Initial Impact Velocity Research Articles

Two novel semi-analytical coefficients of restitution models suited for nonlinear impact behavior in granular systems

This study proposes two novel semi-analytical coefficients of restitution (CoR) models to predict nonlinear impact behavior in granular systems. The models address energy loss at the end of the compression phase, redefining a characteristic length to enhance the equation of motion for colliding particles. The first, the inverse CoR model, derives from the inverse collision approach, introducing a length parameter for its analytical solution. The second, the energy CoR model, is proposed by integrating the damping force in conjunction with the energy conservation principles. Both models are semi-analytical since the characteristic length is numerically determined. Despite differing in derivation, both models account for initial impact velocity and material properties. Comparative analysis highlights their advantages over existing models, with validation through experimental data. Simulations confirm that the models yield accurate predictions for both metal and nonmetal contacts, at high and low impact speeds.

Gradient 2D re-entrant cores for sandwich structures under low-velocity impact

Auxetic metamaterials, known for their unusual properties, are being explored as cores for sandwich structures to improve impact resistance. This study investigated the low-velocity impact response of sandwich panels with various core designs using finite element method (FEM) and experiments on 3D-printed specimens. These cores include pure honeycomb, pure auxetic, and gradient variations with controlled gradients of Poisson’s ratio, transitioning from negative to positive (NTP), positive to negative (PTN), negative-to-positive-to-negative (NTPTN), and positive-to-negative-to-positive (PTNTP). These gradients were achieved by adjusting the unit cell angle within the core. Under quasi-static indentation, the gradient PTN design improved energy absorption by 26% compared to the honeycomb structure, while the gradient NTP structure showed a 9% improvement over the auxetic core. As for the impact tests, the gradient NTP and PTN structures significantly enhanced the indentation resistance of auxetic and honeycomb structures by 21.3% and 6.5%, respectively. Interestingly, while the optimal core for peak energy absorption varied with impact velocity, gradient structures generally provided superior energy absorption, particularly at lower velocities. FEM results at initial impact velocities of 10, 15, 20 m/s confirmed that structures having negative Poisson’s ratio at their top layer exhibited the lowest penetration depth. Additionally, gradient structures, particularly NTP and NTPTN, demonstrated superior energy absorption capability compared to purely auxetic or honeycomb structures, especially at lower velocities. The study highlights the benefits of utilizing gradient auxetic metamaterial cores in high-performance sandwich structures for impact resistance applications. These structures showed minimal localized damage, reduced densification risk due to uniform crushing, and lower penetration depth.

Self-driven transport and heat transfer characteristics of a droplet on a wettability-gradient surface by front-tracking method

Droplet manipulation is a multidisciplinary field with broad applications across various industries. It holds significant potential in areas such as microfluidics, oil–water separation, water harvesting, and heat transfer. However, there is still a lack of comprehensive knowledge regarding droplet migration on restricted surfaces. In this study, we conducted a numerical simulation using the front-tracking method to investigate the heat transfer associated with droplet migration on a cold plate with a wettability gradient. We examined the effects of relative temperature differences, surface wettability, low initial impact velocities (We≤10), and wettability constraints (the width of the wettability stripe capable of driving droplet movement) on various droplet-related heat transfer characteristics and the resulting temperature field distribution. Our key findings indicate that as the temperature difference between the droplet and the surface increases, the heat flux experienced by the droplet after deposition also increases. Additionally, the decline in the heat flux curve during the descending phase becomes more significant. The surface contact angle plays a crucial role in the heat transfer dynamics during droplet migration. Droplets reach thermal equilibrium more quickly on hydrophilic surfaces with smaller contact angles. Higher initial impact velocities initially cause droplets to rebound on the surface, leading to more pronounced fluctuations in transient heat flux during the impact phase. However, as droplets transition from the rebound phase to the migration phase, the impact velocity's influence diminishes. Additionally, the restricted wettability (W*) affects the droplet-surface heat transfer through variations in the wetting area. We observed a fourfold difference in the relative wetting area between W*=0.4 and W*=2.5 in the final stage.

Solidification process of hollow metal droplets impacting a substrate

Recently, there has been a renewed interest in hollow droplet impact, as the internal bubble makes a difference in the spreading morphology during thermal spraying and three-dimensional printing. This paper is dedicated to the solidification process of a hollow metal droplet impacting a cold substrate. The influence of initial impact velocity and substrate temperature on the spreading process is numerically investigated by employing a phase-field method coupled with a solidification model. Solidification was shown to strongly alter droplet spreading and the flow state of the center liquid column. To describe the flow state of the center liquid column, three patterns, namely ‘no-jet’, ‘transition region’, and ‘counter-jet’ are defined. The simulation results show that the formation of the center counter-jet is inhibited by the solidification layer when Péclet number Pe<357, where Pe is the ratio of convection rate to diffusion rate. In addition, the critical Pe at which the phenomenon of counter-jet occurs gradually rises with the substrate temperature falling. Finally, a quantitative analysis of the maximum spreading diameter is proposed by establishing an energy conservation equation. The predicted diameters are in good agreement with the simulated results. It allows us to provide a general expression for the hollow droplets' maximum spreading diameter, using the impact and temperature parameters.

A semi-analytical approach for dynamic responses of monopile-supported offshore wind turbines subjected to accidental loads

Offshore wind energy is leading the way in sustainable energy generation. Offshore wind turbines (OWTs) need to be designed to withstand extreme or accidental loads in Ultimate Limit States (ULS) and Accidental Limit States (ALS), whereby high order eigenmodes may become significant. This paper introduces a semi-analytical approach for efficient and reliable analysis of the dynamic responses of monopile-supported OWTs subjected to accidental loads. A Rayleigh-Ritz solution is initially adopted to determine the high-order natural frequencies and eigenmodes of monopile OWTs, explicitly considering tapered towers and soil-pile interactions. Dynamic responses of OWTs are then calculated depending on the interaction schemes between accidental loads and the structures, e.g. soft contact loads (e.g. slamming, wind) and hard contact loads (e.g. ship collisions, ice impact). For soft contact loading conditions, the loads are considered independent of turbine responses, and the transient dynamic response is computed using the classical modal superposition method. While for hard contact loading conditions, the load actions depend on the contact stiffnesses and responses of the interacting bodies. A numerical contact algorithm is thus developed, and numerical iterations are performed to ensure convergence. The proposed approach is applied to the DTU 10 MW monopile-supported OWT subjected to extreme water slamming and ship collisions, respectively as example applications of soft and hard contact scenarios. The results are verified against nonlinear finite element analysis using USFOS and discussed with respect to the turbine natural frequencies and eigenmodes, contact forces and dynamic responses. A parametric analysis is conducted for ship-OWT collisions, exploring different impact scenarios by varying ship sizes, contact stiffnesses, and initial impact velocities. The proposed approach can serve as a promising tool for accidental load response analysis and the design of monopile OWTs.

The effect of cavity shape on critical high-temperature regions formation pattern and structural evolution difference in explosive particle bed

The occurrence of critical high-temperature regions within explosives is a crucial factor in initiating combustion and explosion. The primary causes of hot regions in cavity-containing explosives are dissipative processes occurring inside the explosive or at its interface, such as shear, friction, viscosity, plasticity, and heat transfer. Currently, there is limited research on the generation and dissipation mechanisms of critical high-temperature regions in cavity-containing explosives during impacts, based on the mesoscale analysis that describes particle motion. In this study, a model based on the discrete element method is employed allowing for an accurate analysis of the dynamic and thermodynamic processes among particles, which systematically considers the shear history between particles, elastoplastic collisions, and heat transfer between particles. The temporal evolution of particle temperature and dissipated work contours during the impact process of explosives with different cavity shapes is analyzed. Explosives with cavities undergo three stages during the impact process: the formation of the trapezoidal high-temperature region, cavity collapse, and dispersion of the particle bed, ultimately leading to the formation of two main critical high-temperature regions: near the cavity and near the wall. The temperature rise of hot particles near the wall can be roughly divided into two stages, and the temperature rise mechanisms are different. Initially, the temperature rise is primarily attributed to plastic dissipation of hot particles, and the same initial impact velocity results in the same temperature rise. During the cavity collapsing, continuous momentum transfer occurs between the hot particles near the wall and the particles in the high-temperature shear bands, deeply influencing the development of the high-temperature shear bands through the movement of the hot particles near the cavity. Therefore, the different collapse modes of hot particles near cavities of different shapes lead to differences in the later temperature evolution of the hot particles near the wall. The unique aggregation processes of hot particles near cavities of various shapes result in distinct high-temperature region morphologies: circular cavity exhibits approximate “——” shape, triangular cavity displays arch shape, and inverted triangular cavity presents “M” shape. Significantly, a new mechanism resulting from the interaction of two opposing “jet “flows for the formation of higher-temperature hot regions near the circular cavity has been discovered.

Analysis of bi-directional functionally graded plate on an elastic foundation subjected to low velocity impact using the refined plate theory

This study investigates the mechanical response of a bi-directional functionally graded plate consisting of three distinct materials when subjected to low-velocity impact. Utilizing the New Refined Plate Theory, the research explores the mechanical behavior of the plate resting on a Pasternak elastic foundation, providing insights useful for engineering applications. The investigation examines various parameters, including initial impact velocity, projectile radius, volume fraction indices, and elastic foundation stiffness, and their effects on critical response characteristics such as contact force, indentation, lateral deflection, and projectile velocity. The theoretical predictions are validated through detailed comparisons with existing literature and numerical simulations, ensuring the reliability and applicability of the proposed methodology. This study introduces a novel approach using refined plate theory to analyze low-velocity impact on 2D-FGMs, providing practical insights for structural analysis. The findings deepen understanding of functionally graded materials and enhance the evaluation of impact-resistant structures. The research highlights the importance of diverse parameters in improving structural performance and reliability, relevant across aerospace, civil, and mechanical engineering. Detailed exploration shows that initial impact velocities and projectile radius enhance impact force and deflection, while volume fraction indices and foundation stiffness influence the dynamic response.

Ejecta velocity and motion model of spherical aluminum alloy projectile hypervelocity impact on basalt

A series of small-scale impact cratering experiments were performed on basalt at velocities of 3.5–6.0 km s−1. The formation and motion process of ejecta were observed by high-speed and ultra-high-speed cameras. The momentum transfer coefficient values and cratering size were measured. Hydrodynamic simulations in 2D were carried out to replicate the impact conditions of the basalt and calibrate model parameters. The contribution of jet, central cratering, and spalling ejection to momentum enhancement was quantitatively analyzed by simulation. Simulation results show that: the mass and the momentum of the jet are less than 1 % of the projectile mass, and the initial momentum, can be ignored. For craters in small-sized basalt, the momentum enhancement mainly comes from the spall region ejecta. The formation mechanism of ejecta at different stages was analyzed based on the shock wave and jet theory. An analytical model is developed for estimating the velocity and motion of ejecta formation at different stages. The model calculation results of the speed of the ejecta formed in different stages are consistent with the numerical results. The maximum velocity of the ejecta formed in the jet and cratering stage depends on the initial impact velocity and the Hugoniot parameters of the projectile/target material. The minimum velocity of the spallation ejecta is linearly related to the spalling strength of the target. The model provides a fast and simple method to calculate the ejecta velocity and estimate the influence range of ejecta under different impact conditions.

Molecular Dynamics Simulation of Dual Nanodroplet Impacts on a Cylindrical Surface.

Droplet impact behavior is ubiquitous in various fields. However, the dynamics and spreading mechanisms of micro- and nanoscale droplet impact on curved surfaces, particularly in the case of multiple droplets, have yet to be fully elucidated. In this study, molecular dynamics (MD) methods are employed to investigate the dynamic evolution of double nanodroplet impact on a nano cylindrical wall. The effects of droplet spacing, initial impact velocity, and wall wettability on droplet impact characteristics are analyzed. The results demonstrate that there are five impact modes of nanoscale double-droplet impacts with nanocylinders: spreading-partial wrapping-splitting-complete detachment (SPSC), spreading-complete wrapping-complete attachment (SCC), spreading-partial wrapping-complete attachment (SPC), spreading-partial wrapping-partial attachment (SPP), and spreading-partial wrapping-fragmentation-partial attachment (SPFP). The droplet spacing has an insignificant effect on the impact modes but affects the droplets' spreading shape in both the axial and radial directions. The initial velocity and wall wettability have significant impacts on the droplet impact modes and liquid film spreading characteristics. As the initial velocity increases, the liquid film's radial and axial spreading distances gradually increase. Under hydrophobic conditions, the spreading of the droplet is dominant in the radial direction, while under hydrophilic conditions, the spreading is dominant in the axial direction. Properly reducing the droplet spacing, increasing the impact velocity, and enhancing the wall hydrophobicity can promote detaching the droplet from the cylindrical wall.

Dynamic penetration behaviors of graphene origami under high-velocity impact

Brittleness remains the key bottleneck for graphene to be used as impact protection materials and this obstacle can be overcome by origami-modified graphene. Herein we employed molecular dynamics simulation to investigate the perforation behaviours of graphene origami (GOri) under ballistic impact from a diamond projectile. We found that the threshold penetration velocity of GOri can be improved significantly by 46.27 % compared with that of its pristine counterpart. Under a small ballistic impact loading at a low speed, GOri experiences a unique unfolding process and hence has improved impact-resistance performance. Depending on the initial velocity of the projectile, three different penetration phenomena are observed, i.e. bounce-back, capture, and perforation state. The penetration energy depends on the roughness of GOri, the initial impact velocity, the projectile's radius and the layer number. This study provides useful insights into the perforation behaviours and energy absorption of GOri and offers useful guidelines for graphene applications as impact protection materials.

The restitution coefficient of a particle repeatedly bouncing off a rough surface

We present a geometric model to investigate the characteristics of the restitution coefficient of a particle–wall collisions process in the case of a structured wall surface. Specifically, we examine the case of a sinusoidal modulation of the roughness heights. We show that (i) The restitution coefficient performs fluctuations around the mean value which also is the value of the local restitution coefficient. These fluctuations are caused by the surface roughness and are due to the exchange of the kinetic energy between the motion in the vertical and horizontal degrees of freedom. (ii) Due to the energy exchange, the restitution coefficient may reach values larger than unity. (iii) The impact phase of the collision has a peculiar pattern, which is fractal-like for initial impact velocities less than 0.99 m/s and potentially chaotic for larger velocities.

Experimental and Numerical Analysis of Aluminum-Polyethylene Composite Structure Subjected to Tension and Perforation Under Dynamic Loading for a Wide Range of Temperatures

The aim of this work consists of identifying the material behavior of Alucobond composite structures subjected to ballistic impact. The composite is made of Aluminum alloy AW5005 and LDPE (low-density polyethylene). The mechanical properties of these materials are described in term of strain rate and temperature dependencies. Quasi-static tensile and compression tests for Alucobond are performed at four different strain rates, i.e. 0.0001 0.001, 0.01, and 0.03 s-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${s}^{-1}$$\\end{document}. Moreover, in dynamic regime the used strain rate ranges in compression and perforation tests are (104\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${10}^{4}$$\\end{document}s-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${s}^{-1}$$\\end{document} ≤ ε˙\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\dot{\\varepsilon }$$\\end{document} ≤ 105\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${10}^{5}$$\\end{document}s-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${s}^{-1}$$\\end{document}) at temperatures ranging from room temperature 20 °C to 100 °C. Various parameters influence the behavior of the Alucobond structure under impact: the geometry and the mechanical properties of the projectile, the initial impact velocity, and the thermomechanical behavior of the target. Numerous quasi-static and dynamic original test results (traction and perforation over a wide range of strain rates at room temperature and high temperature) are presented. Numerical simulations, particularly using the finite element (FE) method with the ABAQUS explicit code, are also effective supplements for theoretical and more detailed experimental investigations, which were carried out to analyze the dynamic behavior of impacted structures.

Analysis of high-speed water entry in semi-sealed cylindrical shells: Cavity formation and self-disturbance characteristics

The high-speed water entry of a semi-sealed cylindrical shell is a complex unsteady process involving the multiphase flow. In order to study the influence of special structure of the semi-sealed cylindrical shell, the fluid-structure interaction method based on Star-CCM+ and ABAQUS is adopted. The results show that semi-sealed cylindrical shells with different structures all form nested cavities, among which the shell with a shorter length forms a nearly spherical cavity, while the shell with a smaller diameter forms a cavity that is close to a long strip shape. When the Mach number of the initial impact velocity is lower than 0.16, the top wall of the shell can be completely restored as the jet leaves the top wall. The von Mises stress at the top wall of the shell is higher than that at the side wall position. The deformation at the top of shells with larger diameter, shorter length, and smaller thickness is greater. The high-speed vertical water entry process of the semi-sealed cylindrical shell exhibits unique self disturbance characteristics, indicating that shells with thicker thickness and a longer length will exhibit obvious deflection after the self-jet phenomenon occurs.

Dynamic behavior of multilayered skin structure: A preliminary numerical and analytical microscopic analysis

High-velocity micro-particle impact on multilayered skin structure is of interest in the framework of transdermal drug delivery system. The understanding of the physical impact process in this phenomenon is complex and lack of experimental investigations in the literature. This work aims to investigate the impact responses of multilayered skin structure impacted by high-velocity micro-scale particle utilizing numerical and analytical analysis. Numerical and analytical analysis were conducted based on Smoothed Particle Hydrodynamics (SPH) method and Poncelet model, respectively. A good agreement exits between analytical and numerical penetration trajectories and velocity-penetration relationships with an initial impact velocity of 200 m/s, while the discrepancies increase with a higher velocity of 600 m/s. The comparison between analytical and numerical results reveals that the developed numerical model is able to reasonably predict the impact responses of different skin layers under micro-particle impact. The present work is a first step to study high-velocity micro-particle impact responses applying real multilayered skin structures and mechanical properties, which could be further investigated to interpret and guide the design of transdermal drug delivery equipment.

Molecular dynamics simulations of droplet coalescence and impact dynamics on the modified surfaces: A review

The effective control of droplet coalescence and impact behaviors on solid surfaces plays a crucial role in various fields, such as material science, environmental science, energy, biomedicine, agriculture, and aerospace. This review aims to summarize recent advancements in the understanding of coalescence and impact dynamics of droplets under different conditions using molecular dynamics (MD) simulations. We highlight diverse approaches that enable the achievement of controllable coalescence and impact behaviors through the manipulation of surface properties, droplet properties, and coalescence and impact conditions. These approaches encompass adjustments in surface structures, surface morphology, and surface wettability, as well as the manipulation of droplet size, viscosity, and components, and the control of initial shape setting and impact velocity. Furthermore, we also introduce the dynamics associated with the coexistence of these two behaviors. Importantly, this review is expected to provide valuable insights for both industrial and technological applications, particularly in the areas of self-cleaning surfaces and microfluidics.

Mechanical properties of refractory HEA WNbTaV and its penetration behavior to aluminum alloy plate

Quasi-static and dynamic compression experiments were conducted on WNbTaV to investigate its mechanical characteristics and its penetration behavior into an aluminum alloy target plate. Additionally, ballistic experiments with WNbTaV projectiles against 2A12 aluminum alloy thin targets were performed. The results indicate that HEA WNbTaV at a strain rate of 10−3 s−1 has a fracture strength of 1340 MPa, a yield strength of around 980 MPa, and a fracture strain of less than 7%. However, its dynamic yield strength is almost twice its quasi-static yield strength, and its dynamic fracture strain is more than twice the quasi-static compression fracture strain.When striking a 2 mm thick 2A12 aluminum alloy target plate with a velocity less than 348.5 m/s, the HEA WNbTaV projectile remains stiff and undeformed. Its maximum velocity before entering the target plate is roughly 273 m/s. Furthermore, within a certain impact velocity range, the residual velocity, initial impact velocity, and ultimate penetration velocity of the HEA WNbTaV projectile penetrating the 2 mm thick 2A12 aluminum alloy target plate meet the following relationships. vr=v02−2.13vb2.

Dynamic mode-I delamination in composite DCB under impact loads with attunable dynamic effect

A dynamic mode-I energy release rate (ERR) of a double cantilever beam (DCB) under impact from a striker is derived for the first time for isotropic and orthotropic composite materials, accounting for DCB properties, a striker mass and an initial impact velocity. This is achieved in the context of structural vibration analysis by employing beam dynamics. It is found that the initial impact velocity determines the magnitude of the ERR, which is proportional to the velocity squared, while the delamination length ratio and the mass ratio between the striker and the DCB defines the time response. To understand the transient effect, a dynamic factor is defined as a function of the mass ratio. This factor decreases with an increasing striker mass, indicating a transition in the dynamic response from flexural-wave dominant to quasi-static-motion dominant, allowing an attunable dynamic effect. The developed theory is verified against the finite-element simulations for isotropic and orthotropic materials as well as experimental verification using published data. This work allows the measurements of fracture toughness under the impact load with the derived analytical solution. In addition, the developed theory can guide a design of impact tests and provide a fundamental understanding of impact-induced fracture for carbon-fiber-reinforced plastics.

Dynamic response characteristics of grooved cylindrical shells in Taylor impact experiments

Buffer energy absorbing structures have very high use value in daily life, industrial production, aerospace and other fields. Cylindrical shells are used as a highly efficient buffer and energy absorbing structure due to their own structure and good mechanical properties. Taylor impact experiments were conducted on three types of structural cylindrical shells (non grooved, inner grooved, and outer grooved) and numerical model was also established to study and analyze the dynamic response characteristics of the three types of structural cylindrical shells. Finally, the deformation mechanism of the cylindrical shell was analyzed theoretically to explore the impact of grooving treatment on the deformation of the cylindrical shell. The results show that with the increase of impact velocity, the length of the cylindrical shells of the three structures decreased, and the diameter of the impact end and the maximum diameter increased. Each of the three specimens had a convergence velocity(convergence velocity: The impact end diameter of cylindrical shell is the initial impact velocity at the maximum diameter), that is, when the impact velocity was greater than or equal to the convergence velocity, its maximum diameter was equal to the diameter of the impact end. When the impact velocity exceeded a certain value, the deformation modes of the three types of cylindrical shells changed. The comparison of experimental and simulation results proved the effectiveness of the numerical model. The maximum stress was always above the impact end face. It was concluded from the theoretical analysis Due to the stress concentration at the groove, the stress distribution and internal stress distribution of the cylindrical shell were affected, which in turn affected the deformation and energy absorption capacity of the cylindrical shell. At the same impact velocity, the outer grooved cylindrical shell has the shortest buffer time and the BW specimen had the most gentle buffer curve before 35μs .

Wetting dynamics of a droplet impact on target-like chemically heterogeneous substrates: The determinations of contact angle

Wetting is a common natural phenomenon with many useful applications. However, some fundamental aspects of wetting theory, such as determining the contact angle, remain unresolved. Two mainstream options are debated: whether the contact angle depends on the contact area or the contact line. To understand this, the present work used many-body dissipative particle dynamics to simulate wetting on chemically heterogeneous substrates. The simulations show that there is a ratio that separates contact angles into two regimes: a stable regime where the contact angles follow the contact-area-based Cassie-Baxter equation, and a fluctuating regime where contact angles are mainly determined by the contact line. The ring/droplet ratio, initial impact velocity, and wettability pair all play a role in the formation of the contact angle. This brief communication provides clear and sound observations to shed light on the determinations of the contact angle.

Development of Hybrid Machine Learning Models for Predicting Permanent Transverse Displacement of Circular Hollow Section Steel Members under Impact Loads

The impact effect is a crucial issue in civil engineering and has received considerable attention for decades. For the first time, this study develops hybrid machine learning models that integrate the novel Extreme Gradient Boosting (XGB) model with Particle Swam Optimization (PSO), Grey Wolf Optimizer (GWO), Moth Flame Optimizer (MFO), Jaya (JA), and Multi-Verse Optimizer (MVO) algorithms for predicting the permanent transverse displacement of circular hollow section (CHS) steel members under impact loads. The hybrid machine learning models are developed using data collected from 357 impact tests of CHS steel members. The efficacy of hybrid machine learning models is evaluated using three performance metrics. The results show that the GWO-XGB model achieves high accuracy and outperforms the other models. The values of R2, RMSE, and MAE obtained from the GWO-XGB model for the test set are 0.981, 2.835 mm, and 1.906 mm, respectively. The SHAP-based model explanation shows that the initial impact velocity of the indenter, the impact mass, and the ratio of impact position to the member length are the most sensitive parameters, followed by the yield strength of the steel member and the member length; meanwhile, member diameter and member thickness are the parameters least sensitive to the permanent transverse displacement of CHS steel members. Finally, this study develops a web application tool to help rapidly estimate the permanent transverse displacement of CHS steel members under impact loads.