Small Deformation Research Articles

Simplified optimization of inerter-enabled tuned mass damper for lightweight-oriented seismic response mitigation of long-span domes

Suspending tuned mass dampers (TMDs) from long-span domes has been studied to mitigate seismic responses of long-span domes. However, the strict weight limitations on the suspension mass in conventional tuned mass dampers (TMDs) hinder their widespread adoption. To address this issue, we introduce the inerter-enabled tuned mass damper (IeTMD) that consists of a suspension mass, tuning spring, and a tuned viscous mass damper (TVMD) sub-system into the seismic vibration mitigation of long-span domes. Under the assumption that long-span domes remain within the elastic range and adhere to the small deformation hypothesis, we have proposed simplified design formulae for IeTMDs, guided by the lightweight-based seismic vibration control criterion. Parametric studies are conducted to illustrate the degree to which an IeTMD can improve the performance of the long-span dome when its key parameters change within certain ranges. The effectiveness of the design strategy in exploiting the damping enhancement effect is confirmed. Time history responses of a benchmark long-span dome demonstrate that the IeTMD has high control efficiency, as bi-directional displacements, accelerations, and base shear are significantly reduced. Comparative analyses between the proposed IeTMD and conventional TMD are conducted. Results show that the IeTMD designed by the simplified design formulae can achieve the target control performance with less suspension mass. Furthermore, the frequency analysis shows that the proposed IeTMD contains a wider control frequency band than conventional TMD, illustrating the promising approach for long-span domes.

А particle model of interaction between weakly non-spherical bubbles

A mathematical model of interaction of weakly non-spherical gas bubbles in liquid is proposed. It is a system оf the second order ODEs in the radii of bubbles, the position vectors of their centers and the amplitudes of their small deformations in the form of spherical harmonics. Compared to the available analogs, the proposed model equations are more accurate in terms of the ratio of the radii of bubbles to the distance between their centers. This allows one to study bubble-bubble interaction at smaller distances between the bubbles. The model equations are quite compact, which simplifies their theoretical analysis and construction of algorithms of their solution. Five problems (dynamics of a single bubble under harmonic excitation, bubble collapse near a plane rigid wall, interaction of three synchronized and nonsynchronized bubbles located in line, and interaction between sixteen bubbles with the centers located on a plane surface) are considered for validation. It is shown that in all cases the proposed model results well agree with the corresponding available experimental data and numerical solutions. For demonstration of the applicability, the proposed model is used to analyze radial oscillations, spatial movements and surface deformations of the bubbles in rectilinear, planar and spatial clusters under harmonic forcing. Initially 125, 121 and 125 bubbles of the clusters are located at the nodes of 1D, 2D and 3D uniform grids, respectively. It is found that the monotonically decaying radial oscillations of the 1D cluster bubbles during one period of forcing are quite similar to those of a single bubble. Unlike this, the attenuation of the radial oscillations of the central bubbles in the 2D and 3D clusters is essentially non-monotonic. The maximum pressures in the central bubbles of the 2D and 3D clusters are significantly higher than in the single and 1D cluster bubbles. In all clusters the maximum deformations of bubbles are in the form of the second spherical harmonics, except for the central bubble of the 3D cluster, the maximum deformations of which are in the form of the fourth harmonics.

Arithmetic and geometric deformations of threefolds

AbstractWe show that mixed‐characteristic and equi‐characteristic small deformations of 3‐dimensional canonical (resp., terminal) singularities with perfect residue field of characteristic are canonical (resp., terminal). We discuss applications to arithmetic and geometric families of 3‐dimensional Fano varieties and minimal models with canonical singularities. Our results are contingent upon the existence of log resolutions for fourfolds.

An approximate formula for the Rayleigh wave velocity in the machined surface with residual stress

The present paper is concerned with the Rayleigh wave propagation in the machined surface with a thin damaged layer with residual stress. We assume that the layer and the half-space are bonded perfectly to each other. Biot’s theory of small deformations influenced by initial stress forms the basis for this study. With the help of the effective boundary condition method, a third-order approximate secular equation of Rayleigh waves is established for the case that the layer and half-space are both orthotropic. In addition, an explicit third-order approximate formula for the Rayleigh wave velocity is derived from the secular equation. By considering a sample of silicon wafer by fine grinding with fine abrasive grains, the accuracy of the approximate formula has been verified. This study is meant to serve as the mathematical foundation for non-destructive testing of residual stress in the practical applications.

Amplitude-Modulated Electrodeformation to Evaluate Mechanical Fatigue of Biological Cells.

Red blood cells (RBCs) are known for their remarkable deformability. They repeatedly undergo considerable deformation when passing through the microcirculation. Reduced deformability is seen in physiologically aged RBCs. Existing techniques to measure cell deformability cannot easily be used for measuring fatigue, the gradual degradation in cell membranes caused by cyclic loads. We present a protocol to evaluate mechanical degradation in RBCs from cyclic shear stresses using amplitude shift keying (ASK) modulation-based electrodeformation in a microfluidic channel. Briefly, the interdigitated electrodes in the microfluidic channel are excited with a low voltage alternating current at radio frequencies using a signal generator. RBCs in suspension respond to the electric field and exhibit positive dielectrophoresis (DEP), which moves cells to the electrode edges. Cells are then stretched due to the electrical forces exerted on the two cell halves, resulting in uniaxial stretching, known as electrodeformation. The level of shear stress and the resultant deformation can be easily adjusted by changing the amplitude of the excitation wave. This enables quantifications of nonlinear deformability of RBCs in response to small and large deformations at high throughput. Modifying the excitation wave with the ASK strategy induces cyclic electrodeformation with programmable loading rates and frequencies. This provides a convenient way for the characterization of RBC fatigue. Our ASK-modulated electrodeformation approach enables, for the first time, a direct measurement of RBC fatigue from cyclic loads. It can be used as a tool for general biomechanical testing, for analyses of cell deformability and fatigue in other cell types and diseased conditions, and can also be combined with strategies to control the microenvironment of cells, such as oxygen tension and biological and chemical cues.

Prediction Parameters for Mining Subsidence Based on Interferometric Synthetic Aperture Radar and Unmanned Aerial Vehicle Collaborative Monitoring

Coal mining induces surface subsidence, making rapid and precise monitoring of this subsidence a key area of current research. To address the limitations of D-InSAR technology in capturing large-gradient deformations in the central subsidence basin and the challenges facing UAVs in accurately monitoring small deformations at the basin’s edge, we propose a method for inverting the expected parameters of surface subsidence by synergistically integrating InSAR and UAV monitoring. We determined the cumulative subsidence of monitoring points along the dip and strike observation line of the Banji 110,801 working face between 10 April 2021 and 28 June 2022, employing D-InSAR and UAV techniques. By leveraging the complementary strengths of both monitoring techniques, we fused the two types of monitoring data and verified the error of the fusion data to be within 10 cm through leveling data verification. Simulation experiments utilizing the probability integration method and the Broyden–Fletcher–Goldfarb–Shanno (BFGS) optimization algorithm confirmed that the 10 cm data source error remains within the required limits for probability integration parameter inversion. Finally, the BFGS algorithm was employed to invert the parameters of the probability integration method based on the fusion data results. Subsequently, these inversion parameters were used to predict the subsidence at the monitoring point and were compared with the level measured data. The results demonstrate that the use of collaborative InSAR and UAV monitoring technology for inverting the expected parameters of surface subsidence in the mining area yields superior results, aligning with the actual patterns of ground surface movement and deformation. This study addresses the global need for unmanned monitoring of mining-related subsidence. It employs InSAR and UAV technologies in a synergistic approach to monitor surface subsidence in mining regions. This approach harnesses the strengths of multiple data sources and presents a novel concept for the unmanned monitoring of surface subsidence in mining areas, contributing to environmental protection efforts.

LOS Deformation Correction Method for DInSAR in Mining Areas by Fusing Ground Data without Control Points

The traditional leveling, total station, and global navigation satellite system (GNSS) and the new differential interferometric synthetic aperture radar (DInSAR) and terrestrial laser scanning (TLS) systems have their own advantages and limitations in the deformation monitoring of mining areas. It is difficult to obtain accurate deformation information only using single-source measurement data. In this study, we propose an LOS deformation correction method for DInSAR in mining areas by fusing ground data without control points. Based on free space data, small deformations at the edges of mining influence areas accurately obtained using DInSAR. By combining leveling/GNSS and TLS methods, it was possible to obtain large deformations in central areas without the need for control points located outside the mining influence range. For overcoming the non-uniform coordinates of the “space–ground” data and the limited overlap of the effective measurement ranges, the subsidence prediction model was employed to assist in its fusion. In addition, in LOS deformation correction, we retained the non-full cycle phase of DInSAR and replaced the full cycle phase with the one from the data fusion. Engineering experiments have shown that the correction results preserve the differences in the LOS deformations at the edge areas of the mine influence range, and they recover the lost LOS deformations at the center areas. Using the difference in the LOS deformation before and after correction as the verification indicator, the maximum absolute value of the errors after correction was 143 mm, which was approximately 6.4% of the maximum LOS deformation. In addition, there were still two errors that were large (−112 mm and −89 mm, respectively), and the absolute values of errors were not more than 75 mm. For all errors, the mean absolute value was 36 mm. Compared with 399 mm before correction, the error was reduced by 91%. This study provides technical support and theoretical reference for deformation monitoring and control in mining areas.

Hybrid unsupervised paradigm based deformable image fusion for 4D CT lung image modality

Deformable image registration plays a critical role in various clinical applications (e.g., image fusion, atlas creation, and tumors targeting). In radiation therapy, especially in the context of fast registration of computed tomography (CT) lung image modalities, it is used to determine the geometric transformation by relating the anatomic points in two images. The main challenge lies in effectively addressing the nonlinear large and small deformation between the inspiration and expiration phases. In this work, we propose an unsupervised hybrid paradigm-based registration network (HPRN) for the registration of 4D CT lung images without relying on ground truth data. The proposed HPRN exhibits effective learning of multi-scale and multi-resolution features, leading to the computation of a more accurate Deformation Vector Field (DVF). Furthermore, we incorporate the regularization, image similarity and Jacobian determinant loss functions, which results in improving capability in dealing with complex large and small deformations. We evaluate the effectiveness of the proposed model on the publicly accessible DIRLab 4DCT lung image dataset, which shows the effectiveness of the proposed framework by achieving better Target Registration Error (2.04±1.42mm) compared to other state-of-the-art unsupervised image registration algorithms.

Fractional viscoelastic models for the estimation of the frequency response of rubber bushings based on relaxation tests

Estimation of the viscoelastic properties of rubber bushings at very high frequencies (up to 2 kHz) is a challenge for many damping component manufacturers in the design stage of a quality monitoring procedure. This investigation is focused on the capability of lower strain rate testing procedures, such as relaxation tests, to estimate and extrapolate the dynamic behavior of rubber bushings from low to moderate frequencies. Fractional Zener models are employed to approach bushing behavior in experimental relaxation tests, thus leading to a linear viscoelastic model which is employed to estimate the dynamic behavior of rubber bushing under harmonics loads up to 150 Hz. The validation of this extrapolation procedure is performed by comparing these analytical results with experimental dynamic harmonic tests applied to the same rubber bushings. The deviation between both curves demonstrates that it is difficult to compare the behavior from very small deformation rates (relaxation tests) to higher deformation rates (harmonic dynamic tests) due to the nonlinear behavior of the rubber and its amplitude dependence. However, this investigation demonstrates that the relaxation tests contain enough data to define the frequency behavior of linear viscoelastic materials up to moderate frequencies.

Investigating the impact of biomimetic pinna shape variations on clutter echoes received from natural environments

Bat species navigating dense vegetation based on biosonar have to obtain the necessary sensory information from “clutter echoes”, i.e., echoes that are superpositions of contributions from many reflecting facets (e.g., leaves) and hence have highly unpredictable waveforms. Prior results have suggested that pinna motions could aid in direction-finding tasks based on deterministic echo patterns. This raises the question whether varying pinna shapes could also have a function significance for challenging biosonar tasks performed on clutter echoes. As a first, task-independent step to test this hypothesis it has been investigated whether different pinna shapes have a consistent effect on clutter echoes despite the random nature of these signals. This was accomplished using a dedicated laboratory setup that produced large amounts of uncorrelated clutter echo data by agitating an artificial foliage with fans between echoes. Deep learning methods were then applied to identify the pinna shape that received a given clutter echo. A two-dimensional convolutional neural network operating on spectrograms achieved 90% validation accuracy in this task. This finding demonstrates that even small pinna deformations can impart consistent effects on the clutter echoes. Ongoing research is directed at analyzing the nature of the signal properties that the successful classifications were based on.

ELASTIC FIELDS AT CORNERS OF HIGHLY STRETCHABLE MATERIALS ARE CONCENTRATED BUT BOUNDED

ABSTRACT Corners concentrate elastic fields and often initiate fracture. For small deformations, it is well established that the elastic field around a corner is power-law singular. For large deformations, we show here that the elastic field around a corner is concentrated but bounded. We conduct computation and an experiment on the lap shear of a highly stretchable material. A rectangular sample was sandwiched between two rigid substrates, and the edges of the stretchable material met the substrates at 90° corners. The substrates were pulled to shear the sample. We computed the large-deformation elastic field by assuming several models of elasticity. The theory of elasticity has no length scale, and lap shear is characterized by a single length, the thickness of the sample. Consequently, the field in the sample was independent of any length once the spatial coordinates were normalized by the thickness. We then lap sheared samples of a polyacrylamide hydrogel of various thicknesses. For all samples, fracture initiated from corners, at a load independent of thickness. These experimental findings agree with the computational prediction that large-deformation elastic fields at corners are concentrated but bounded.

Design and energy absorption of star-shaped nesting cells and gradient lattice structures with negative Poisson’s ratio effect

Star-shaped lattice structures with negative Poisson’s ratio (NPR) effect have a prospective application in the fields of aerospace, vehicle and civil protection due to their excellent capabilities of energy absorption. However, existing gradient lattice structures with NPR effect require significant deformation, making them unsuitable for small space deformation collision buffers in equipment like aircraft and automobiles. To address this issue, this study designs several new star-shaped cell structures (r1, r2, r3), homogeneous structures (R1, R2, R3), and gradient structures (“X”, “V”, “Λ”, “O”). Then the NPR effect, stress–strain curves, specific energy absorption of these structures are studied by the means of quasi-static compression experiments and finite element analysis. The results indicate that among the cell structures, r3 shows the best equivalent elastic modulus, NPR effect, and energy absorption effect, particularly for small deformation. In the case of homogeneous lattice structures, R3 exhibits the highest compressive strength and energy absorption. For gradient lattice structures, the type of gradient has minimal impact on the mechanical properties, but the stress strength and energy absorption improve with an increase in the number of layers. These results could provide a theoretical guidance for the application of NPR structures in buildings, vehicle, and other security protection fields to meet practical engineering needs.

Simulation model of contact interaction during surface strengthening of steel parts

In the processes of surface strengthening of steel parts, the stress-strain state is decisive for explaining the physical processes of strengthening, forming the dimensions of the contact area. Analytical dependences of contact parameters are quite approximate. In this work, based on the Ansys software complex, a simulated model of the contact of a truncated torus with a cylinder is proposed, which demonstrates the kinetics of the process of pressing a hard alloy tool into a steel workpiece - a cylinder. The experiment was conducted for 4 seconds in order to determine the maximum level of stresses, the distribution of stresses and the amount of residual stresses after removing the load. The clamping force was applied mainly in the zone of elastic deformations. The results showed an uneven stress distribution with a maximum in the center of the contact spot of 1082 MPa. After changing the load direction, small residual deformations at the level of 0.00311 μm were observed in the center of the contact patch. This indicates a violation of the elastic region on a small contact area, which does not affect the general nature of the stress distribution and can be removed during the finishing process. The results of simulation of the stressed state are used for the correlation with the observed structural changes of the material during the action of thermal and power stresses. The stress peak was formed at a distance of 200 μm, which contributes to the formation of maximum values of microhardness at this depth.

On the Influence of the Surface Electric Charge on the Regularities of the Formation of Faraday Ripples on the Surface of a Low-Viscosity Liquid

The purpose of the study is to analyze the effect of a surface electric charge on the formation conditions of the Faraday ripples on a horizontal surface of a low-viscosity liquid in a vibration field.Methods. The problem is solved analytically in the limit of small amplitude deformation of the free surface of the liquid. The final relation is derived under the condition that the dissipation is small. The liquid was considered ideally conductive with a surface-distributed electric charge. Results. A simple analytical expression is derived that quantitatively describes the effect of suppression of the Faraday ripple if the surface density of the electric charge increases. It is shown that the increase in the surface density of the electric charge significantly enlarge the threshold value of the vibration field amplitude, the excess of which leads to the formation of ripples. The threshold value of the vibration amplitude is proportional to the viscosity of the liquid and depends on its density, surface tension coefficient and the specific horizontal scale of the ripple.Conclusion. The Faraday’s ripple formed on the surface of a liquid in a vertically oscillating container is very sensitive to the value of the surface density of the electric charge. An increase of the surface charge density leads to suppression of the ripple formation. The effect can be used to prevent the appearance of parasitic convective flows that arise in liquid layers placed in vibration fields. The physical mechanism of Faraday ripple suppression is the rivalry between two qualitatively different types of flows near the liquid surface. Increasing the surface charge density changes the balance of surface forces in such a way as to promote the appearance of aperiodic motions and suppress oscillatory ones. In particular, oscillatory motions responsible for the development of Faraday instability caused by vertical vibrations of the liquid container are suppressed.

Modelling of the deformation behaviour of a magnetic hydrogel in a magnetic field gradient

An ink made of alginate and methylcellulose with embedded magnetite microparticles was developed for extrusion printing. Constructs, so-called scaffolds, are colonised with cells which can be activated by mechanical stimulation. In this work, a defined magnetic field gradient is applied to achieve non-contact deformation. However, the deformation behaviour or relevant material parameters of the hybrid material are unknown. While the properties were determined with experiments adapted to hydrogels, a separate experimental set-up for micro-computed tomography, adapting the Maxwell configuration, was developed to investigate the deformation behaviour. These analyses were performed depending on ageing and particle concentration. For these tests, strands were used as bending beams, since these are simple and well known systems. Firstly, a model for the bending curve was erected, which defines a range in which the real bending curve would be expected. It was compared with the measured bending curves. There was very good agreement for the first days. On day 14, the measured bending curves were still within the calculated range, but at the lower limit due to the shortcomings of the model as the violation of the small deformations condition at this point. Secondly, the bending as a function of incubation duration was observed by a series of radiograms when a magnetic field gradient was applied. From this, a functional approach was formulated to describe the system response. Some parameters have already been identified, for others a proposal is given. Thirdly, microscopic analyses were carried out to observe the effects of the field gradient on particle distribution and structure. It was revealed that a homogeneous particle distribution was found even after 2.5 h. Also, in the direction of the field gradient, no chains were formed and no damage of the network could be detected. The obtained results show, that the material is suitable for mechanical stimulation.

PC-Reg: A pyramidal prediction–correction approach for large deformation image registration

Deformable image registration plays an important role in medical image analysis. Deep neural networks such as VoxelMorph and TransMorph are fast, but limited to small deformations and face challenges in the presence of large deformations. To tackle large deformations in medical image registration, we propose PC-Reg, a pyramidal Prediction and Correction method for deformable registration, which treats multi-scale registration akin to solving an ordinary differential equation (ODE) across scales. Starting with a zero-initialized deformation at the coarse level, PC-Reg follows the predictor–corrector regime and progressively predicts a residual flow and a correction flow to update the deformation vector field through different scales. The prediction in each scale can be regarded as a single step of ODE integration. PC-Reg can be easily extended to diffeomorphic registration and is able to alleviate the multiscale accumulated upsampling and diffeomorphic integration error. Further, to transfer details from full resolution to low scale, we introduce a distillation loss, where the output is used as the target label for intermediate outputs. Experiments on inter-patient deformable registration show that the proposed method significantly improves registration not only for large but also for small deformations.

Study on the deformation of inter-rib shell plate of reinforced conical shell structure under deep-water-explosion loading

The reinforced cylindrical and conical column structures are widely used structural forms in underwater vehicle structures. In this paper, the reinforced conical shell structure in the transition compartment of underwater vehicles was used as the research object. Based on the shock wave propagation theory and ABAQUS acoustic structure coupling numerical simulation method, the numerical simulation model of conical shell structure under deep-water explosion load was established.The deep-water explosion simulation of conical shell structure under the conditions of different water depths, charges and explosion distances was carried out, and the deformation and failure mode of small depressions in the shell plate between ribs of stiffened conical shell structure was obtained, that was, independent small pits were formed along the axis direction. According to the theory of elastic-plastic deformation of plate and shell structure, the small pits of shell and plate between ribs were approximated as the deformation of trapezoidal plate, and the deformation function of trapezoidal plate was obtained by coordinate transformation. The deformation energy of plate and shell was divided into bending deformation energy and midplane strain energy. By establishing the correlation between explosion energy and deformation energy, the theoretical calculation model of the small pit deformation mode of shell and plate between ribs was obtained.

Effective Stiffness and Seismic Response Modification Models Recommended for Cantilever Circular Columns of RC Bridges, First Part: Serviceability Limit State

This paper’s main aim was to explain the process of characterising the structural over-strength factor (R), seismic behaviour factor (Q), and the effective elastic stiffness, Keff, of cantilever-reinforced concrete (RC) urban bridge columns with solid circular cross-sections for use in seismic design under the Serviceability Limit State (SLS). Similarly, mathematical models have been proposed to determine the average values of effective stiffness and seismic response modification factors suggested for cantilever-reinforced concrete bridge columns at SLS. This is because multiple design codes stipulate that cantilever RC bridge columns must meet the SLS requirements. Therefore, to comply, the lateral displacement ductility demand must not exceed unity after a moderate or small earthquake. While the behaviour of the materials remains in the elastic range, this performance criterion can be conservative. If the materials undergo small deformations, the slight damage can be quickly repaired to meet the SLS.

Modeling a sample size-dependency of martensitic phase transformation using a mesoscale framework

Predicting a sample size-dependency of the constitutive response of any material system when it is being used in nano- and micro-scale devices, such as NEMS and MEMS, is very crucial for their design process. This also includes the shape memory alloys (SMAs), where predicting a sample size-dependency of the phase transformation process is the key aspect. Many experimental studies with micropillar compression tests showed an increase in critical stress to transformation and an increase in transformation hardening as the sample size decreases below a critical size. In this work, we have employed and extended a recently developed mesoscale framework to model such size effects in SMAs. A plane strain tensile SMA strip of finite width is analyzed within a small deformation framework. The martensitic transformation regions are modeled as Eshelby inclusions in an austenite phase matrix. Circular potential nucleation sites are considered with a square packing for their spatial locations and with nucleation stress assigned to each site from a Gaussian distribution. The combination of the Gaussian distribution of nucleation stress and the size of the nucleation site represents the underlying SMA material microstructure. Our numerical analysis, with varying values of the aspect ratio between the strip width and the nucleation site size, provides a critical value of the aspect ratio characterizing a transitioning length scale between a bulk vs. a sample size-dependent phase transformation behavior. At the transition, the critical stress to phase transformation and the transformation hardening increase drastically as the aspect ratio decreases below its critical value. The limitations of these predictions are discussed with existing literature on experimental observations, and some perspectives to improve the model are stated.

Effects of alkalinization and addition of pea protein as a co-protein to zein for the development of gluten-free doughs

The effects of adding pea protein isolate (PPI) as a co-protein to calcium hydroxide deamidated zein were evaluated by fundamental rheological properties of gluten-free doughs measured at room temperature and FT-IR. Rice starch was used as a carbohydrate source at a constant concentration. Gluten-free doughs prepared with PPI, PPI + zein, zein under alkaline conditions, and PPI + zein under alkaline conditions were compared with a control sample containing gluten. Small and large deformation rheological tests indicated that the combination of PPI and the alkaline treatment of zein improved the gluten-free rheological properties, leading to a similar rheological performance to the control containing gluten. The sole addition of PPI to zein, or the alkaline deamidation of zein alone, did not generate doughs with desirable rheological behaviors. Quantification of the different conformations of the protein's secondary structure by FT-IR analysis confirmed that better rheological properties of dough containing PPI and zein under alkaline conditions are associated with higher amounts of β-sheets conformations. The use of zein is often limited to temperatures above its glass transition temperature (≈28 °C), but the results from this study provide important insights for the application of zein at room temperature in gluten-free doughs.