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Keywords = flow stress curve

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29 pages, 5505 KiB  
Article
Triaxial Response and Elastoplastic Constitutive Model for Artificially Cemented Granular Materials
by Xiaochun Yu, Yuchen Ye, Anyu Yang and Jie Yang
Buildings 2025, 15(15), 2721; https://doi.org/10.3390/buildings15152721 (registering DOI) - 1 Aug 2025
Abstract
Because artificially cemented granular (ACG) materials employ diverse combinations of aggregates and binders—including cemented soil, low-cement-content cemented sand and gravel (LCSG), and concrete—their stress–strain responses vary widely. In LCSG, the binder dosage is typically limited to 40–80 kg/m3 and the sand–gravel skeleton [...] Read more.
Because artificially cemented granular (ACG) materials employ diverse combinations of aggregates and binders—including cemented soil, low-cement-content cemented sand and gravel (LCSG), and concrete—their stress–strain responses vary widely. In LCSG, the binder dosage is typically limited to 40–80 kg/m3 and the sand–gravel skeleton is often obtained directly from on-site or nearby excavation spoil, endowing the material with a markedly lower embodied carbon footprint and strong alignment with current low-carbon, green-construction objectives. Yet, such heterogeneity makes a single material-specific constitutive model inadequate for predicting the mechanical behavior of other ACG variants, thereby constraining broader applications in dam construction and foundation reinforcement. This study systematically summarizes and analyzes the stress–strain and volumetric strain–axial strain characteristics of ACG materials under conventional triaxial conditions. Generalized hyperbolic and parabolic equations are employed to describe these two families of curves, and closed-form expressions are proposed for key mechanical indices—peak strength, elastic modulus, and shear dilation behavior. Building on generalized plasticity theory, we derive the plastic flow direction vector, loading direction vector, and plastic modulus, and develop a concise, transferable elastoplastic model suitable for the full spectrum of ACG materials. Validation against triaxial data for rock-fill materials, LCSG, and cemented coal–gangue backfill shows that the model reproduces the stress and deformation paths of each material class with high accuracy. Quantitative evaluation of the peak values indicates that the proposed constitutive model predicts peak deviatoric stress with an error of 1.36% and peak volumetric strain with an error of 3.78%. The corresponding coefficients of determination R2 between the predicted and measured values are 0.997 for peak stress and 0.987 for peak volumetric strain, demonstrating the excellent engineering accuracy of the proposed model. The results provide a unified theoretical basis for deploying ACG—particularly its low-cement, locally sourced variants—in low-carbon dam construction, foundation rehabilitation, and other sustainable civil engineering projects. Full article
(This article belongs to the Special Issue Low Carbon and Green Materials in Construction—3rd Edition)
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18 pages, 4813 KiB  
Article
Dynamic Recrystallization Model of High-Temperature Deformation and Finite Element Analysis of Microstructure Evolution of 14Cr1Mo Pressure Vessel Steel
by Baoning Yu, Bo Zhang, Ruxing Shi, Feng Mao, Shizhong Wei and Duhang Yang
Materials 2025, 18(15), 3531; https://doi.org/10.3390/ma18153531 - 28 Jul 2025
Viewed by 247
Abstract
Due to the frequent occurrence of coarse-grained structures in large hydrogenation tube sheets, their hydrogen resistance and corrosion resistance deteriorate, significantly shortening their service life. Therefore, microstructure evolution must be strictly controlled during the forging process. High-temperature compression tests were simulated using a [...] Read more.
Due to the frequent occurrence of coarse-grained structures in large hydrogenation tube sheets, their hydrogen resistance and corrosion resistance deteriorate, significantly shortening their service life. Therefore, microstructure evolution must be strictly controlled during the forging process. High-temperature compression tests were simulated using a Gleeble-1500D thermal simulator to investigate the hot deformation behavior of 14Cr1Mo pressure vessel steel under deformation conditions of 1050–1250 °C and strain rates of 0.01–1 s−1. Based on the experimental data, the flow stress curve of 14Cr1Mo steel was obtained, and its thermal deformation behavior was analyzed. Furthermore, the dynamic recrystallization (DRX) kinetic model and grain size model of 14Cr1Mo steel were established. These models were then integrated into the finite element software Forge® to validate the accuracy of the DRX models. The results showed excellent agreement between the simulated and experimentally measured grain sizes, with a maximum deviation of less than 8%, confirming the high accuracy of the dynamic recrystallization models. These models provide a theoretical basis for finite element simulation and microstructure control in the manufacturing of super-large pressure vessel tube sheet forgings. Full article
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17 pages, 3321 KiB  
Article
Multi-Objective Automated Machine Learning for Inversion of Mesoscopic Parameters in Discrete Element Contact Models
by Xu Ao, Shengpeng Hao, Yuyu Zhang and Wenyu Xu
Appl. Sci. 2025, 15(15), 8181; https://doi.org/10.3390/app15158181 - 23 Jul 2025
Viewed by 151
Abstract
Accurate calibration of mesoscopic contact model parameters is essential for ensuring the reliability of Particle Flow Code in Three Dimensions (PFC3D) simulations in geotechnical engineering. Trial-and-error approaches are often used to determine the parameters of the contact model, but they are time-consuming, labor-intensive, [...] Read more.
Accurate calibration of mesoscopic contact model parameters is essential for ensuring the reliability of Particle Flow Code in Three Dimensions (PFC3D) simulations in geotechnical engineering. Trial-and-error approaches are often used to determine the parameters of the contact model, but they are time-consuming, labor-intensive, and offer no guarantee of parameter validity or simulation credibility. Although conventional machine learning techniques have been applied to invert the contact model parameters, they are hampered by the difficulty of selecting the optimal hyperparameters and, in some cases, insufficient data, which limits both the predictive accuracy and robustness. In this study, a total of 361 PFC3D uniaxial compression simulations using a linear parallel bond model with varied mesoscopic parameters were generated to capture a wide range of rock and geotechnical material behaviors. From each stress–strain curve, eight characteristic points were extracted as inputs to a multi-objective Automated Machine Learning (AutoML) model designed to invert three key mesoscopic parameters, i.e., the elastic modulus (E), stiffness ratio (ks/kn), and degraded elastic modulus (Ed). The developed AutoML model, comprising two hidden layers of 256 and 32 neurons with ReLU activation function, achieved coefficients of determination (R2) of 0.992, 0.710, and 0.521 for E, ks/kn, and Ed, respectively, demonstrating acceptable predictive accuracy and generalizability. The multi-objective AutoML model was also applied to invert the parameters from three independent uniaxial compression tests on rock-like materials to validate its practical performance. The close match between the experimental and numerically simulated stress–strain curves confirmed the model’s reliability for mesoscopic parameter inversion in PFC3D. Full article
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22 pages, 3727 KiB  
Article
Johnson–Cook Constitutive Model Parameters Estimation of 22MnB5 Hot Stamping Steel for Automotive Application Produced via the TSCR Process
by Yuxin Song, Yaowen Xu and Gengwei Yang
Metals 2025, 15(7), 811; https://doi.org/10.3390/met15070811 - 20 Jul 2025
Viewed by 2784
Abstract
In the industrial practice of metal forming, the consistent and reasonable characterization of the material behavior under the coupling effect of strain, strain rate, and temperature on the material flow stress is very important for the design and optimization of process parameters. The [...] Read more.
In the industrial practice of metal forming, the consistent and reasonable characterization of the material behavior under the coupling effect of strain, strain rate, and temperature on the material flow stress is very important for the design and optimization of process parameters. The purpose of this work was to establish an appropriate constitutive model to characterize the rheological behavior of a hot-formed steel plate (22MnB5 steel) produced through the TSCR (Thin Slab Casting and Rolling) process under practical deformation temperatures (150–250 °C) and strain rates (0.001–3000 s−1). Subsequently, the material flow behavior was modeled and predicted using the Johnson–Cook flow stress constitutive model. In this study, uniaxial tensile tests were conducted on 22MnB5 steel at room temperature under varying strain rates, along with elevated-temperature tensile tests at different strain rates, to obtain the engineering stress–strain curves and analyze the mechanical properties under various conditions. The results show that during room-temperature tensile testing within the strain rate range of 10−3 to 300 s−1, the 22MnB5 steel exhibited overall yield strength and tensile strength of approximately 1500 MPa, and uniform elongation and fracture elongation of about 7% and 12%, respectively. When the strain rate reached 1000–3000 s−1, the yield strength and tensile strength were approximately 2000 MPa, while the uniform elongation and fracture elongation were about 6% and 10%, respectively. Based on the experimental results, a modified Johnson–Cook constitutive model was developed and calibrated. Compared with the original model, the modified Johnson–Cook model exhibited a higher coefficient of determination (R2), indicating improved fitting accuracy. In addition, to predict the material’s damage behavior, three distinct specimen geometries were designed for quasi-static strain rate uniaxial tensile testing at ambient temperature. The Johnson–Cook failure criterion was implemented, with its constitutive parameters calibrated through integrated finite element analysis to establish the damage model. The determined damage parameters from this investigation can be effectively implemented in metal forming simulations, providing valuable predictive capabilities regarding workpiece material performance. Full article
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22 pages, 16747 KiB  
Article
Development of a Technique for Toughness Estimation in Dual-Phase Steels Using Representative Volume Elements
by Amin Latifi Vanjani, Hari M. Simha and Alexander Bardelcik
Metals 2025, 15(7), 788; https://doi.org/10.3390/met15070788 - 11 Jul 2025
Viewed by 212
Abstract
A novel approach to estimating the absorbed energy (toughness) in a uniaxial tensile test with only knowledge of the microstructure is presented. The flow behavior of each Dual-Phase (DP) steel grade is predicted using idealized Representative Volume Elements (RVEs) up to uniform elongation. [...] Read more.
A novel approach to estimating the absorbed energy (toughness) in a uniaxial tensile test with only knowledge of the microstructure is presented. The flow behavior of each Dual-Phase (DP) steel grade is predicted using idealized Representative Volume Elements (RVEs) up to uniform elongation. To estimate the flow behavior beyond uniform elongation, the stress-modified fracture strain in a non-local damage model was implemented in Abaqus. Damage parameters were calibrated using Finite Element (FE) simulations of purely ferritic tensile specimens. The damage parameters remained unchanged, except for the coefficient of triaxiality. This coefficient was adjusted based on the average triaxiality of ferrite elements at the instability point of the uniaxially loaded RVEs for each DP steel grade. The proposed approach comprises two steps: micron-sized RVEs to predict the flow behavior up to the point of uniform elongation and the average triaxiality and full-scale tensile-test simulations to predict the rest of the curves. The results show that the damage parameters calibrated for high-strain ferrite effectively estimate the absorbed energy during failure in tension tests. This approach is also geometry-independent; varying the geometry of the tensile specimen, including miniature or notched specimens, still yields predicted absorbed energies that are in good agreement with the experimental results. Full article
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17 pages, 6874 KiB  
Article
A Modified Fatigue Life Prediction Model for Cyclic Hardening/Softening Steel
by Zhibin Shen, Zhihui Cai, Hong Wang, Bo Xu, Linye Zhang, Yuxuan Song and Zengliang Gao
Materials 2025, 18(14), 3274; https://doi.org/10.3390/ma18143274 - 11 Jul 2025
Viewed by 311
Abstract
The accumulation of fatigue damage is primarily caused by cyclic plastic deformation. In low-cycle fatigue, cyclic plastic deformation is the dominant deformation mode. In high-cycle fatigue, although most deformation is elastic, plastic deformation may still occur in localized regions of stress concentration and [...] Read more.
The accumulation of fatigue damage is primarily caused by cyclic plastic deformation. In low-cycle fatigue, cyclic plastic deformation is the dominant deformation mode. In high-cycle fatigue, although most deformation is elastic, plastic deformation may still occur in localized regions of stress concentration and plays a critical role in the initiation of fatigue cracks. Considering that cyclic plastic deformation can be characterized by hysteresis loops, this study modifies the flow stress equation and the cyclic plastic deformation relationship based on stress–strain hysteresis loops at half-life cycles under different strain amplitudes. An improved model for life prediction that incorporates the effects of strain amplitude is proposed. The results of experiments on 310S stainless steel and 1045 carbon steel demonstrate that the model achieved prediction errors within a factor of two and provided reliable predictions for both high-cycle and low-cycle fatigue life across the entire ε-N curve. Full article
(This article belongs to the Section Metals and Alloys)
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10 pages, 1046 KiB  
Article
Are Urethral Pressure Profile Measurements Effective in Diagnosing Urodynamic Stress Incontinence in Women Presenting with Stress or Mixed Urinary Incontinence? Results from a Cross-Sectional Study
by Konstantinos Pantazis, Themistoklis Mikos, Sofia Tsiapakidou, Iakovos Theodoulidis, Stamatios Petousis, Konstantinos Dinas, Antonio Schiattarella, Antonio Simone Laganà and Apostolos P. Athanasiadis
Medicina 2025, 61(7), 1206; https://doi.org/10.3390/medicina61071206 - 1 Jul 2025
Viewed by 258
Abstract
Background and Objectives: This study aims to evaluate the relevance of urethral pressure profile (UPP) measurements in the diagnosis of urodynamic stress incontinence (USI) in women with stress and mixed urinary incontinence (SUI and MUI). Materials and Methods: A cross-sectional chart [...] Read more.
Background and Objectives: This study aims to evaluate the relevance of urethral pressure profile (UPP) measurements in the diagnosis of urodynamic stress incontinence (USI) in women with stress and mixed urinary incontinence (SUI and MUI). Materials and Methods: A cross-sectional chart review was used. All patients who had urodynamic studies (UDSs) in the urogynecology unit of an academic hospital over the last 6 months and complained of SUI or MUI were analyzed. Clinical examination included prolapse grading with the POP-Q system. The presenting symptoms, initial diagnosis before UDS, and results from flow studies—cystometrography (CMG), which included a 1-3-5 cough test at 300–350 mL bladder filling, and urethral pressure profilometry (UPP)—were recorded. p < 0.05 was considered significant in all statistical comparison tests; receiver operator characteristic (ROC) curves were also used to determine the best predictor of SUI diagnosis. Results: In total, 57 women were included in this study, with a mean age of 60.7 (±9.3). Upon UDS, 28 women (49.1%) demonstrated USI (Group 1), while 29 women (50.9%) did not demonstrate USI (Group 2). No differences between the two groups were noted during free uroflowmetry and the filling phase of CMG. However, the women in Group 2 had a significantly lower MUCP, FUL, and post-void residual after pressure flow compared to the women in Group 1 (p = 0.038, 0.003, and 0.04, respectively, upon Student’s t test for independent parameters). The ROC analysis indicated that when using MUCP and FUL for the diagnosis of USI, the AUCs are 0.663 (0.525–0.782) and 0.756 (0.623–0.861), respectively. Conclusions: By exhibiting correlations between low MUCP/FUL and USI, UPP appears to be a valid test for USI. The value of UPP in diagnosing USI in those with SUI and MUI appears to be clinically important. Further studies are needed in non-SUI patients, in addition to SUI subgroups and various incontinence treatment groups. Full article
(This article belongs to the Special Issue New Insights into Gynecological Disease)
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25 pages, 5582 KiB  
Article
Integrated Hydrologic–Hydraulic Modeling Framework for Flood Risk Assessment of Rural Bridge Infrastructure in Northwestern Pakistan
by Muhammad Kashif, Wang Bin, Hamza Shams, Muhammad Jhangeer Khan, Marwa Metwally, S. K. Towfek and Amal H. Alharbi
Water 2025, 17(13), 1893; https://doi.org/10.3390/w17131893 - 25 Jun 2025
Viewed by 513
Abstract
This study presents a flood risk assessment of five rural bridges along the monsoon-prone Khar–Mohmand Gat corridor in Northwestern Pakistan using an integrated hydrologic and hydraulic modeling framework. Hydrologic simulations for 50- and 100-year design storms were performed using the Hydrologic Engineering Center’s [...] Read more.
This study presents a flood risk assessment of five rural bridges along the monsoon-prone Khar–Mohmand Gat corridor in Northwestern Pakistan using an integrated hydrologic and hydraulic modeling framework. Hydrologic simulations for 50- and 100-year design storms were performed using the Hydrologic Engineering Center’s Hydrologic Modeling System (HEC-HMS), with watershed delineation conducted via Geographic Information Systems (GIS). Calibration was based on regional rainfall data from the Peshawar station using a Soil Conservation Service Curve Number (SCS-CN) of 86 and time of concentration calculated using Kirpich’s method. The resulting hydrographs were used in two-dimensional hydraulic simulations using the Hydrologic Engineering Center’s River Analysis System (HEC-RAS) to evaluate water surface elevations, flow velocities, and Froude numbers at each bridge site. The findings reveal that all bridges can convey peak flows without overtopping under current climatic conditions. However, Bridges 3 to 5 experience near-critical to supercritical flow conditions, with velocities ranging from 3.43 to 4.75 m/s and Froude numbers between 0.92 and 1.04, indicating high vulnerability to local scour. Bridge 2 shows moderate risk, while Bridge 1 faces the least hydraulic stress. The applied modeling framework effectively identifies structures requiring priority intervention and demonstrates a practical methodology for assessing flood risk in ungauged, data-scarce, and semi-arid regions. Full article
(This article belongs to the Special Issue Numerical Modelling in Hydraulic Engineering)
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17 pages, 1488 KiB  
Article
Study on Seepage Model of Staged-Fractured Horizontal Well in Low Permeability Reservoir
by Jian Song, Zongxiao Ren, Zhan Qu, Xinzhu Wang, Jiajun Cao, Xuemei Luo and Miao Wang
Processes 2025, 13(6), 1934; https://doi.org/10.3390/pr13061934 - 18 Jun 2025
Viewed by 283
Abstract
This study addresses the coupled influence of the threshold pressure gradient and stress sensitivity during the seepage process in low-permeability reservoirs. By integrating Laplace transform, perturbation transform, the image principle, and the superposition principle, a non-steady-state seepage model for segmented-fractured horizontal wells considering [...] Read more.
This study addresses the coupled influence of the threshold pressure gradient and stress sensitivity during the seepage process in low-permeability reservoirs. By integrating Laplace transform, perturbation transform, the image principle, and the superposition principle, a non-steady-state seepage model for segmented-fractured horizontal wells considering both effects is established for the first time. The analytical solution of the point source function including the threshold pressure gradient (λ) and stress sensitivity effect (permeability modulus α) is innovatively derived and extended to closed-boundary reservoirs. The model accuracy is verified by CMG numerical simulation (with an error of only 1.02%). Based on this, the seepage process is divided into four stages: I linear flow (pressure derivative slope of 0.5), II fracture radial flow (slope of 0), III dual radial flow (slope of 0.36), and IV pseudo-radial flow (slope of 0). Sensitivity analysis indicates the following: (1) The threshold pressure gradient significantly increases the seepage resistance in the late stage (the pressure curve shows a significant upward curvature when λ = 0.1 MPa/m); (2) Stress sensitivity dominates the energy dissipation in the middle and late stages (a closed-boundary-like feature is presented when α > 0.1 MPa−1); (3) The half-length of fractures dominates the early flow (a 100 m fracture reduces the pressure drop by 40% compared to a 20 m fracture). This model resolves the accuracy deficiency of traditional single-effect models and provides theoretical support for the development effect evaluation and well test interpretation of fractured horizontal wells in low-permeability reservoirs. Full article
(This article belongs to the Section Energy Systems)
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20 pages, 3723 KiB  
Article
Effect of Salinity on the Steady-State and Dynamic Rheological Behavior of Illite Clay
by Zhichao Liang, Wenyuan Ren, Sha Li, Aijun Zhang, Wenjing Mi, Yuguo Wang and Bin Dang
Buildings 2025, 15(12), 2067; https://doi.org/10.3390/buildings15122067 - 16 Jun 2025
Viewed by 283
Abstract
The rheological behavior of clay in a water–salt environment determines the long-term deformation and structural stability of building materials and geotechnical engineering. In this study, the effects of salinity on the rheological behavior and microstructure stability of the clay mineral illite were investigated [...] Read more.
The rheological behavior of clay in a water–salt environment determines the long-term deformation and structural stability of building materials and geotechnical engineering. In this study, the effects of salinity on the rheological behavior and microstructure stability of the clay mineral illite were investigated through steady-state and dynamic rheological tests. The results reveal that specimens with different salinities exhibit shear thinning behavior during the steady-state rheological test. When the shear rate is higher than 0.5 s−1, the flow curves are described well by the Herschel–Bulkley model. As the salinity increases from 0 to 1.8 mol/L, the yield stress varies from 1500 to 3500 Pa. With the increase in salinity, the consistency factor of the specimens increases, while the flow coefficient decreases. Under dynamic loading, high-salinity specimens exhibit higher modulus and yield stresses, thereby enhancing the stability of the microstructure. The viscoelastic–plastic constitutive model under dynamic loading has been established, which can effectively describe and calculate the long-term deformation of clay minerals. These research results provide reference and guidance for understanding the rheological behavior of clay. Full article
(This article belongs to the Section Building Structures)
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18 pages, 2811 KiB  
Article
Numerical Simulation of Turbulent Flow in River Bends and Confluences Using the k-ω SST Turbulence Model and Comparison with Standard and Realizable k-ε Models
by Rawaa Shaheed, Abdolmajid Mohammadian and Alaa Mohammed Shaheed
Hydrology 2025, 12(6), 145; https://doi.org/10.3390/hydrology12060145 - 11 Jun 2025
Viewed by 1360
Abstract
River bends and confluences are critical features in fluvial environments where complex flow patterns, including secondary currents, turbulence, and surface changes, strongly influence sediment transport, river morphology, and water quality. The accurate prediction of these flow characteristics is essential for hydraulic engineering applications. [...] Read more.
River bends and confluences are critical features in fluvial environments where complex flow patterns, including secondary currents, turbulence, and surface changes, strongly influence sediment transport, river morphology, and water quality. The accurate prediction of these flow characteristics is essential for hydraulic engineering applications. In this study, we present a numerical simulation of turbulent flow in river bends and confluences, with special consideration given to the dynamic interaction between free-surface variations and closed-surface constraints. The simulations were performed using OpenFOAM, an open-source computational fluid dynamics (CFDs) platform, with the k-ω SST (Shear Stress Transport) turbulence model, which is well-suited for capturing boundary layer behavior and complex turbulence structures. The finite volume method (FVM) is used to simulate and examine the behavior of the secondary current in channel bends and confluences. Two sets of experimental data, one with a sharply curved channel and the other with a confluent channel, were used to compare the numerical results and to evaluate the validity of the model. This study focuses on investigating to what extent the k-ω SST turbulence model can capture the effects of secondary flow and surface changes on flow hydrodynamics, analyzing velocity profiles and turbulence effects. The results are validated against experimental data, demonstrating the model’s ability to reasonably replicate flow features under both free- and closed-surface conditions. This study provides insights into the performance of the k-ω SST model in simulating the impact of geometrical constraints on flow regimes, offering a computationally robust and reasonable tool for river engineering and water resources management, particularly in the context of hydraulic structure design and erosion control in curved and confluence regions. Full article
(This article belongs to the Special Issue Hydrodynamics and Water Quality of Rivers and Lakes)
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10 pages, 1472 KiB  
Technical Note
Modeling of Tensile Tests Flow Curves Using an Explicit Piecewise Inverse Approach
by Aditya Vuppala, Holger Brüggemann, David Bailly and Emad Scharifi
Metals 2025, 15(6), 638; https://doi.org/10.3390/met15060638 - 5 Jun 2025
Viewed by 433
Abstract
Tensile tests are a common method for characterizing plastic behavior for sheet metal forming applications. During tensile testing at the beginning of the deformation, the stress state is uniaxial; however, as the deformation proceeds, the state changes to triaxial, making the post-processing of [...] Read more.
Tensile tests are a common method for characterizing plastic behavior for sheet metal forming applications. During tensile testing at the beginning of the deformation, the stress state is uniaxial; however, as the deformation proceeds, the state changes to triaxial, making the post-processing of experimental data challenging using analytical methods. In contrast, inverse approaches in which the behavior is represented by constitutive equations and the parameters are fitted using an iterative procedure are extremely dependent on the empirical equation chosen at the outset and can be computationally expensive. The inverse piecewise flow curve determination method, previously developed for compression tests, is extended in this paper to tensile testing. A stepwise approach is proposed to calculate constant strain rate flow curves accounting for the unique characteristics of tensile deformation. To capture the effects of localized strain rate variations during necking, a parallel flow curve determination strategy is introduced. Tensile test flow curves for manganese-boron steel 22MnB5, a material commonly used in hot stamping applications, are determined, and the approach is demonstrated for virtual force–displacement curves. It has been shown that these curves can replicate the virtual experimental flow curves data with a maximum deviation of 1%. Full article
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21 pages, 12520 KiB  
Article
Stress Estimation in Viscous Flows Using an Iterative Tikhonov Regularized Stokes Inverse Model
by Yuanhao Gao, Yang Wang and Jizhou Zhang
Mathematics 2025, 13(11), 1884; https://doi.org/10.3390/math13111884 - 4 Jun 2025
Viewed by 311
Abstract
In this paper, we propose and develop a stationary Stokes Inverse Model (SIM) to estimate the stress distributions that are difficult to measure directly in flows. We estimate the driving stresses from the velocities by solving the inverse problem governed by Stokes equations [...] Read more.
In this paper, we propose and develop a stationary Stokes Inverse Model (SIM) to estimate the stress distributions that are difficult to measure directly in flows. We estimate the driving stresses from the velocities by solving the inverse problem governed by Stokes equations under iterative Tikhonov (IT) regularization. We investigate the heuristic L-curve criterion to determine the proper regularization parameter. The solution existence and uniqueness for the Stokes inverse problem have been analyzed. We also conducted convergence analysis and error estimation for perturbed data, providing a fast and stable convergence. The finite element method is applied to the numerical approach. Following the theoretical investigation and formulation, we validate the model and demonstrate that the velocity data closely match the velocity fields that were reconstructed using the computed stress distributions. In particular, the proposed SIM can be used to reliably derive the stress distributions for the flows governed by the Stokes equations with small Reynolds number. Additionally, the model is robust to a certain number of perturbations, which enables the precise and effective estimation of the stress distributions. The proposed stationary SIM may be widely applicable in the estimation of stresses from experimental velocity fields in engineering and biological applications. Full article
(This article belongs to the Special Issue Mathematical Modeling for Fluid Mechanics)
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21 pages, 2034 KiB  
Article
Stabilization of Sandy Soil Against Internal Erosion Using Fly Ash with Alkali-Activated Binder
by Mohammad Almasaeid, Mousa Attom, Magdi El-Emam and Mohamad G. Arab
Water 2025, 17(10), 1552; https://doi.org/10.3390/w17101552 - 21 May 2025
Viewed by 1445
Abstract
Seepage forces due to the flow of water inside embankment hydraulic structures, such as dams or levees, result in internal erosion or piping. This will result in a reduction in soil strength, causing the failure of hydraulic structures. Stabilization of the soil is [...] Read more.
Seepage forces due to the flow of water inside embankment hydraulic structures, such as dams or levees, result in internal erosion or piping. This will result in a reduction in soil strength, causing the failure of hydraulic structures. Stabilization of the soil is one of the most effective approaches to avoid such catastrophic failure and prevent significant loss of life and property. The objective of this research is to stabilize sandy soil against internal erosion using fly ash (FA) alone and fly ash mixed with alkali-activated binder (NaOH). Although fly ash is commonly used for clay soil, its reactivity with alkali activators like NaOH makes it a potential candidate for stabilizing non-cohesive sandy soils when combined with alkaline solutions. A well-graded sandy soil was selected and mixed with fly ash alone and fly ash with sodium hydroxide at different percentages. Compaction curves were determined for each percentage, and specimens from the mix were remolded at 98% relative compaction and optimum moisture content corresponding to the compaction curve value. The hole erosion test (HET) was employed to evaluate internal erosion parameters. During the hole erosion test, seepage conditions were simulated by applying a controlled water flow through remolded specimens to replicate erosion caused by internal seepage forces. Additionally, the internal erosion parameters were evaluated at different curing times (2 days, 7 days, and 28 days were selected to capture short-term, intermediate, and long-term effects of chemical reactions on soil stabilization). Parameters such as the friction factor, coefficient of soil erosion, and critical shear stress were obtained, and the erosion rate index (IHET) was determined. It was found that using FA–NaOH significantly reduced internal erosion and increased the erosion rate index and the critical shear of the soil. The addition of 10% fly ash mixed with activated-alkali binder at 7 days curing time stabilized the soil against erosion. At this percentage, the erosion rate index equal to 5.3 and soil was categorized as: “very slow erosion”. However, mixing the sand with fly ash alone has a small or insignificant effect on the internal erosion of the soil, especially at higher percentages of fly ash. The optimum percentage of fly ash alone to improve the soil resistance to internal erosion was found to be 5% at 28 days of curing time where the soil rated as “moderately slow”. Full article
(This article belongs to the Special Issue Soil Erosion and Sedimentation by Water)
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21 pages, 5020 KiB  
Article
Influence of Heat Transfer on Stress Components in Metallic Plates Weakened by Multi-Curved Holes
by Faizah M. Alharbi and Nafeesa G. Alhendi
Axioms 2025, 14(5), 369; https://doi.org/10.3390/axioms14050369 - 14 May 2025
Viewed by 382
Abstract
This manuscript addresses an application study by employing a mathematical model of a thermoelastic plate weakened by multi-curved holes under the effect of stress forces in the presence of heat conduction. When the initial heat flow is directed to the plate system, complex [...] Read more.
This manuscript addresses an application study by employing a mathematical model of a thermoelastic plate weakened by multi-curved holes under the effect of stress forces in the presence of heat conduction. When the initial heat flow is directed to the plate system, complex variable procedures are used to compute the basic Goursat functions, taking into account the time-dependent variables through conformal mapping, which transfers the domain to the exterior of a unit circle. The problem reduces to a general form of a contact problem in two dimensions, which is called an integrodifferential equation of the second type with the Cauchy kernel. Additionally, different hole shapes are generated using Maple 2023. Computational simulations are performed to determine the normal and shear stress components in the presence and absence of heat effects at various times. Furthermore, numerical calculations of Goursat functions are carried out and graphically displayed for some specific materials. This investigation provides valuable information about industries, such as those regarding ceramic tile, glass, rubber, paint, ceramic pigment, and metal alloys. Full article
(This article belongs to the Special Issue Mathematical Methods in the Applied Sciences, 2nd Edition)
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