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Search Results (247)

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Keywords = stress exponent

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16 pages, 4429 KB  
Article
Pore Structure Evolution in Marine Sands Under Laterally Constrained Axial Loading
by Xia-Tao Zhang, Cheng-Liang Ji, Le-Le Liu, Hui-Long Ma and Deng-Feng Fu
J. Mar. Sci. Eng. 2025, 13(12), 2367; https://doi.org/10.3390/jmse13122367 - 12 Dec 2025
Viewed by 409
Abstract
Installation in sand is sensitive to its evolving pore structure, yet design models rarely update permeability for real-time fabric changes. This study tracks the stress-dependent pore size distribution of coarse sand under laterally constrained compression using high-resolution X-ray nano-CT. Scans taken at six [...] Read more.
Installation in sand is sensitive to its evolving pore structure, yet design models rarely update permeability for real-time fabric changes. This study tracks the stress-dependent pore size distribution of coarse sand under laterally constrained compression using high-resolution X-ray nano-CT. Scans taken at six axial stress levels show that the distribution shifts toward smaller radii while keeping its log-normal shape. A single shifting factor, defined as the current median radius normalized by the initial value, captures this translation. The factor decays with axial stress according to a power law, and the exponent as well as the reference pressure are calibrated from void ratio data. The resulting closed-form expression links mean effective stress to pore radius statistics without extra fitting once the compressibility constants are known. This quantitative relation between effective stress and pore size distribution has great potential to be embedded into coupled hydro-mechanical solvers, enabling engineers to refresh hydraulic permeability at every computation step, improving predictions of excess pore pressure and soil resistance during suction anchor penetration for floating wind foundations. Full article
(This article belongs to the Section Ocean Engineering)
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19 pages, 7771 KB  
Article
Research on the Hot Deformation Behavior and Mechanism of a New Nickel-Based P/M Superalloy
by Yifan Liu, Yanhui Yang, Jie Yang, Yaliang Zhu, Xiaofeng Wang, Weiwei Xia, Xianghui Meng and Kelu Zhong
Crystals 2025, 15(12), 1046; https://doi.org/10.3390/cryst15121046 - 8 Dec 2025
Viewed by 333
Abstract
Based on hot-compression simulations combined with SEM and TEM analyses, the high-temperature deformation behavior and mechanisms of a new nickel-based powder superalloy FGH101 were investigated over 1020–1110 °C and strain rates of 0.001–0.05 s−1. From the experimental data, the variations in [...] Read more.
Based on hot-compression simulations combined with SEM and TEM analyses, the high-temperature deformation behavior and mechanisms of a new nickel-based powder superalloy FGH101 were investigated over 1020–1110 °C and strain rates of 0.001–0.05 s−1. From the experimental data, the variations in the strain-rate sensitivity index m, the apparent activation energy for hot deformation Q, and the grain-size exponent p were determined as functions of strain rate and temperature. Hot deformation processing maps and mechanism maps incorporating dislocation density were established. The processing maps clearly revealed the evolution of formable regions at different temperatures and strains, while the mechanism maps successfully predicted the dislocation evolution and its operative hot deformation mechanisms by introducing the grain size evolution corrected by Burgers-vector compensation and the rheological flow stress behavior compensated by the modulus. The results indicated an optimal processing window of 1060–1100 °C at 0.001–0.003 s−1. Within the tested regime, as the strain rate decreased, the operative mechanism for grain-boundary sliding transitioned from pipe-diffusion control to lattice-diffusion control. These findings provide a solid theoretical basis for the design and optimization of the isothermal forging process of the new FGH101 alloy. Full article
(This article belongs to the Section Crystalline Metals and Alloys)
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12 pages, 1394 KB  
Article
Power-Law Time Exponent n and Time-to-Failure in 4H-SiC MOSFETs: Beyond Fixed Reaction–Diffusion Theory
by Mamta Dhyani, Smriti Singh, Nir Tzhayek and Joseph B. Bernstein
Micromachines 2025, 16(12), 1351; https://doi.org/10.3390/mi16121351 - 28 Nov 2025
Cited by 1 | Viewed by 813
Abstract
This work investigates bias-temperature instability (BTI) in 1700 V 4H-SiC MOSFETs under realistic 1 MHz switching conditions with simultaneous gate and drain stress. Threshold-voltage measurements reveal that the degradation does not follow the classical Reaction–Diffusion behavior typically assumed for silicon devices. Instead, the [...] Read more.
This work investigates bias-temperature instability (BTI) in 1700 V 4H-SiC MOSFETs under realistic 1 MHz switching conditions with simultaneous gate and drain stress. Threshold-voltage measurements reveal that the degradation does not follow the classical Reaction–Diffusion behavior typically assumed for silicon devices. Instead, the power-law exponent n shows a clear increase at the largest negative gate bias (−10 V), indicating a field-driven trap-generation mechanism. Temperature-dependent stress tests further show a negative activation energy (−0.466 eV), consistent with degradation accelerating at lower temperatures due to suppressed detrapping. The results demonstrate that conventional silicon BTI models cannot be directly applied to SiC technologies and that fixed-n lifetime extrapolation leads to significant errors. A bias-dependent, field-driven framework for estimating time-to-failure is proposed, offering more accurate and practical reliability prediction for high-power SiC converter applications. Full article
(This article belongs to the Collection Women in Micromachines)
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18 pages, 4356 KB  
Article
The Impact of C-Rate, Float Charging and Temperature on Pouch Lithium-Ion Battery Swelling
by Sahithi Maddipatla, Lingxi Kong, Michael Osterman, Jonghoon Kim and Michael Pecht
Batteries 2025, 11(11), 419; https://doi.org/10.3390/batteries11110419 - 14 Nov 2025
Viewed by 1124
Abstract
Swelling in pouch batteries poses reliability issues and safety hazards, resulting in product damage, fires, and explosions. This study examines swelling based on the impact of C-rate and temperature during charge–discharge tests, and upper voltage limit and temperature during constant voltage/float charging tests. [...] Read more.
Swelling in pouch batteries poses reliability issues and safety hazards, resulting in product damage, fires, and explosions. This study examines swelling based on the impact of C-rate and temperature during charge–discharge tests, and upper voltage limit and temperature during constant voltage/float charging tests. Internal cell dynamics related to swelling are analyzed using equivalent circuit model parameters from electrochemical impedance spectroscopy tests, and correlations with thickness are established. Constant voltage charging experiments show that swelling follows an initial increase, a plateau, and then a rapid escalation. The onset of rapid swelling accelerated with temperature and voltage, thereby reducing the time to the knee point. A double-exponent swelling model is developed to predict the evolution of thickness under various stress conditions. The results demonstrate that monitoring swelling rate and magnitude can serve as an effective diagnostic for identifying abnormal cell behavior. Full article
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20 pages, 2673 KB  
Article
Shear-Thickening Superplastic Transitions in High-Entropy Oxides
by Salma El-Azab, Sichao Chen, Julie M. Schoenung and Alexander D. Dupuy
Ceramics 2025, 8(4), 136; https://doi.org/10.3390/ceramics8040136 - 10 Nov 2025
Viewed by 539
Abstract
Despite significant interest in their functional properties, the mechanical behavior of high-entropy oxides (HEOs) is not well studied, particularly at elevated temperatures. Bulk (Co,Cu,Mg,Ni,Zn)O (transition metal (TM)-HEO) samples were deformed under compression at applied stresses and temperatures ranging from 5 to 31 MPa [...] Read more.
Despite significant interest in their functional properties, the mechanical behavior of high-entropy oxides (HEOs) is not well studied, particularly at elevated temperatures. Bulk (Co,Cu,Mg,Ni,Zn)O (transition metal (TM)-HEO) samples were deformed under compression at applied stresses and temperatures ranging from 5 to 31 MPa and 600 to 850 °C, respectively. All of the deformation conditions result in creep stress exponents of n < 3, indicating that TM-HEO exhibits superplastic deformation. A transition from structural to solution-precipitation-based superplasticity is observed during deformation above 650 °C. Additionally, TM-HEO exhibits shear-thickening behavior when deformed at stresses above 9 MPa. The formation and behavior of a Cu-rich tenorite secondary phase during deformation is identified as a key factor underpinning the deformation mechanisms. The microstructure and phase state of TM-HEO before deformation also influenced the behavior, with finer grain sizes and increasing concentrations of Cu-rich tenorite, resulting in the increased prevalence of solution-precipitation deformation. While complex, the results of this study indicate that TM-HEO deforms through known superplastic deformation mechanisms. Superplasticity is a highly efficient manufacturing method and could prove to be a valuable strategy for forming HEO ceramics into complex geometries. Full article
(This article belongs to the Special Issue Mechanical Behavior and Reliability of Engineering Ceramics)
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20 pages, 5641 KB  
Article
Comparative Analysis of Cyclic Properties and Fractography of AA2519 Aluminum Alloy Samples with Different Fatigue Lives
by Robert Sołtysiak, Maciej Kotyk and Joanna Małecka
Materials 2025, 18(21), 5021; https://doi.org/10.3390/ma18215021 - 4 Nov 2025
Viewed by 539
Abstract
The article presents an analysis of the outcomes for AA2519 aluminum alloy exposed to variable loads. The variable loads were implemented with a strain control program consisting of incremental steps and increasing/decreasing multiple steps. Tests were conducted at higher and lower strain ranges [...] Read more.
The article presents an analysis of the outcomes for AA2519 aluminum alloy exposed to variable loads. The variable loads were implemented with a strain control program consisting of incremental steps and increasing/decreasing multiple steps. Tests were conducted at higher and lower strain ranges and yielded lower (LFL test) and higher (HFL test) fatigue life, respectively. The values of plastic strain, cyclic modulus, cyclic yield strength, and fractography were analyzed. Based on the analysis of the test results, a criterion was established for the division of the tested fatigue properties into two parts for which the strength coefficient and strain hardening exponent were determined. An analytical description of the cyclic stress–strain curve for the entire range of results obtained from the LFL and HFL tests was proposed. Compared to other available models describing material properties, good compliance was obtained with the experimental results for both the LFL and HFL tests. Full article
(This article belongs to the Section Metals and Alloys)
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21 pages, 6725 KB  
Article
Microstructure-Dependent Creep Mechanisms in Heat-Treated CZ1 Zr Alloy at 380 °C
by Haoyu Shi, Jianqiang Wang, Meiqing Chen, Pengliang Liu, Zhixuan Xia, Chenyang Lu, Rui Gao, Weiyang Li, Yujie Zhang, Zhengxiong Su and Jing Hu
Nanomaterials 2025, 15(21), 1624; https://doi.org/10.3390/nano15211624 - 24 Oct 2025
Viewed by 670
Abstract
This study investigates the stress-dependent creep behavior of a CZ1 Zr alloy exhibiting two distinct microstructural states induced by different annealing treatments. Creep tests were conducted at 380 °C under applied stresses of 140 MPa and 260 MPa. CZ1-2 (fully recrystallized), characterized by [...] Read more.
This study investigates the stress-dependent creep behavior of a CZ1 Zr alloy exhibiting two distinct microstructural states induced by different annealing treatments. Creep tests were conducted at 380 °C under applied stresses of 140 MPa and 260 MPa. CZ1-2 (fully recrystallized), characterized by coarse grains and low dislocation density, demonstrated superior creep resistance under low stress due to suppressed dislocation activity and diffusion-dominated deformation. Stress exponent analysis revealed n = 5 for CZ1-1 (partially recrystallized) and n = 10 for CZ1-2, confirming a mechanism transition from steady-state dislocation climb to power-law breakdown. TEM characterization provided direct evidence of evolving dislocation networks, stacking faults, and second-phase particle redistribution. These findings underscore the critical role of microstructural conditioning in governing creep pathways and provide a mechanistic basis for tailoring Zr alloys to stress-specific service environments in advanced nuclear applications. Full article
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21 pages, 5267 KB  
Article
Effect of Increased Extrusion Ram Speed and Liquid Nitrogen Cooling on the Mechanical Properties of 6060 Aluminum Alloy
by Evangelos Giarmas, Emmanouil Tzimtzimis, Konstantinos Tsongas, Apostolos Korlos, Constantine David and Dimitrios Tzetzis
Metals 2025, 15(10), 1136; https://doi.org/10.3390/met15101136 - 12 Oct 2025
Viewed by 866
Abstract
This study investigates the impact of increased extrusion ram speed—achieved by utilizing liquid nitrogen as a die cooling agent—on the mechanical properties of a 6060-aluminum alloy. Mechanical characterization of the extruded profiles was performed using both tensile and nanoindentation tests. In addition, nanoindentation [...] Read more.
This study investigates the impact of increased extrusion ram speed—achieved by utilizing liquid nitrogen as a die cooling agent—on the mechanical properties of a 6060-aluminum alloy. Mechanical characterization of the extruded profiles was performed using both tensile and nanoindentation tests. In addition, nanoindentation was employed to evaluate creep behaviour and to extract key parameters, such as the steady-state creep strain rate. The findings indicate that while the enhanced ram speed has a minimal influence on Ultimate Tensile Strength (UTS) and Yield Tensile Strength (YTS), it has a more noticeable effect on elongation. Finite Element Analysis (FEA) was used in conjunction with nanoindentation data to model the mechanical behaviour of the alloy, showing good agreement with experimental tensile test results. This confirms the effectiveness of FEA-assisted nanoindentation as a reliable tool for mechanical assessment. Moreover, the results demonstrate that creep displacement is significantly influenced by the increased ram speed. However, the steady-state creep strain rate remained largely unaffected by variations in ram speed with the use of liquid nitrogen as a coolant. Notably, the creep stress exponent (n) was found to increase with higher ram speeds enabled by liquid nitrogen cooling. Full article
(This article belongs to the Special Issue Research and Application of Lightweight Metals)
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16 pages, 1356 KB  
Article
Predictive Numerical Modeling of Inelastic Buckling for Process Optimization in Cold Forging of Aluminum, Stainless Steel, and Copper
by Dan Lagat, Huzeifa Munawar, Eliakim Akhusama, Alfayo Alugongo and Hilary Rutto
Processes 2025, 13(10), 3177; https://doi.org/10.3390/pr13103177 - 7 Oct 2025
Viewed by 869
Abstract
The growing demand for precision and consistency in the forging industry has heightened the need for predictive simulation tools. While extensive research has focused on parameters such as flow stress, die wear, billet fracture, and residual stresses, the phenomenon of billet buckling, especially [...] Read more.
The growing demand for precision and consistency in the forging industry has heightened the need for predictive simulation tools. While extensive research has focused on parameters such as flow stress, die wear, billet fracture, and residual stresses, the phenomenon of billet buckling, especially during cold upset forging, remains underexplored. Most existing models address only elastic buckling for slender billets using classical approaches like Euler and Rankine-Gordon formulae, which are not suitable for inelastic deformation in shorter billets. This study presents a numerical model developed to analyze inelastic buckling during cold forging and to determine associated stresses and deflection characteristics. The model was validated through finite element simulations across a range of billet geometries (10–40 mm diameter, 120 mm length), materials (aluminum, stainless steel, and copper), and friction coefficients (µ = 0.12, 0.16, and 0.35). Stress distributions were evaluated against die stroke, with particular emphasis on the influence of strain hardening and geometry. The results showed that billet geometry and strain-hardening exponent significantly affect buckling behavior, whereas friction had a secondary effect, mainly altering overall stress levels. A nonlinear regression approach incorporating material properties, geometric parameters, and friction was used to formulate the numerical model. The developed model effectively estimated buckling stresses across various conditions but could not precisely predict buckling points based on stress differentials. This work contributes a novel framework for integrating material, geometric, and process variables into stress prediction during forging, advancing defect control strategies in industrial metal forming. Full article
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25 pages, 7449 KB  
Article
Influence of Volumetric Geometry on Meteorological Time Series Measurements: Fractality and Thermal Flows
by Patricio Pacheco Hernández, Gustavo Navarro Ahumada, Eduardo Mera Garrido and Diego Zemelman de la Cerda
Fractal Fract. 2025, 9(10), 639; https://doi.org/10.3390/fractalfract9100639 - 30 Sep 2025
Viewed by 768
Abstract
This work analyzes the behavior of the boundary layer subjected to stresses by obstacles using hourly measurements, in the form of time series, of meteorological variables (temperature (T), relative humidity (RH), and magnitude of the wind speed (WS)) in a given period. The [...] Read more.
This work analyzes the behavior of the boundary layer subjected to stresses by obstacles using hourly measurements, in the form of time series, of meteorological variables (temperature (T), relative humidity (RH), and magnitude of the wind speed (WS)) in a given period. The study region is Santiago, the capital of Chile. The measurement location is in a rugged basin geography with a nearly pristine atmospheric environment. The time series are analyzed through chaos theory, demonstrating that they are chaotic through the calculation of the parameters Lyapunov exponent (λ > 0), correlation dimension (DC < 5), Kolmogorov entropy (SK > 0), Hurst exponent (0.5 < H < 1), and Lempel–Ziv complexity (LZ > 0). These series are simultaneous measurements of the variables of interest, before and after, of three different volumetric geometries arranged as obstacles: a parallelepiped, a cylinder, and a miniature mountain. The three geometries are subject to the influence of the wind and present the same cross-sectional area facing the measuring instruments oriented in the same way. The entropies calculated for each variable in each geometry are compared. It is demonstrated, in a first approximation, that volumetric geometry impacts the magnitude of the entropic fluxes associated with the measured variables, which can affect micrometeorology and, by extension, the climate in general. Furthermore, the study examines which geometry favors greater information loss or greater fractality in the measured variables. Full article
(This article belongs to the Special Issue Fractals in Earthquake and Atmospheric Science)
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21 pages, 6078 KB  
Article
Integrating Microstructures and Dual Constitutive Models in Instrumented Indentation Technique for Mechanical Properties Evaluation of Metallic Materials
by Yubiao Zhang, Bin Wang, Yonggang Zhang, Shuai Wang, Shun Zhang and He Xue
Materials 2025, 18(17), 4159; https://doi.org/10.3390/ma18174159 - 4 Sep 2025
Cited by 1 | Viewed by 1036
Abstract
Local variations in mechanical properties are commonly observed in engineering structures, driven by complex manufacturing histories and harsh service environments. The evaluation of mechanical properties accurately constitutes a fundamental requirement for structural integrity assessment. The Instrumented Indentation Technique (IIT) can play a critical [...] Read more.
Local variations in mechanical properties are commonly observed in engineering structures, driven by complex manufacturing histories and harsh service environments. The evaluation of mechanical properties accurately constitutes a fundamental requirement for structural integrity assessment. The Instrumented Indentation Technique (IIT) can play a critical role in the in-site testing of local properties. However, it could be often a challenge to correlate indentation characteristics with uniaxial stress–strain relationships. In this study, we investigated quantitatively the connection between the indentation responses of commonly used metals and their plastic properties using the finite element inversion method. Materials typically exhibit plastic deformation mechanisms characterized by either linear or power-law hardening behaviors. Consequently, conventional prediction methods based on a single constitutive model may no longer be universally applicable. Hence, this study developed methods for acquiring mechanical properties suitable for either the power-law and linear hardening model, or combined, respectively, based on analyses of microstructures of materials exhibiting different hardening behaviors. We proposed a novel integrated IIT incorporating microstructures and material-specific constitutive models. Moreover, the inter-dependency between microstructural evolution and hardening behaviors was systematically investigated. The proposed method was validated on representative engineering steels, including austenitic stainless steel, structural steel, and low-alloy steel. The predicted deviations in yield strength and strain hardening exponent are broadly within 10%, with the maximum error at 12%. This study is expected to provide a fundamental framework for the advancement of IIT and structural integrity assessment. Full article
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17 pages, 3737 KB  
Article
Sintering Kinetics, Mechanical Properties, and Electrical Conductivity of Ti-67 at% Al Targets Fabricated via Spark Plasma Sintering
by Qizhong Li, Weiyan Wang, Yibing Su, Yuzhe Han, Meijun Yang, Takashi Goto and Rong Tu
Coatings 2025, 15(9), 1029; https://doi.org/10.3390/coatings15091029 - 3 Sep 2025
Viewed by 995
Abstract
Ti–Al alloys have widespread applications as targets in hard coatings by PVD (Physical Vapor Deposition). While the importance of target density is recognized, the densification mechanisms of Ti-67 at% Al targets, particularly during spark plasma sintering (SPS), remain poorly understood, hindering process optimization. [...] Read more.
Ti–Al alloys have widespread applications as targets in hard coatings by PVD (Physical Vapor Deposition). While the importance of target density is recognized, the densification mechanisms of Ti-67 at% Al targets, particularly during spark plasma sintering (SPS), remain poorly understood, hindering process optimization. This study aims to clarify these mechanisms by fabricating Ti-67 at% Al targets via SPS and examining their densification behavior through a detailed analysis of the creep model based on the stress exponent (n) and apparent activation energy (Qd). The target’s relative density gradually increased in the temperature range of 370–530 °C, whereas the grain size remained relatively constant, indicating that the densification process dominated during this period. The results reveal that densification is primarily controlled by intergranular diffusion (n ≈ 2, Qd = 97.29 kJ/mol) and dislocation climbing (n ≈ 3, Qd = 158.74 kJ/mol). The target’s relative density reached 98.25% at 530 °C, with a corresponding grain size of 10.86 ± 1.08 μm. Additionally, as the temperature increased, the Vickers hardness of the target increased from 61.56 HV to 129.66 HV, and the electrical conductivity rose from 0.23 S/cm to 0.86 S/cm. This work provides a fundamental understanding of the densification kinetics in Ti-67 at% Al alloys during SPS, establishing a crucial guideline for fabricating high-performance PVD targets. Full article
(This article belongs to the Special Issue Corrosion Resistant Coatings in Civil Engineering)
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13 pages, 954 KB  
Article
Interfacial Adhesion of Mouthrinses to Orthodontic Metal Wires: Surface Film Viscoelasticity Effect
by Stanisław Pogorzelski, Krzysztof Dorywalski, Katarzyna Boniewicz-Szmyt and Paweł Rochowski
Materials 2025, 18(17), 4065; https://doi.org/10.3390/ma18174065 - 29 Aug 2025
Viewed by 768
Abstract
This study concerns the evaluation of adhesive and wettability energetic signatures of a model orthodontic wire exposed to commercial mouthrinses. The surface wetting properties were evaluated from the contact angle hysteresis (CAH) approach applied to dynamic contact angle data derived from [...] Read more.
This study concerns the evaluation of adhesive and wettability energetic signatures of a model orthodontic wire exposed to commercial mouthrinses. The surface wetting properties were evaluated from the contact angle hysteresis (CAH) approach applied to dynamic contact angle data derived from the original drop on a vertical filament method. Young, advancing, receding CA apart from adhesive film pressure, surface energy, work of adhesion, etc. were chosen as interfacial interaction indicators, allowing for the optimal concentration and placement of the key component(s) accumulation to be predicted for effective antibacterial activity to eliminate plaque formation on the prosthetic materials. Surfactant compounds when adsorb at interfaces confer rheological properties to the surfaces, leading to surface relaxation, which depends on the timescale of the deformation. The surface dilatational complex modulus E, with compression elasticity Ed and viscosity Ei parts, determined in the stress–relaxation Langmuir trough measurements, exhibited the viscoelastic surface film behavior with the relaxation times (0.41–3.13 s), pointing to the vertically segregated film structure as distinct, stratified layers with the most insoluble compound on the system top (as indicated with the 2D polymer film scaling theory exponent y = 12.9–15.5). Kinetic rheology parameters could affect the wettability, adhesion, and spreading characteristics of mouthrinse liquids. Full article
(This article belongs to the Section Thin Films and Interfaces)
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21 pages, 1696 KB  
Article
Residual Stress Estimation in Structures Composed of One-Dimensional Elements via Total Potential Energy Minimization Using Evolutionary Algorithms
by Fatih Uzun and Alexander M. Korsunsky
J. Manuf. Mater. Process. 2025, 9(9), 292; https://doi.org/10.3390/jmmp9090292 - 28 Aug 2025
Cited by 2 | Viewed by 1501
Abstract
This study introduces a novel energy-based inverse method for estimating residual stresses in structures composed of one-dimensional elements undergoing elastic–plastic deformation. The problem is reformulated as a global optimization task governed by the principle of minimum total potential energy. Rather than solving equilibrium [...] Read more.
This study introduces a novel energy-based inverse method for estimating residual stresses in structures composed of one-dimensional elements undergoing elastic–plastic deformation. The problem is reformulated as a global optimization task governed by the principle of minimum total potential energy. Rather than solving equilibrium equations directly, the internal stress distribution is inferred by minimizing the structure’s total potential energy using a real-coded genetic algorithm. This approach avoids gradient-based solvers, matrix assembly, and incremental loading, making it suitable for nonlinear and history-dependent systems. Plastic deformation is encoded through element-wise stress-free lengths, and a dynamic fitness exponent strategy adaptively controls selection pressure during the evolutionary process. The method is validated on single- and multi-bar truss structures under axial tensile loading, using a bilinear elastoplastic material model. The results are benchmarked against nonlinear finite element simulations and analytical calculations, demonstrating excellent predictive capability with stress errors typically below 1%. In multi-material systems, the technique accurately reconstructs tensile and compressive residual stresses arising from elastic–plastic mismatch using only post-load geometry. These results demonstrate the method’s robustness and accuracy, offering a fully non-incremental, variational alternative to traditional inverse approaches. Its flexibility and computational efficiency make it a promising tool for residual stress estimation in complex structural applications involving plasticity and material heterogeneity. Full article
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15 pages, 5326 KB  
Article
Study on the Construction of a Nonlinear Creep Constitutive Model of Salt-Gypsum Rock in the Bayan Deep and the Critical Value of Wellbore Shrinkage Liquid Column Pressure
by Penglin Liu, Aobo Yin, Tairan Liang, Wen Sun, Wei Lian, Bo Zhang, Shanpo Jia and Jinchuan Huang
Processes 2025, 13(9), 2747; https://doi.org/10.3390/pr13092747 - 28 Aug 2025
Viewed by 623
Abstract
Aiming at the problems of borehole shrinkage and pipe sticking caused by creep in salt-gypsum rock formations during deep well drilling, multi-field coupling creep experiments on deep salt-bearing gypsum mudstone were carried out. Furthermore, a nonlinear creep constitutive model was constructed based on [...] Read more.
Aiming at the problems of borehole shrinkage and pipe sticking caused by creep in salt-gypsum rock formations during deep well drilling, multi-field coupling creep experiments on deep salt-bearing gypsum mudstone were carried out. Furthermore, a nonlinear creep constitutive model was constructed based on the Drucker–Prager criterion, and the critical value of liquid column pressure for borehole shrinkage was determined through numerical simulation. Experiments show that at 140 °C, salt-gypsum rock is mainly subjected to brittle failure with single shear fracture, while at 180 °C, multiple sets of cross-cutting shear bands form, shifting to plastic flow-dominated composite failure. The coupling effect of confining pressure and deviatoric stress is temperature-dependent; the critical deviatoric stress is independent of confining pressure at 140 °C, but decreases significantly with increasing confining pressure at 180 °C, revealing that salt-gypsum rock is more prone to plastic flow under high temperatures and confining pressure. The creep constitutive equation was further determined, and fitting parameters show that the stress exponent m = 2–5 and the time exponent n decrease linearly with the increase in deviatoric stress, and the model can accurately describe the characteristics of three-stage creep. The numerical simulation found that there is a nonlinear relationship between the drilling fluid density and borehole shrinkage; the shrinkage rate exceeds 1.47% when the density is ≤2.0 g/cm3, and the expansion amount is >1.0 mm when ≥2.4 g/cm3. The critical safe density range is 2.1–2.3 g/cm3, which is consistent with the field data in the Bayan area. The research results provide an experimental basis and quantitative method for the dynamic regulation of drilling fluid density in deep gypsum rock formations, and have engineering guiding significance for preventing borehole wall instability. Full article
(This article belongs to the Section Energy Systems)
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