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Search Results (432)

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Keywords = smoothed particle hydrodynamics

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74 pages, 14431 KB  
Review
Dynamic Compaction for Ground Improvement: Mechanisms, Governing Parameters, Environmental Impacts, and Multiscale Research Approaches
by Syed Husnain Ali Shah, Thanh T. Nguyen and Hadi Khabbaz
Sustainability 2026, 18(12), 5827; https://doi.org/10.3390/su18125827 - 8 Jun 2026
Viewed by 180
Abstract
Dynamic compaction (DC) is a widely used ground-improvement technique due to its cost-effectiveness, low environmental impact, and high adaptability. Despite its simple implementation, compaction efficiency is governed by multiple interacting factors, including tamping energy and soil properties, which poses challenges to practical design. [...] Read more.
Dynamic compaction (DC) is a widely used ground-improvement technique due to its cost-effectiveness, low environmental impact, and high adaptability. Despite its simple implementation, compaction efficiency is governed by multiple interacting factors, including tamping energy and soil properties, which poses challenges to practical design. Although numerous investigations have been reported, a comprehensive review systematically linking the various aspects of the DC technique through multiple approaches remains lacking. This paper addresses this gap by integrating and critically evaluating findings from field studies, controlled laboratory experiments, analytical studies, and numerical modeling to establish an effective framework for dynamic compaction applications. In addition, the environmental performance of DC is critically assessed, demonstrating its relatively low environmental footprint compared to material-intensive ground-improvement techniques, as impacts are primarily governed by construction energy rather than material production, although vibration and noise remain key considerations. The findings indicate that DC performance is controlled by the combined effects of the tamper mass, drop height, and geometry, together with impact spacing, number of blows, and initial soil properties. Field studies show that densification depth and uniformity are influenced by the fines percentage, drainage conditions, and applied energy levels, often requiring appropriate tamping strategies to mitigate pore water effects. Laboratory investigations highlight the dominant role of tamper mass over drop height in stress transmission and penetration depth and demonstrate how the tamper shape and impact sequence govern crater formation and strain localization. Numerical models employing finite element, discrete element, smoothed particle hydrodynamics, and hybrid approaches provide insight into stress wave propagation, pore pressure evolution, and soil–structure interaction. However, limitations remain in simulating sequential tamping, boundary conditions, and coupled hydro-mechanical behavior. This review highlights the need for cross-validated modeling, advanced instrumentation, and machine learning integration to support predictive, site-responsive dynamic compaction design in complex geotechnical settings. Full article
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15 pages, 3747 KB  
Article
Numerical Investigation of Fragment Impact and Penetration into Concrete Using the Adaptive SPH Method
by Seung-han You, Jin-kook Kim, Sung-wook Kim, Jae-heum Moon and Won-woo Kim
Appl. Sci. 2026, 16(11), 5386; https://doi.org/10.3390/app16115386 - 28 May 2026
Viewed by 196
Abstract
Structural damage under blast conditions is significantly influenced by high-velocity primary fragments, which can induce severe local penetration and threaten the safety of protective structures. In this study, the penetration behavior of concrete subjected to primary fragment impact was investigated using the Adaptive [...] Read more.
Structural damage under blast conditions is significantly influenced by high-velocity primary fragments, which can induce severe local penetration and threaten the safety of protective structures. In this study, the penetration behavior of concrete subjected to primary fragment impact was investigated using the Adaptive Smoothed Particle Hydrodynamics (SPH) method implemented in LS-DYNA. The numerical model was first validated against gas-gun experimental results, demonstrating improved prediction accuracy compared to the conventional Lagrangian approach. In particular, the Adaptive SPH method effectively mitigated premature element erosion, resulting in a residual velocity prediction error of approximately 5.9%. Based on the validated model, a parametric study was conducted to evaluate the effects of fragment mass (3.7–44 g) and impact velocity (750–1000 m/s) on concrete penetration behavior. The results showed that most fragments were capable of perforating a 100 mm thick concrete wall at velocities above 1000 m/s, while partial penetration occurred only under limited conditions. Furthermore, a strong logarithmic relationship between fragment mass and residual velocity was identified, and predictive equations with high reliability (R2 ≥ 0.98) were proposed. These findings demonstrate the applicability of the Adaptive SPH approach for realistic penetration analysis and provide practical insights for the design and safety assessment of protective concrete structures. Full article
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30 pages, 18433 KB  
Article
An Adaptive Coupling of Edge-Based Smoothed FEM and SPH with a Bidirectional Element-Particle Transformation Algorithm for Laser Powder Bed Fusion
by Ming Suo and Ting Long
Materials 2026, 19(11), 2264; https://doi.org/10.3390/ma19112264 - 27 May 2026
Viewed by 287
Abstract
Laser powder bed fusion (LPBF) poses significant simulation challenges due to its highly nonlinear thermo-fluid-solid coupling. To address this, we propose an adaptive framework coupling the edge-based smoothed finite element method (ES-FEM) and smoothed particle hydrodynamics (SPH) via a bidirectional element-particle transformation algorithm. [...] Read more.
Laser powder bed fusion (LPBF) poses significant simulation challenges due to its highly nonlinear thermo-fluid-solid coupling. To address this, we propose an adaptive framework coupling the edge-based smoothed finite element method (ES-FEM) and smoothed particle hydrodynamics (SPH) via a bidirectional element-particle transformation algorithm. This integration leverages ES-FEM for modeling solid thermo-mechanical responses and SPH for resolving melt pool dynamics, enabling fully coupled simulation of temperature, fluid flow, and stress within a unified model. The framework comprises three key components: a nodal mass normalization scheme ensuring conservation during transformations, a ghost particle algorithm for solid-fluid heat transfer and interaction, and a bidirectional finite-element-to-particle conversion mechanism. This work represents the first implementation of bidirectional coupling between mesh-free Lagrangian SPH and Lagrangian FEM. The validation against benchmark cases confirms the framework’s accuracy in capturing transient thermal, hydrodynamic, and mechanical behavior. It successfully reproduces key LPBF phenomena, including melt pool morphology, Marangoni flows, and residual stress evolution, demonstrating its suitability for high-fidelity LPBF process simulation. It should be noted that the current ES-FEM-SPH framework has not taken into account the recoil pressure, evaporation, and the interaction between the powder and the molten pool. The powder is regarded as a rigid body. Future work will focus on incorporating these neglected physical factors to further improve the predictive capability of the proposed framework. Full article
(This article belongs to the Section Metals and Alloys)
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26 pages, 4108 KB  
Article
Real-Time Two-Way Fluid–Rigid Body Interaction via SDF Coupling with GPU-Accelerated SPH and Volumetric Rendering
by Muhammad Waseem and Min Hong
Mathematics 2026, 14(11), 1845; https://doi.org/10.3390/math14111845 - 26 May 2026
Viewed by 222
Abstract
We present a unified GPU-accelerated framework for real-time Smoothed Particle Hydrodynamics (SPH) fluid simulation with two-way rigid body coupling, secondary particle effects, and volumetric rendering, implemented entirely within the Unity game engine. The framework employs a weakly compressible SPH formulation with O( [...] Read more.
We present a unified GPU-accelerated framework for real-time Smoothed Particle Hydrodynamics (SPH) fluid simulation with two-way rigid body coupling, secondary particle effects, and volumetric rendering, implemented entirely within the Unity game engine. The framework employs a weakly compressible SPH formulation with O(n) count sort-based spatial hashing and introduces a signed distance field (SDF) coupling system that evaluates three representative geometric primitives, sphere, cylinder, and torus, of increasing topological complexity directly on the GPU. Bidirectional force exchange is achieved through lock-free atomic compare-and-swap impulse accumulation, enabling thousands of fluid particles to interact simultaneously with each rigid body without serialization. A GPU stream compaction–based secondary particle system generates and classifies foam, spray, and bubble effects in real time, while a volumetric rendering pipeline samples fluid density into a 3D texture for SDF-composited volume rendering without surface mesh extraction. A conditional kernel dispatch strategy eliminates GPU cycles for disabled subsystems, and dynamic buffer management reduces memory pressure through runtime allocation. The system sustains above 54 frames per second at four million particles on a consumer-grade GPU, with sub-linear frame time scaling and a 1.70× speedup from dynamic buffer allocation over static pre-allocation. Full article
(This article belongs to the Special Issue Mathematical Applications in Computer Graphics)
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25 pages, 7893 KB  
Article
Study on Dynamic Evolution of Anti-Penetration Performance of Polyurea Reinforced Concrete Target Based on FE-SPH Coupling Method
by Pengfei Liu, Yiyuan Chen, Jie Wei and Yun Wei
Buildings 2026, 16(11), 2076; https://doi.org/10.3390/buildings16112076 - 23 May 2026
Viewed by 179
Abstract
Addressing the issues of brittle spalling and debris scattering commonly observed in Normal Concrete (NC) under high-velocity impact loading, this study investigates the resistance of polyurea-reinforced concrete targets against high-velocity bullet penetration. High-velocity projectile penetration tests were conducted at approximately 510 m/s to [...] Read more.
Addressing the issues of brittle spalling and debris scattering commonly observed in Normal Concrete (NC) under high-velocity impact loading, this study investigates the resistance of polyurea-reinforced concrete targets against high-velocity bullet penetration. High-velocity projectile penetration tests were conducted at approximately 510 m/s to comparatively analyze the failure modes of plain concrete targets and targets reinforced with polyurea coatings of varying thicknesses. Furthermore, a three-dimensional numerical model based on the coupled Finite Element-Smoothed Particle Hydrodynamics (FE-SPH) algorithm was constructed to overcome the numerical instabilities inherent in traditional finite element methods when handling large material deformations and debris flows. The experimental results indicate that while the polyurea coating has a limited direct effect on reducing the depth of penetration (DOP)—showing marginal reductions of 1.8% and 2.3% for 2 mm and 5 mm coatings, respectively—it demonstrates a significant physical confinement effect. Notably, the 5 mm polyurea coating effectively suppresses brittle spalling on the impact face, reducing the crater diameter by 15.5% compared to the plain concrete target and restricting the propagation of radial cracks. Energy analysis and interface pressure monitoring reveal that the polyurea coating employs a “peak-shaving and valley-filling” mechanism driven by mechanical impedance mismatch, transforming transient impacts into steady-state compression with lower energy density. Consequently, this significantly enhances the overall impact toughness and secondary protection capability of the structure. These findings provide critical references for the refined reinforcement design of existing defensive structures. Full article
(This article belongs to the Section Building Materials, and Repair & Renovation)
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21 pages, 5741 KB  
Article
Improved WCSPH-DEM Coupling for Analyzing Fluid–Solid Interactions
by Changjun Zou and Zhihua Shi
Modelling 2026, 7(3), 96; https://doi.org/10.3390/modelling7030096 - 15 May 2026
Viewed by 200
Abstract
Fluid–structure interaction (FSI) research is crucial for applications in fields such as naval engineering, geological hazards, and biomechanics. Traditional grid-based methods (such as CFD) often face challenges in simulating large-deformation flow fields and complex boundary conditions, where mesh distortion can compromise simulation accuracy. [...] Read more.
Fluid–structure interaction (FSI) research is crucial for applications in fields such as naval engineering, geological hazards, and biomechanics. Traditional grid-based methods (such as CFD) often face challenges in simulating large-deformation flow fields and complex boundary conditions, where mesh distortion can compromise simulation accuracy. Building upon the DualSPHysics5.2 framework, this study leverages the strengths of weakly compressible SPH (WCSPH) in modeling free surface flows and large-deformation fluids, as well as the discrete element method (DEM), for accurately describing particle collisions and fragmentation behaviors. We propose an improved MSPH-DEM coupling algorithm that incorporates moving least squares (MLS) correction for kernel function gradient optimization. This algorithm utilizes MLS-based gradient correction to achieve smoother fluid surfaces as well as bidirectional coupling between fluids and particles. Experimental validation demonstrates that in dam break simulations, this method reduces pressure errors. In the dam break impacting a cube experiment, it enhances accuracy, while in the dam break impacting a baffle experiment, the horizontal displacement of marker points closely aligns with the experimental values from Liao et al. This approach effectively improves the accuracy of the simulations of FSI problems, offering a more reliable numerical simulation methodology for engineering applications such as geological hazard prevention. Full article
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22 pages, 2930 KB  
Article
ISPH Simulation of Non-Equilibrium Suspended Sediment Transport Using a Generalized Sediment Transport Equation
by Sai Ge, Shaowu Li, Ye Liu, Yang Shi, Dong Wang and Tinghao Yang
J. Mar. Sci. Eng. 2026, 14(10), 900; https://doi.org/10.3390/jmse14100900 - 12 May 2026
Viewed by 207
Abstract
Non-equilibrium suspended sediment transport is the most general state in engineering practice. Earlier analytical and numerical models for non-equilibrium suspended sediment transport were primarily designed for specific case studies and lack universal applicability. This work aims to develop a generalized two-dimensional (2D) numerical [...] Read more.
Non-equilibrium suspended sediment transport is the most general state in engineering practice. Earlier analytical and numerical models for non-equilibrium suspended sediment transport were primarily designed for specific case studies and lack universal applicability. This work aims to develop a generalized two-dimensional (2D) numerical model based on the incompressible smoothed particle hydrodynamics (ISPH) approach for simulating non-equilibrium suspended sediment transport. The model integrates a generalized bottom boundary condition that accounts for both deposition velocity and equilibrium concentration. The impact of turbulence, as well as the hindered settling effect, is also included in the model. The efficacy of the model was assessed using results from analytical or semi-analytical models under 1D unsteady and 2D steady sediment transport modes, as well as from laboratory experiments for 2D unsteady sediment transport. This model reveals the physical mechanism of the hindered settling effect. The effect is most significant in the main suspension zone, where particles interact frequently. In the near-bottom zone, it is limited by physical constraints, and the settling velocity reaches its minimum. In the top zone, the effect is limited by the very low particle concentration, where particle interactions are negligible. The model also captures the different responses caused by different distributions of the turbulent viscosity coefficient and the bottom reference concentration. Full article
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23 pages, 5441 KB  
Article
Nested Fluid–Structure Interaction Predictive Modeling of Fetal Brain Stress During Maternal Trauma
by Jonathan Mayer, Molly Bekbolatova, Timothy Devine, Paula Ryo and Milan Toma
Biology 2026, 15(10), 761; https://doi.org/10.3390/biology15100761 - 11 May 2026
Viewed by 451
Abstract
Background: Mechanical trauma during pregnancy from motor vehicle accidents, falls, and maternal seizures poses significant risks to fetal development. The fetus is protected by multiple hierarchical layers including the uterine wall, amniotic fluid, and cerebrospinal fluid surrounding the brain. Despite the clinical significance [...] Read more.
Background: Mechanical trauma during pregnancy from motor vehicle accidents, falls, and maternal seizures poses significant risks to fetal development. The fetus is protected by multiple hierarchical layers including the uterine wall, amniotic fluid, and cerebrospinal fluid surrounding the brain. Despite the clinical significance of maternal trauma occurring in approximately six to eight percent of pregnancies, previous computational studies have focused primarily on amniotic fluid protection while treating the fetus as a homogeneous structure, without examining the nested protective architecture comprising both amniotic fluid and cerebrospinal fluid as an integrated system. Methods: This investigation implements a nested fluid–structure interaction framework simultaneously capturing three hierarchically organized systems: the uterine wall interacting with amniotic fluid, amniotic fluid interacting with the fetal body, and the cranial system comprising skull, cerebrospinal fluid, and brain tissue. The computational architecture employs smoothed particle hydrodynamics for fluid domains coupled with finite element methods for solid structures. Boundary conditions representing traumatic forces were obtained through experimental protocols using an instrumented medical simulation mannequin performing seizure movements. Results: Computational simulations predicted that amniotic fluid absorbed the majority of impact forces through hydraulic cushioning, while cerebrospinal fluid provided additional stress reduction through pressure redistribution, with model predictions suggesting total stress reduction exceeding ninety percent. Peak fetal brain stress values predicted by the model were below injury thresholds reported in adult neural tissue literature, though direct applicability of these thresholds to fetal tissue remains uncertain. The fetal brain exhibited minimal movement relative to the skull despite complex force cascades. Stress distributions showed elevated values in the frontal lobe and brainstem, though magnitudes remained within ranges that the model suggests may be tolerable. Conclusions: Computational modeling suggests that the nested fluid protection architecture operates as an integrated hierarchical system providing potential mechanical protection through sequential energy dissipation. These findings represent model predictions requiring experimental and clinical validation before translation to clinical practice. Full article
(This article belongs to the Special Issue Advances in Biomechanics in Physiology and Pathology)
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23 pages, 5816 KB  
Article
Simulations of Wave–Structure Interactions in Incompressible SPH Using Modified Dynamic Boundary Conditions
by Marco Simone, Giovanni Cannata and Georgios Fourtakas
J. Mar. Sci. Eng. 2026, 14(9), 863; https://doi.org/10.3390/jmse14090863 - 5 May 2026
Viewed by 327
Abstract
The simulation of free-surface flows in hydraulic engineering presents several challenges due to the intrinsic complexity of modeling a fluid that continuously deforms and evolves over time. In this context, the Smoothed Particle Hydrodynamics (SPH) method, a Lagrangian approach that represents the fluid [...] Read more.
The simulation of free-surface flows in hydraulic engineering presents several challenges due to the intrinsic complexity of modeling a fluid that continuously deforms and evolves over time. In this context, the Smoothed Particle Hydrodynamics (SPH) method, a Lagrangian approach that represents the fluid as a set of moving particles, is better suited than traditional grid-based methods. However, compared to the latter, the SPH method also exhibits certain drawbacks, including increased difficulty in handling wall boundary conditions and a higher computational cost. This work proposes an original wall boundary treatment technique that, to the best of our knowledge, is applied in the Incompressible SPH (ISPH) approach for the first time. The proposed treatment relies on boundary particles external to the fluid and internal extrapolation points, where pressure is computed to enforce Neumann boundary conditions in a consistent manner. During the development of this technique, several intrinsic advantages over existing methods in the literature are identified. A series of numerical benchmarks are conducted to verify the validity of the proposed ISPH model. Numerical results show good agreement with experimental data reported in the literature, confirming the effectiveness of the proposed numerical model in reproducing free-surface flow hydraulic phenomena. Full article
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26 pages, 15027 KB  
Article
New Leading-Edge Reinforcement Design of Aircraft Wing to Withstand Bird Collision
by Suppasin Ngamlikitlert, Minsung Kim and Suwin Sleesongsom
Biomimetics 2026, 11(5), 305; https://doi.org/10.3390/biomimetics11050305 - 29 Apr 2026
Viewed by 999
Abstract
Bird strikes are a key threat to aircraft wing leading edges. This investigation evaluates a honeycomb block reinforcement concept to improve bird strike resistance while maintaining structural efficiency. A validated simulation was developed using an explicit dynamic finite element approach, in which the [...] Read more.
Bird strikes are a key threat to aircraft wing leading edges. This investigation evaluates a honeycomb block reinforcement concept to improve bird strike resistance while maintaining structural efficiency. A validated simulation was developed using an explicit dynamic finite element approach, in which the bird was modeled as a soft body using smoothed particle hydrodynamics, and the wing leading edge was represented with a honeycomb block reinforcement concept. A design of experiments based on McKay Latin hypercube sampling was applied to comprehensively examine the effects of the geometric parameters on the maximum von Mises stress and maximum deformation. Response surface regression models were then constructed to approximate the impact responses and analyze the model correctness. These models were subsequently integrated into a constrained optimization methodology using sequential quadratic programming and population-based integrated learning to minimize deformation while limiting stress below the material yield threshold. The optimized honeycomb and skin configuration demonstrated a noticeable optimization of the maximum deformation within the yield stress limit compared with the baseline design. The results confirm that the proposed honeycomb block reinforcement concept, combined with a regression-based optimization strategy, constitutes a practical, computationally effective approach to improving bird strike resistance and provides a feasible design option for future impact-resistant wing leading-edge designs. Full article
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27 pages, 4534 KB  
Article
Chasing a Complete Understanding of the Yanshangou Landslide in the Baihetan Reservoir Area
by Jian-Ping Chen, An-Chi Shi, Zi-Hao Niu, Yu Xu, Zhen-Hua Zhang, Ming-Liang Chen and Lei Wang
Water 2026, 18(9), 1018; https://doi.org/10.3390/w18091018 - 24 Apr 2026
Viewed by 545
Abstract
The Yanshangou landslide, located in the Baihetan Reservoir area, poses severe potential threats to the normal operation of the reservoir due to its distinct deformation characteristics and high sensitivity to reservoir water level fluctuations. This study systematically investigates the geological background, deformation characteristics, [...] Read more.
The Yanshangou landslide, located in the Baihetan Reservoir area, poses severe potential threats to the normal operation of the reservoir due to its distinct deformation characteristics and high sensitivity to reservoir water level fluctuations. This study systematically investigates the geological background, deformation characteristics, stability evolution, and landslide-induced surge hazards of the Yanshangou landslide in the Baihetan Reservoir area. This work only considers the influence of reservoir water level fluctuations, which is the dominant factor controlling the current progressive deformation of the landslide. Field surveys and GNSS/deep displacement monitoring results revealed that the Yanshangou landslide exhibits obvious staged deformation characteristics, and the landslide deformation rate was closely coupled with the dynamic changes in reservoir water level. A slope stability evaluation method integrating the Morgenstern–Price limit equilibrium method and Richard’s equation was established, and the results indicated that the Yanshangou landslide has low saturated permeability. Therefore, its factor of safety (FOS) presents a clear four-stage variation trend in response to reservoir water level fluctuations. A Smoothed Particle Hydrodynamics (SPH)-based numerical model was further developed to simulate the landslide-induced surges under two typical reservoir water level scenarios (815 m and 765 m). The simulation results demonstrated that a high reservoir water level led to more intense surges with greater height and higher velocity, while a low reservoir water level resulted in surges with a wider propagation range along the reservoir bank. The research findings of this study provide a comprehensive theoretical basis and detailed data support for the prevention and mitigation of geological hazards in the Baihetan Reservoir area, and also offer a reference for the hazard management of similar reservoir landslides worldwide. Full article
(This article belongs to the Section Hydrogeology)
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23 pages, 11381 KB  
Article
Physics-Guided Machine Learning Surrogates for Bird Strike Analysis on Rotating Jet Engine Blades Through a Comparative Study of Lagrangian and SPH Simulations
by Mohammad Khalid Hasan Nabil, Jubayer Ahmed Sajid, Ivan Grgić, Jure Marijić and Saiaf Bin Rayhan
Modelling 2026, 7(3), 80; https://doi.org/10.3390/modelling7030080 - 24 Apr 2026
Viewed by 804
Abstract
Bird strike events on rotating jet engine fan blades pose significant risks to aviation safety, yet high-fidelity numerical simulations remain computationally expensive, limiting their use in parametric design studies. This study develops a physics-guided machine learning surrogate framework for predicting bird strike response [...] Read more.
Bird strike events on rotating jet engine fan blades pose significant risks to aviation safety, yet high-fidelity numerical simulations remain computationally expensive, limiting their use in parametric design studies. This study develops a physics-guided machine learning surrogate framework for predicting bird strike response on rotating Ti-6Al-4V fan blades, systematically comparing Lagrangian (gelatin-based, Mooney–Rivlin) and Smoothed Particle Hydrodynamics (SPH, water-like) formulations. A total of 100 explicit dynamic simulations were conducted in ANSYS LS-DYNA (R2) (50 per formulation), varying bird impact velocity and blade angular speed. Random Forest, Support Vector Regression, Polynomial Regression, and XGBoost regression models were trained and evaluated using five-fold cross-validation. Results demonstrate that SPH-based surrogates achieve superior predictive accuracy, with Random Forest yielding R2 = 0.9938 for maximum deformation and R2 = 0.9962 for total energy dissipation. In contrast, Lagrangian-based stress surrogates exhibited severe performance degradation (R2 = 0.24) due to mesh-dependent numerical noise. The trained surrogates achieved computational speed-up factors of 104–105 relative to direct simulation. These findings establish that surrogate model reliability is fundamentally governed by the numerical quality of the training data, providing guidance for integrating machine learning with impact simulation workflows in aero-engine blade design. Full article
(This article belongs to the Section Modelling in Engineering Structures)
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20 pages, 7311 KB  
Article
Numerical Simulation Study on Region Tracking of Jet Formation and Armor-Piercing Process of Zirconium Alloy Shaped Charge Liner
by Yan Wang, Yifan Du, Xingwei Liu and Jinxu Liu
Technologies 2026, 14(4), 216; https://doi.org/10.3390/technologies14040216 - 8 Apr 2026
Viewed by 593
Abstract
Zr alloy-shaped charge liners (SCLs) offer broad application prospects due to their multiple post-penetration damage effects. However, research on these liners is still in its early stages. The mechanisms of jet formation and penetration for Zr alloys SCL remain unclear, and the specific [...] Read more.
Zr alloy-shaped charge liners (SCLs) offer broad application prospects due to their multiple post-penetration damage effects. However, research on these liners is still in its early stages. The mechanisms of jet formation and penetration for Zr alloys SCL remain unclear, and the specific contribution of different liner regions to the penetration process is not yet understood. This gap in knowledge has limited their structural design to a black-box correlation between global structural parameters and macroscopic penetration efficiency. To address this gap, a region-tracing Smoothed Particle Hydrodynamics (SPH) simulation was employed. Following a strategy of “wall thickness layering + axial segmentation,” the Zr alloy liner was partitioned into ten characteristic regions. This methodology facilitated the tracking of material transport from each region during jet formation and penetration into an AISI 1045 steel target. The contribution of each region to the penetration depth was then quantitatively assessed via post-processing. For the first time, the “critical region” contributing most to penetration depth was identified, and the influence of the liner’s cone angle and wall thickness on the contribution of each region was revealed. This study enhances the theoretical framework for understanding the damage effects of Zr alloy shaped charge liners. It not only advances the fundamental understanding of jet penetration mechanisms but also provides a theoretical basis for the refined design and performance optimization of these liners. Full article
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27 pages, 2341 KB  
Article
An Improved Conservative Hybrid Method with Adaptive Mesh Refinement for Passive-Scalar Transport on Deforming Interfaces
by Yu Fan and Chunyan Liu
Mathematics 2026, 14(7), 1146; https://doi.org/10.3390/math14071146 - 29 Mar 2026
Viewed by 413
Abstract
This paper presents an improved hybrid Eulerian–Lagrangian framework, which has been augmented with an adaptive mesh refinement technique, for simulating passive scalar transport on deforming interfaces. We capture interface deformation using an Eulerian level-set method while solving the interfacial transport equation with a [...] Read more.
This paper presents an improved hybrid Eulerian–Lagrangian framework, which has been augmented with an adaptive mesh refinement technique, for simulating passive scalar transport on deforming interfaces. We capture interface deformation using an Eulerian level-set method while solving the interfacial transport equation with a single-layer smoothed particle hydrodynamics method. As a result, the proposed hybrid approach combines the high efficiency of the Eulerian formulation with the strict mass conservation property of smoothed particle hydrodynamics method. To further accelerate the simulations, we employ adaptive mesh refinement for the Eulerian solver and restrict particles to the finest refinement level. To mitigate Lagrangian particle clustering, we adopt a remeshing procedure that generates particle distributions adapted to the local interface geometry on the finest mesh. This remeshing also enables accurate, mass-conservative reconstruction of the interfacial concentration field. Moreover, by incorporating an adaptive remeshing strategy, we tune the remeshing frequency to balance computational cost and accuracy. The accuracy and robustness of the proposed method are demonstrated through a suite of benchmark test cases. Additionally, we evaluate the effectiveness of adaptive mesh refinement through benchmark test cases, verifying its compatibility with the interfacial smoothed particle hydrodynamics method and quantifying the resulting speedup. Full article
(This article belongs to the Special Issue Numerical Methods for Scientific Computing)
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24 pages, 10940 KB  
Review
On the Use of the Meshless Material Point Method for Microelectronic Devices
by Sjoerd D. M. de Jong, Willem D. van Driel and Guoqi Zhang
Mathematics 2026, 14(5), 866; https://doi.org/10.3390/math14050866 - 4 Mar 2026
Viewed by 675
Abstract
In this work, the Material Point Method (MPM) is reviewed for application in the microelectronics industry. Microelectronic processes often involve large deformations, evolving interfaces, multiphysics coupling, and complex geometries that challenge conventional mesh-based methods such as the finite element method (FEM). Meshless methods [...] Read more.
In this work, the Material Point Method (MPM) is reviewed for application in the microelectronics industry. Microelectronic processes often involve large deformations, evolving interfaces, multiphysics coupling, and complex geometries that challenge conventional mesh-based methods such as the finite element method (FEM). Meshless methods provide an alternative solution that avoids these issues. A comparison is made between Smoothed Particle Hydrodynamics (SPH), Element Free Galerkin (EFG), peridynamics, Radial Basis Function–Finite Difference (RBF-FD), and MPM, evaluated with respect to convergence, consistency and stability, boundary enforcement, adaptivity, coupling, and industrial applicability. Based on this assessment, MPM and its main variants (BSMPM, GIMP, CPDI, and TLMPM) are examined in depth. The method’s ability to address large deformations, moving interfaces, contact, history-dependent material behavior, and multiphysics interactions is examined. The underfill process is used as a representative use case to illustrate challenges such as free surface flow, void formation, thermomechanical coupling, and residual stress. Overall, MPM shows strong potential, although further benchmarking and validation are required for widespread industrial adoption. Full article
(This article belongs to the Special Issue Advances in Meshless Methods and Their Applications)
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