis based on structural-electromagnetic coupling model

The dimensional tolerances greatly impact the structural-electromagnetic performance of spaceborne synthetic aperture radar (SAR) antenna. However, few works have conducted the tolerance allocation of the extendible support structure to guarantee system reliability. To bridge the above gap, an integrated optimization methodology is proposed to design the dimensional tolerances with the structural-electromagnetic coupling model in this study. First, the absolute nodal coordinate formulation is developed to predict the structural deformation triggered by the dimensional deviations. Then, the coupling relationship between the displacement field and the electromagnetic field is elucidated for the SAR system. Subsequently, taking advantage of the surrogate model and the parallel update criterion, the interval uncertainty quantification stemming from dimensional tolerances is executed to quickly identify the worst-case scenarios of structural response. Moreover, a multi-point selection strategy is incorporated into the adaptive Bayesian probabilistic integration with active learning, which significantly improves the computational efficiency of electromagnetic reliability. Based on the above tolerance analysis, the inverse optimization design of the dimensional tolerance is realized by the particle swarm algorithm. Finally, the effectiveness and superiority of the proposed methods are validated in the case study. Our innovative framework and analytical methodology not only furnish a comprehensive structural-electromagnetic coupling model but also transition the design paradigm from experiential to robust tolerance allocation.

Interplay of photonic, electrical, and inertial loads on the stability of rotating sector perovskite sandwich plates with a GPL-based nanocomposite core

The bifurcation stability of sandwich sector plates, primarily constructed from lead halide perovskite skins known for their significant photostrictive and electrostrictive properties, is explored. These properties render them highly relevant for multiphysics applications. The influence of a photo-induced thermal environment on the behavior of these plates is also examined. A notable challenge, the inherent stiffness of these structures, is addressed by integrating a nanocomposite laminated core composed of a polymer matrix and graphene platelet (GPL) reinforcers. The GPLs are distributed throughout the core layers according to functionally graded models, significantly enhancing structural integrity. To effectively model the core environment, the Halpin-Tsai micromechanical rule is employed. The structural displacement field is modeled using the first-order shear deformation theory. Moreover, the von-Kármán geometrically nonlinear strain-displacement relations are applied. The constitutive relationships are governed by the theory of linear photo-thermo-electro-elasticity, providing a framework for the analysis of perovskite-based structures. The reorganization of bifurcation points from the pre-buckling route and the linearization of stability equations are performed using the adjacent-equilibrium criterion. The generalized differential quadrature (GDQ) method is utilized to solve the equilibrium equations of pre-buckling and the stability equations of buckling. This comprehensive investigation reveals the critical influence of photonic, electrical, and rotational stimuli on the stability characteristics of advanced perovskite-based sandwich sector plates, demonstrating potential advancements in multiphysics applications.

In-Plane Vibrations of Elastic Lattice Plates and Their Continuous Approximations

This paper presents an analytical study on the in-plane vibrations of a rectangular elastic lattice plate. The plane lattice is modelled considering central and angular interactions. The lattice difference equations are shown to coincide with a spatial finite difference scheme of the corresponding continuous plate. The considered lattice converges to a 2D linear isotropic elastic continuum at the asymptotic limit for a sufficiently small lattice spacing. This continuum has a free Poisson’s ratio, which must be lower than that foreseen by the rare-constant theory, to preserve the definite positiveness of the associated discrete energy. Exact solutions for the in-plane eigenfrequencies and modes are analytically derived for the discrete plate. The stiffness characterising the lattice interactions at the boundary is corrected to preserve the symmetry properties of the discrete displacement field. Two classes of constraints are considered, i.e., sliding supports at the nodes, one normal and the other parallel to the boundary. For both boundary conditions, a single equation for the eigenfrequency spectrum is derived, with two families of eigenmodes. Such behaviour of the lattice plate is like that of the continuous plate, the eigenfrequency spectrum of which has been given by Rayleigh. The convergence of the spectrum of the lattice plate towards the spectrum of the continuous plate from below is confirmed. Two continuous size-dependent plate models, considering the strain gradient elasticity and non-local elasticity, respectively, are built from the lattice difference equations and are shown to approximate the plane lattice accurately.

Intrinsic fracture toughness of a soft viscoelastic adhesive

The fracture toughness of inelastic materials consists of an intrinsic component associated with the crack tip fracture process and a dissipative component due to bulk dissipation. Experimental characterization of the intrinsic component of fracture toughness is important for understanding the fracture mechanism and predictive modeling of the fracture behavior. Here we present an experimental study on the intrinsic toughness of a soft viscoelastic adhesive. We first obtained full-field and full-history data of the displacement and deformation fields in pure shear fracture tests using a particle tracking method. By combining these data with a nonlinear constitutive model, we extracted the intrinsic toughness through an energy balance analysis. A two-stage crack propagation behavior was observed in our fracture experiments: under monotonic loading the crack first underwent a slow propagation stage and then suddenly entered a fast propagation stage. We found that the intrinsic toughness was highly scattered for the slow propagation stage, but remained consistent for the fast propagation stage. Further examination of the fracture surface and the onset of fast propagation revealed that transition from the slow to the fast propagation stage was governed by the applied stretch and was likely due to a change in the crack tip fracture process.

Error Correction of the RapidEye Sub-Pixel Correlation: A Case Study of the 2019 Ridgecrest Earthquake Sequence.

The optical image sub-pixel correlation (SPC) technique is an important method for monitoring large-scale surface deformation. RapidEye images, distinguished by their short revisit period and high spatial resolution, are crucial data sources for monitoring surface deformation. However, few studies have comprehensively analyzed the error sources and correction methods of the deformation field obtained from RapidEye images. We used RapidEye images without surface deformation to analyze potential errors in the offset fields. We found that the errors in RapidEye offset fields primarily consist of decorrelation noise, orbit error, and attitude jitter distortions. To mitigate decorrelation noise, the careful selection of offset pairs coupled with spatial filtering is essential. Orbit error can be effectively mitigated by the polynomial fitting method. To address attitude jitter distortions, we introduced a linear fitting approach that incorporated the coherence of attitude jitter. To demonstrate the performance of the proposed methods, we utilized RapidEye images to extract the coseismic displacement field of the 2019 Ridgecrest earthquake sequence. The two-dimensional (2D) offset field contained deformation signals extracted from two earthquakes, with a maximum offset of 2.8 m in the E-W direction and 2.4 m in the N-S direction. A comparison with GNSS observations indicates that, after error correction, the mean relative precision of the offset field improved by 92% in the E-W direction and by 89% in the N-S direction. This robust enhancement underscores the effectiveness of the proposed error correction methods for RapidEye data. This study sheds light on large-scale surface deformation monitoring using RapidEye images.

Characterization on fibre kinking fracture of laminated composites under combined compression and shear at high loading rate

This paper presented a novel method to characterize the fracture toughness and cohesive law of laminated composites under combined compression and shear at high loading rate. Compact compression specimens with off-axis fibres which introduce the in-plane shear stresses were conducted on the uniaxial bidirectional electromagnetic Hopkinson bar system and the displacement field and strain field were recorded by the high-speed camera for the digital image correlation analysis and J-integral calculation. The results reveal that the in-plane shear stresses bring the increase of fracture toughness at crack initiation and propagation and advance the damage initiation of the specimens. The fracture surfaces indicate that the shear stresses cause the fibre bundles' shear failure during the formation of the kink band, accompanied by more energy dissipation with the increase of off-axis angle.

Inferring cellular contractile forces and work using deep morphology traction microscopy

Traction-force microscopy (TFM) has emerged as a widely used standard methodology to measure cell-generated traction forces and determine their role in regulating cell behavior. While TFM platforms have enabled many discoveries, their implementation remains limited due to complex experimental procedures, specialized substrates, and the ill-posed inverse problem whereby low-magnitude high-frequency noise in the displacement field severely contaminates the resulting traction measurements. Here, we introduce deep morphology traction microscopy (DeepMorphoTM), a deep-learning alternative to conventional TFM approaches. DeepMorphoTM first infers cell-induced substrate displacement solely from a sequence of cell shapes and subsequently computes cellular traction forces, thus avoiding the requirement of a specialized fiduciarily marked deformable substrate or force-free reference image. Rather, this technique drastically simplifies the overall experimental methodology, imaging, and analysis needed to conduct cell-contractility measurements. We demonstrate that DeepMorphoTM quantitatively matches conventional TFM results while offering stability against the biological variability in cell contractility for a given cell shape. Without high-frequency noise in the inferred displacement, DeepMorphoTM also resolves the ill-posedness of traction computation, increasing the consistency and accuracy of traction analysis. We demonstrate the accurate extrapolation across several cell types and substrate materials, suggesting robustness of the methodology. Accordingly, we present DeepMorphoTM as a capable yet simpler alternative to conventional TFM for characterizing cellular contractility in two dimensions.

Graph Neural Networks for Geometry Design in Plastic Regime

In this work, we extend MeshGraphNets to simulate collisions involving plastic material, previously limited to hyperelastic, addressing higher non-linearities and energy dissipation. While previous work estimated only the displacement field, our approach also resolves the complete tensor stress field, under different boundary conditions and geometries.

A Numerical Study of Fault Reactivation Mechanisms in CO2 Storage.

Due to extensive industrialization and ongoing fossil fuel consumption, CO2 emissions have significantly contributed to climate change and rising greenhouse gas levels. The collection and storage of CO2 in subsurface geological formations have been proposed as a feasible alternative. The well-documented In Salah storage site is the subject of the chosen case study. For the numerical analysis, a two-dimensional finite element simulation of fault reactivation processes was conducted in the context of the CO2 storage. The goal of this research is to conduct a mechanistic numerical analysis of a typical CO2 storage condition. The selected analysis domain is 4 km (width) × 2 km (depth) and includes all important domains and formations (overburden, main caprock, lower caprock, and underburden) of the In Salah site. The simulation results indicate that the influence of fault reactivation under 32 MPa of base injection pressure results in peak vertical deformation of 0.044 m in the caprock and a vertical displacement magnitude of 0.015-0.020 m at the surface level (Z = 0 m). The derived vertical deformation findings at the surface level are in agreement with the data obtained from the in situ InSAR monitoring system in 2009. The effects of the changes in the fault dip angle, key caprock mechanical parameters, and in situ stress ratio on the displacement profile are evaluated within the parametric study. In comparison to the benchmark numerical run, the scenario ratio of k = 0.5 led to a significant reduction in the displacement. The simulation in which the fault dip angle was 30° produced a more pessimistic result with a larger displacement field. This could be an indication of heightened fault reactivation risks associated with low-angle faults in storage sites with strong horizontal stress regimes due to the combined effect of increased shear stress and reduced inherent frictional resistance on the fault plane. Considering that a vertical fault dip angle (90°) and an additional three 20 m long vertical fractures above the reservoir produced similar vertical displacement observed with the fault dipping at a 60° angle, this indicated that the vertical faults in the vicinity of the storage site pose limited safety risks to the integrity of the sealing rock.

A mixed-element phase field method for the fracture analysis of beams

The prediction of fracture in thin structures is crucial for the safety assessments in various fields of engineering. Modeling methods such as the phase-field method typically assume damage to be constant across the thickness of structural models like beams, plates and shells which, especially in load cases coupling stretching and bending, is an imperfect approximation. In this contribution, fracture behaviors along the thickness direction of Euler–Bernoulli beam considering axial deformation are addressed with a phase-field modeling approach. To achieve this, a mixed-element beam model is introduced, which combines 1D beam elements representing the displacement field with 2D rectangular elements describing a crack phase-field. The nonlinear coupled governing equations are solved using a staggered scheme. The transfer of variables between the coupled fields occurs at the quadrature points which in turn need to have corresponding geometric locations. Numerical examples ranging from the problems of fracture in standalone beams to lattice structures show the applicability of the approach, and detailed comparisons with a standard 2D model confirm its accuracy and efficiency.

A random elastoplastic framework of relationships between CBR and Young’s modulus for coarse-grained soils

The material quality indicator most commonly used for the quality of road materials is the California Bearing Ratio test (CBR). In addition, the CBR test provides a value commonly used to correlate with the resilient modulus (used in the design and analysis of pavement) due to its cost-effectiveness. This test measures soil resistance to penetration by a punch and compares it with the pressure measured in a standard material at the same penetration (2.5 mm or 5 mm). However, this test lacks physical explanations regarding mechanical behavior because the CBR value only compares soil penetration resistance with the pressure measured in a standard material. Another issue arises from the scattered results obtained from both equations and tests, highlighting the need for variability analysis of the CBR test to assess the effect of the different geotechnical variables on the CBR value. For this purpose, simulations using FEM (Finite Element Method) considering random soil parameters were performed for the CBR test. These FEMs included a linear elastic model and two failure criteria (Mohr–Coulomb and Drucker-Prager with a cap) and were prepared for granular soils. The evaluation shows that the increase or decrease in the CBR value is a function of the elastic modulus, yield stress, and friction angle. Moreover, the simulations expand the knowledge of the shearing mechanisms, generated stresses, displacement fields, and load sharing when the CBR test is made. From these results, a physical explanation of test results can be done. FEM simulations showed stress zones in conditions of elastic, compression, and shear behavior. These zones can explain the importance of elastic modulus, yielding stress, and friction angle in the CBR value. From numerical results, a new equation was proposed and compared with practical equations proposed by international standards and other sources to estimate the probability of underestimated values CBR according to the correlations used.

Towards to Theory of the X-ray Diffraction Tomography of Crystals with Nano-Sized Defects

X-ray diffraction tomography is an innovative method that is widely used to obtain 2D-phase-contrast diffraction images and their subsequent 3D-reconstruction of structural defects in crystals. The most frequent objects of research are linear and helical dislocations in a crystal, for which plane wave diffraction images are the most informative, since they do not contain additional interference artifacts unrelated to the images of the defects themselves. In this work the results of modeling and analysis of 2D plane wave diffraction images of a nano-dimensional Coulomb-type defect in a Si(111) thin crystal are presented based on the construction of numerical solutions of the dynamic Takagi-Taupin equations. An adapted physical expression for the elastic displacement field of the point defect, which excludes singularity at the defect location in the crystal, is used. A criterion for evaluating the accuracy of numerical solutions of the Takagi-Taupin equations is proposed and used in calculations. It is shown that in the case of the Coulomb-type defect elastic displacement field, out of the two difference algorithms for solving the Takagi-Taupin equations used in their numerical solution, only the algorithm for solving the Takagi-Taupin equations where the displacement field function enters in exponential form is acceptable in terms of the required accuracy-duration of the calculations.

Physics-informed neural network estimation of material properties in soft tissue nonlinear biomechanical models

AbstractThe development of biophysical models for clinical applications is rapidly advancing in the research community, thanks to their predictive nature and their ability to assist the interpretation of clinical data. However, high-resolution and accurate multi-physics computational models are computationally expensive and their personalisation involves fine calibration of a large number of parameters, which may be space-dependent, challenging their clinical translation. In this work, we propose a new approach, which relies on the combination of physics-informed neural networks (PINNs) with three-dimensional soft tissue nonlinear biomechanical models, capable of reconstructing displacement fields and estimating heterogeneous patient-specific biophysical properties and secondary variables such as stresses and strains. The proposed learning algorithm encodes information from a limited amount of displacement and, in some cases, strain data, that can be routinely acquired in the clinical setting, and combines it with the physics of the problem, represented by a mathematical model based on partial differential equations, to regularise the problem and improve its convergence properties. Several benchmarks are presented to show the accuracy and robustness of the proposed method with respect to noise and model uncertainty and its great potential to enable the effective identification of patient-specific, heterogeneous physical properties, e.g. tissue stiffness properties. In particular, we demonstrate the capability of PINNs to detect the presence, location and severity of scar tissue, which is beneficial to develop personalised simulation models for disease diagnosis, especially for cardiac applications.

Using unsupervised learning based convolutional neural networks to solve Digital Image Correlation

Digital Image Correlation (DIC) is a robust, non-contact method for full-field deformation measurement widely used in photomechanics. Based on subset image matching and an iterative optimization architecture, traditional DIC deformation field analysis requires manual selection of such calculation parameters as subset size, rendering it challenging to balance spatial resolution and measurement resolution in non-uniform field measurements. The requirement of manual parameter adjustment is lowered by a recently emerged supervised learning-based neural network DIC method, as it establishes a direct correlation between images and deformation fields using deep neural networks (DNN). However, its generalization and accuracy are contingent on the scope and variety of the dataset because it requires training with a large number of simulated speckle images of deformation fields with known standards. This paper proposes an unsupervised learning neural network based DIC measurement method that circumvents the need for standard deformation fields and achieves high precision analysis of deformed fields. It constructs a loss function based on the photometric consistency assumption of speckle images before and after deformation and allows the neural network model to directly extract displacement information from the gray data of the “reference image-deformed image” pair. Meanwhile, the model is enhanced accordingly by further introducing displacement continuity constraints to enhance accuracy and mitigate noise interference. Validation through both simulated and real experiments shows that the proposed approach surpasses traditional subset DIC in measuring non-uniform deformation fields with higher precision. It also offers superior flexibility and adaptability over supervised learning-based neural network DIC methods by eliminating the need for a large training dataset, allowing for immediate application in displacement field analysis.

Emergent Inhomogeneity and Nonlocality in a Graphene Field-Effect Transistor on a Near-Parallel Moiré Superlattice of Transition Metal Dichalcogenides.

At near-parallel orientation, twisted bilayers of transition metal dichalcogenides exhibit interlayer charge transfer-driven out-of-plane ferroelectricity. Here, we report detailed electrical transport in a dual-gated graphene field-effect transistor placed on a 2.1° twisted bilayer WSe2. We observe hysteretic transfer characteristics and an emergent charge inhomogeneity with multiple local Dirac points evolving with an increasing electric displacement field (D). Concomitantly, we also observe a strong nonlocal voltage signal at D ∼ 0 V/nm that decreases rapidly with increasing D. A linear scaling of the nonlocal signal with longitudinal resistance suggests edge mode transport, which we attribute to the breaking of valley symmetry of graphene due to the spatially fluctuating electric field from the underlying polarized moiré domains. A quantitative analysis suggests the emergence of finite-size domains in graphene that modulate the charge and the valley currents simultaneously. This work underlines the impact of interfacial ferroelectricity that can trigger a new generation of devices.

Wave propagation in bidirectional functionally graded tapered beams incorporating porosity effect

This study addresses wave propagation in beams made of bidirectional functionally graded materials (BDFG) and having nonuniform cross section by using a quasi-3D analytical solution. For the first time, this aspect will be studied. The mechanical characteristics of the beams are supposed to be variable in both axial and transvers direction according to a specific law depending on the porosity. The mathematical formulation used is based on a displacement field containing indeterminate terms and requiring a few variables to be determined. The thickness and width of the beams are assumed to be linearly variable in the longitudinal direction. The equations governing the simply supported beams are obtained by applying the principle of virtual work and are then analytically solved to obtain the phase velocities and wave frequencies. In addition, the validation results reveal excellent concordance of the proposed theory with those given in the literature. Then, a detailed parametric study is carried out to investigate the influence of the several geometrical and material parameters on the wave propagation in BDFG tapered beams. It is observed that these parameters have significant impact on the wave propagation in BDFG tapered porous beams. These results can be used as benchmark solutions for future studies.