Spring Model Research Articles

Homogenization using lattice spring models for couple stress theory under plane strain deformation

Homogenization using lattice spring models for couple stress theory under plane strain deformation

Numerically evaluate axial force variations of jointed precast piles during construction

The axial force variation along the length of the jointed precast pile is influenced by the hard soil layer properties during construction. For this purpose, this research proposes an innovative concept of spring model of jointed precast pile to evaluate the axial force variations along the length to consider some variable parameters (i.e. soil elastic moduli, soil Poisson’s ratios, hammer loads, compressive strengths and sizes of precast piles). The linear elastic analysis is performed by using finite element-based software ETABS v. 18.1.1 to consider 3-nodded line element of the jointed precast pile. Variable parameters are influenced to increase the normalized axial force of the jointed precast pile because of increasing stiffness, self-weight, etc. The difference in result of 6.84% may indicate a good agreement with the verification of the numerical analysis. The rates of the normalized axial force increments for variable soil elastic moduli, soil Poisson’s ratios, and precast pile sizes are found to be (1 to 2) %, (1.25 to 1.75) %, and (27 to 36) %, respectively. In addition, the maximum axial force increment rate is found to be 0.47% for precast pile sizes of 400 × 400 and 450 × 450 mm.

A Seasonal Fresh Tea Yield Estimation Method with Machine Learning Algorithms at Field Scale Integrating UAV RGB and Sentinel-2 Imagery

Traditional methods for estimating tea yield mainly rely on manual sampling surveys and empirical estimation, which are labor-intensive and time-consuming. Accurately estimating fresh tea production in different seasons has become a challenging task. It is possible to estimate the seasonal yield of tea at the field scale by using the spatial resolution of 10 m, 5-day revisit period and rich spectral information of Sentinel-2 imagery. This study integrated Sentinel-2 images and uncrewed aerial vehicle (UAV) RGB imagery to develop six regression models at the field scale, which were employed for the estimation of seasonal and annual fresh tea yields of the Yunlong Tea Cooperatives in Yixiang Town, Pu’er City, China. Firstly, we gathered fresh tea production data from 133 farmers in the cooperative over the past five years and obtained UAV RGB and Sentinel-2 imagery. Secondly, 23 spectral features were extracted from Sentinel-2 images. Based on the UAV images, the parcel of each farmer was positioned and three topographic features of slope, aspect, and elevation were extracted. Subsequently, these 26 features were screened using the random forest algorithm and Pearson correlation analysis. Thirdly, we applied six different regression algorithms to establish fresh tea yield models for each season and evaluated their estimation accuracy. The results showed that random forest regression models were the optimal choice for estimating spring and summer yields, with the spring model achieving an R2 value of 0.45, an RMSE of 40.38 kg/acre, and an rRMSE of 40.79%. Similarly, the summer model achieved an R2 value of 0.5, an RMSE of 78.46 kg/acre, and an rRMSE of 39.81%. For autumn and annual yield estimation, voting regression models demonstrated superior performance, with the autumn model achieving an R2 value of 0.42, an RMSE of 70.6 kg/acre, and an rRMSE of 39.77%, and the annual model attained an R2 value of 0.47, an RMSE of 168.7 kg/acre, and an rRMSE of 34.62%. This study provides a promising new method for estimating fresh tea yield in different seasons at the field scale.

Numerical evaluation of the internal fracture mechanism of horizontal loop connections in precast elements under the influence of transverse reinforcement

AbstractThis study numerically evaluated the flexural capacity and fracture mechanism of precast reinforced concrete beams connected with in situ horizontal loop connections employing the three‐dimensional rigid body spring model (3D‐RBSM) for modeling of concrete and beam elements (BEs) for modeling of steel, respectively. The research analyzed the performance of continuous horizontal loop connections with and without transverse reinforcement, considering varying vertical spacing between loops and transverse steel ratios. The numerical model effectively captured the test load displacement relationships by incorporating the model parameters like Young's modulus, tensile strength, fracture energy, compressive strength, cohesion, and angle of internal friction for concrete along with mechanical properties of steel and revealed that loop joints without transverse reinforcement exhibited loop type failure. In contrast, specimens with transverse reinforcement improved the peak load and caused compression failure. It was discovered that transverse rebars on the continuous side of the joint experience more strain; particularly, the maximum strain occurred in the corner rebars within the curved sections of U‐rebars. Moreover, the increased vertical spacing between the loop rebars increased the diagonal crack propagation and demonstrated the loop‐type failure. Further, a larger circumferential area of transverse rebar offered greater bond strength and confinement to the concrete core and reproduced the maximum deformation capacity, ductility, and compression failure.

Dispersion characteristics of Lamb wave in a multilayered magnetoelectroelastic plate with an imperfect interface

In this study, we investigate Lamb wave propagation in a multilayered magnetoelectroelastic plate with an imperfect magnetoelectroelastic interface using the generalized linear spring model (GLSM). The dispersion relation of the Lamb wave is obtained using an improved Legendre polynomial expansion method, which converts the wave problem into a linear eigenvalue system. The effectiveness of the present method was verified through comparison with two existing cases: SH wave in a bilayer plate with an imperfect interface and Lamb wave in a bilayer plate with a perfect interface. Numerical examples were presented for various multilayered plates composed of BaTiO3/CoFe2O4. The effects of the spring constant combinations, including the degree of mechanical, electric, and magnetic interface imperfections, layer thickness ratio, electromagnetic boundary condition, and stacking sequence on the dispersion characteristics are illustrated. The effect of the thickness ratio on the magneto-electromechanical coupling factor and the sensitivity of the phase velocity at different frequencies to changes in the interface characteristics are also discussed. The present investigation is of practical interest for developing new layered composite structures made of smart piezoelectric and piezomagnetic materials for engineering applications.

Analysis of imperfect interfaces in cobalt ferrite plates using a linear spring model: a comparative study with terfenol-D

PurposeThis research aims to explore the transmission of seismic surface waves through a two magneto-strictive materials i.e. cobalt ferrite and Terfenol-D when embedded in a plate-substrate configuration with non-ideal interface. The study focuses on understanding the impact of width of the plates, imperfect parameter, heterogeneity parameter on both the materials cobalt ferrite and Terfenol-D under magnetically open and short conditions.MethodologyTo achieve this, the study employs a variable-separable technique following Direct Sturm-Liouville method and appropriate boundary conditions to derive frequency relations for both magnetically open and short circuit scenarios. Numerical simulations are conducted to investigate the effects of width of the plates, imperfect parameter, heterogeneity parameter on both the materials cobalt ferrite and Terfenol-D under magnetically open and short conditions.FindingsThe research findings indicate that the phase velocity is increasing more in Terfenol-D as compared to Cobalt ferrite, either the case magnetically open or closed. Graphical comparisons highlight the impact of width plates, imperfect parameter, heterogeneity parameter on the characteristics on wave propagation clearly.Research limitationsThe study is confined to linear wave propagation and does not consider nonlinear effects. Additionally, the analysis is based on idealized material properties and interface conditions.Practical implicationsThe results of this research can contribute to the design and optimization of sensors, energy harvesters, and wave manipulation devices utilizing piezomagnetic materials. Understanding the behaviour of surface waves in these structures is crucial for their effective application.OriginalityThis study offers a comprehensive analysis of surface wave propagation in two different types of piezomagnetic composite structure by considering heterogeneity and interface conditions. The comparative study of different piezomagnetic models and the incorporation of heterogeneity and interface conditions contribute to the originality of the research.

General Solution for Longitudinal Response of Shield Tunnel Considering the Effects of Joints and Soil Shear Resistance

ABSTRACTThis study introduces a general solution for assessing the longitudinal response of shield tunnels, incorporating the combined effects of joints and soil shear resistance. The analysis employs the Timoshenko beam spring model atop a Vlasov foundation, subjected to arbitrary loads and various boundary conditions. Governing equations and relevant boundary conditions are derived using a variational formulation. Validation is conducted against existing simplified analytical solutions and finite element method simulations, showing the efficacy of the proposed solution. Comparative analyses of different models are undertaken based on the potential energy considerations. Additionally, a parametric study explores influential factors such as subgrade shear and reaction coefficients, as well as joint stiffnesses. Findings highlight the significance of accounting for the soil shear resistance and caution against underestimation when using equivalent continuous beam models. The proposed solution improves the prediction accuracy for the longitudinal response of shield tunnels and offers several benefits including compatibility with other analytical models, computation efficiency, and versatility in considering diverse loads and boundary conditions.

Seismic Fragility Analysis of Offshore Wind Turbines Considering Site-Specific Ground Responses

This study investigated the seismic performance and assessed the seismic fragility of an existing pentapod suction-bucket-supported offshore wind turbine, focusing on the amplification of earthquake ground motions. A simplified suction bucket–soil interaction model with nonlinear spring elements was employed within a finite element framework, linking the suction bucket and soil to hypothetical points on the OWT structures at the mudline. Unlike conventional approaches using bedrock earthquake records, this study utilized free-field surface motions as input, derived from bedrock ground motions through one-dimensional wave theory propagation to estimate soil-layer-induced amplification effects. The validity of the simplified model was confirmed, enabling effective assessment of seismic vulnerability through fragility curves. These curves revealed that the amplification effect increases the vulnerability of the OWT system, raising the probability of exceeding damage limit states such as horizontal displacement of the tower top, tower stress, and horizontal displacement at the mudline during small to moderate earthquakes, while decreasing this likelihood during strong earthquakes. Comparisons between the Full Model and the simplified Spring Model reveal that the simplified model reduces computational time by approximately 75%, with similar seismic response accuracy, making it a valuable tool for rapid seismic assessments. This research contributes to enhancing seismic design practices for suction-bucket-supported offshore wind turbines by employing a minimalist finite element model approach.

Coarse-graining bistability with the Martini force field

An increasing interest in molecular structures whose long-term dynamics resemble those of bistable mechanical systems promotes the search of possible candidates that may operate as two-state switching units. Of particular interest are the systems that are capable to exhibit such bistable effects as spontaneous vibrations, stochastic resonance, and spontaneous synchronization. Previously, in all-atom molecular dynamics simulations, it has been demonstrated that short pyridine–furan springs show these bistable phenomena. In this article, we introduce a coarse-grained model of such springs and investigate the possibility to observe the bistability effects, such as spontaneous vibrations. Our findings allow the studies of short pyridine–furan springs at large time and length scales and open field for further computational research of large bistable systems.

Phase diagram and boundary of impact outcomes

This study investigates the outcomes of droplet impact under varying impact velocities (Weber numbers) and surface wettability, using experimental methods, with a particular focus on the boundaries between these outcomes. Three primary outcomes were identified at lower Weber numbers (We ≤ 100): deposition, partial rebound, and complete rebound. Discrepancies were observed between existing boundary models for rebound (partial and complete) and deposition, and the actual experimental results. To address this, a new model was developed based on the “water spring model” proposed by Balance et al., incorporating the effects of contact line dissipation and adhesion forces. This model showed improved accuracy in predicting these outcomes. At higher Weber numbers (We > 100) and contact angles (θ > 100°), two main outcomes, receding breakup and prompt splash, were observed. By comparing the instability stresses driving these outcomes, a novel predictive boundary for receding breakup and prompt splash was proposed. This model's accuracy was validated through experimental data from phase diagrams. This research offers new insights into understanding droplet impact behavior under different surface wettability conditions.

Complete dynamic model of a Slinky based on torsion springs

In this paper a dynamic torsion spring model is extended to be applicable to Slinky's with a wide range of possible initial configurations. In the extended model the coil-on-coil impact is modelled by conserving momentum and modelling the impact as an inelastic impact with a zero coefficient of restitution. The extended model is applied to a plastic Slinky and a steel Slinky. The extended model is demonstrated to have the qualitatively correct dynamic behavior. The extended torsion spring model is now in a form to be applied to a wide range of Slinky behavior such as pseudo-levitation, wave propagation phenomena and stair walking.

Modeling and Optimization of Energy Harvesters for Specific Applications Using COMSOL and Equivalent Spring Models.

Energy harvesting from natural sources, including bodily movements, vehicle engine vibrations, and ocean waves, poses challenges due to the broad range of frequency bands involved. Piezoelectric materials are frequently used in energy harvesters, although their effectiveness depends on aligning the device's natural frequency with the frequency of the target energy source. This study models energy harvesters customized for specific applications by adjusting their natural frequencies to match the required bandwidth. We evaluate commercially available piezoelectric transducers and model them using COMSOL Multiphysics alongside an equivalent spring-mass schematic approach, enabling precise adjustments to optimize energy capture. The proposed system achieves a maximum power output of 160 µW and a power density of 187.35 µW/cm3 at a natural frequency of 65 Hz. Furthermore, the theoretical maximum power density is calculated as 692.97 W/m3, demonstrating the system's potential for high energy efficiency under optimal conditions. Simulations are validated against experimental data to ensure accuracy. Our findings provide a design framework for optimizing energy harvester performance across diverse energy sources, leading to more efficient and application-specific devices for varied environmental conditions.

Semi-Monolithic Multijunction Devices for Unassisted Photoelectrochemical Water Splitting

Although foundational to multi-junction (MJ) photoelectrochemical (PEC) device synthesis, monolithic integration presents major limitations in process compatibility. Consequently, conductive adhesive-based interconnection scheme emerged as a suitable method to overcome limitations and to integrate incompatible material classes into MJ devices without compromising the integrity of the constituent layers. As the conductive adhesive generally employ a polymer matrix, the conductivity of this composite material depends on the conductive filler material. Among which, a core-shell type silver coated PMMA (Ag-PMMA) conductive microsphere filler has gained significant interest in the PV and PEC community due to its ability to exhibit reliable out-of-plane electrical conductivity (0.1 Ω-cm2) and good optical transparency (T > 90%), as we demonstrate for an epoxy-based transparent conductive composite (TCC) consisting of low particle loading (0.1 - 5 vol%).By implementation of the Ag-PMMA based TCC paired with a device exfoliation method, further referred to as semi-monolithic integration, independently processed substrate-grown single junction (SJ) devices were successively bonded and transferred via exfoliation onto a single host substrate to create a MJ device. As a proof-of-concept demonstration, we constructed the world’s first whole-chalcopyrite triple junction MJ device comprising 1.13 eV and 1.44 eV Cu(In,Ga)Se2 and 1.85 eV CuGa3Se5 sub-cells, with the TCC acting as the recombination layer between each sub-cell. The device exhibited an open circuit voltage of 1.85 V and is capable of splitting water with an STH efficiency of 3% in a PV-electrolysis configuration. Furthermore, a TCC-based bifacial MJ device comprising 1.7eV perovskite and 1.1eV Cu(In,Ga)Se2 sub-cells exhibited STH efficiency exceeding 10% in a PV-electrolysis configuration.Although the use of Ag-PMMA based TCC has shown to be an effective approach to prepare MJ devices, mechanical and electrical design and optimization is required to reliably appropriate the TCC as an optoelectronic device interconnect and to scale the semi-monolithic integration method. In the context of mechanical optimization, it has been shown that the degree of deformation of conductive microsphere filler is a key factor in establishing electrical connections. Up until now, the load-deformation characteristic of a single Ag-PMMA microsphere has not been measured. As such, we present in this communication a mechanical model based on measured load-deformation characteristics of a single Ag-PMMA microsphere to facilitate a spring model to better predict the deformation of multi-particle systems with respect to applied load. Furthermore, a finite element electrical model is implemented to determine the effects of electrical contacts across the sub-cell emitter layer and the resulting charge transport resistive losses. Hence, we demonstrate the critical factors influencing the quality of TCC as an anisotropic electrical interconnection layer, and provide a computational mechanical and electrical model to understand and mitigate parasitic resistive losses.

Topological Properties of Network Spring Models that Determine Terminal Distributions of Plastic Deformations

Topological Properties of Network Spring Models that Determine Terminal Distributions of Plastic Deformations

Stiffness model for pneumatic spring with air-diaphragm coupling effect

An accurate pneumatic spring stiffness model is essential for achieving subhertz, quasi-zero stiffness vibration isolation in optical experiments, precision measurements, and semiconductor manufacturing involving heavy equipment. Conventional stiffness models for pneumatic springs with diaphragms often neglect the effect of the elastic diaphragm, making it difficult to accurately characterise pneumatic spring stiffness. This paper presents an innovative pneumatic spring stiffness model that incorporates the air-diaphragm coupling effect—a phenomenon in which the air and diaphragm interact synergistically to affect stiffness. The inclusion of this coupling effect alters the effective area and volume of the pneumatic spring, two critical parameters influencing stiffness. Detailed mechanical and geometrical derivations are provided to establish an accurate stiffness model. A modification coefficient is introduced to quantify the air-diaphragm coupling effect on stiffness, and various factors influencing this coefficient, as well as their impact on stiffness, are examined. An experiment was conducted to validate the proposed model, showing a relative error of less than 1.65 % between the experimental and theoretical results. Considering the air-diaphragm coupling effect, the absolute error approximation was reduced by an order of magnitude, and the relative stiffness decreased by 11.05 % and 8.26 % in Experiments 1 and 2, respectively. Owing to its high precision, the proposed model provides theoretical guidance for the engineering design of pneumatic springs and facilitates the accurate matching of quasi-zero stiffness vibration isolation systems for heavy equipment in ultra-precision applications.

Comprehensive analysis of mode-I cracking in ice: Exploring full-range rate dependency

Ice, as a crystalline material, demonstrates a unique response in its mode-I fracture toughness to variations in loading rates, characterized by an initial decrease and subsequent increase in toughness. This phenomenon has been explored in limited studies. In this work, an extensive numerical analysis of mode-I ice cracking is conducted by using the distinct lattice spring model (DLSM). Norton-Bailey Drucker-Prager DLSM (NB-DP-DLSM) is initially employed to investigate the classical explanations of creep and stress relaxation for the anomaly observed in ice’s fracture toughness at lower loading rates, but this approach does not successfully replicate the experimentally observed strain rate dependency. Then, two rate-dependent constitutive models are introduced to further examine the mode-I fracture mechanics of ice. Our numerical simulations of three-point bending tests show that the relationship between fracture toughness and strain rate at lower levels is more accurately captured by rate-dependent models. For higher strain rates, our numerical modeling of notched semi-circular bending tests indicates that a rate-independent constitutive model can replicate the loading rate dependency of ice’s mode-I fracture toughness. In conclusion, these observations suggest that a reverse-stage-like dynamic constitutive model for DLSM can potentially capture the full range of loading rate dependencies observed in ice.

Design, Modeling, and Characteristics Analysis of Halbach Permanent Magnetic Spring

Magnetic springs, which can be used to replace traditional mechanical springs, have many advantages, such as necessitating no physical contact, generating no friction, no vibration or noise, and having a long lifespan. Nevertheless, their strong nonlinearity limits their widespread application. In this study, we developed a novel permanent magnet spring to address this issue: a Halbach permanent magnetic spring, with a large levitation force and an approximately linear force characteristic curve. First, we introduce the structure and the parameters of the Halbach permanent magnetic spring. Second, we describe the levitation force performance and the stiffness performance of the Halbach permanent magnetic spring using finite element analysis. Third, we analyze the trends through which different parameters influence the levitation force performance and stiffness performance. Finally, we provide recommendations for the future design of and improvement in the Halbach permanent magnetic spring.

Dynamic Modeling of Suspension with Air Spring

The present work aims to model a ¼ vehicle semi-active suspension, using a combination of air spring and magneto-rheological damper. The modeling of the magneto-rheological damper will be based on the Wang model, which will be calibrated through experimental tests. The air spring model will be employed to compare performance between discrete mechanical models and the thermodynamic model. Various semi-active control strategies, such as bang-bang type skyhook/groundhook and PID, will be explored for comparison with existing selective passive systems on the market. The study of the air suspension with magneto-rheological damper will be evaluated from the perspective of comfort and drivability, following standardized parameters (ISO 2631:1978).

Development of Johnson-Cook-Distinct Lattice Spring Model and its application in projectile penetration into metal targets

Projectile penetration into metal targets plays an important role in modern protective structure engineering, damage assessmentin terrorist attacks, and car clash accident analysis, etc. The penetration process of metal target has been characterized by large deformation, high temperature, high pressure, and dynamic damage, which can be classified as a continuous-discontinuous dynamical process. To capture the dynamic responses of metal materials subjected to high-speed penetration, Johnson-Cook model has been implemented in a continuum-discrete model, namely, Distinct Lattice Spring Model (DLSM). This is achieved by redefining the constitutive model in DLSM, with plasticity hardening (plastic strain effects), strain rate, temperature, damage evolution, equation of state, etc., being taken into account, thus developing a new numerical model called JC-DLSM model. This model is validated through studying Taylor rod high-speed impact experiments, thin metal plate penetration experiments, and projectile impact experiments on titanium alloy targets. Good agreement between numerical modelling and experimental data has been achieved for all cases considered, thereby demonstrating the capability of JC-DLSM to reproduce the damage characteristics and ballistic limits of metals under high-speed impact/penetration. Then, the impacts of projectile shape, metal target surface configuration on the characteristics of penetration damage patterns have been investigated. This contributes to a better understanding of the damage mechanisms of metal targets upon penetration or impact, facilitating the computational means for analysing and optimizing the penetration resistance of protective engineering structures.

The effect of the floor-wall interaction on the post-elastic rocking behaviour of segmented CLT shear walls

This paper investigates the impact of floor-wall interaction on the lateral rocking behaviour of two-panel segmented Cross-Laminated Timber (CLT) shear walls through experimental testing and numerical analyses. The study extends a simplified equivalent spring modelling approach to the post-elastic domain to accurately simulate the effects of floor-wall interaction. Experimental withdrawal tests on four types of floor-to-wall connections, utilizing Fully Threaded Screws (FTSs) and Partially Threaded Screws (PTSs) at varying inclinations, revealed that FTSs exhibited higher stiffness and load-carrying capacity but lower deformation capacity compared to PTSs. The maximum force of FTS connections was about twice that of PTS connections, while PTS connections achieved ultimate displacements up to seven times greater. Numerical analyses using a parametric framework showed that floor-wall interaction increases the stiffness and lateral load-carrying capacity of segmented shear walls, with a significant reduction in deformation capacity. These analyses also demonstrated that the equivalent spring can effectively replicate the influence of floor-wall interaction on shear wall lateral response. Expressions for calculating the strength and ductility of this equivalent spring were developed, considering a limited set of geometric and mechanical parameters. These expressions provide a simplified yet accurate method for estimating the effects of floor-wall interaction. The findings suggest that understanding the interaction between floor and wall elements is crucial for optimizing the performance of segmented CLT shear walls in seismic and lateral load scenarios.