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24 pages, 9218 KB  
Article
Anisotropic Evolution of Pore–Fracture Structures and Fractional-Order Porosity Modeling of Deep-Bedded Coal
by Jun Wang, Zixiong Qi, Weiyuan Mou, Haonan Yue, Shaobo Zhao, Shihang Xu, Yue Yang and Hongwei Zhou
Fractal Fract. 2026, 10(8), 553; https://doi.org/10.3390/fractalfract10080553 - 13 Aug 2026
Viewed by 126
Abstract
Understanding the anisotropic mechanical behavior and pore–fracture structure (PFS) evolution of bedded coal under mining disturbance is critical for gas extraction and hazard prevention in deep coal mining. This study employed low-field nuclear magnetic resonance (NMR) and fractal analysis to characterize the PFS [...] Read more.
Understanding the anisotropic mechanical behavior and pore–fracture structure (PFS) evolution of bedded coal under mining disturbance is critical for gas extraction and hazard prevention in deep coal mining. This study employed low-field nuclear magnetic resonance (NMR) and fractal analysis to characterize the PFS of water-saturated coal samples with bedding angles of 0°, 30°, 45°, 60°, and 90°. The pore system was classified into adsorption and seepage pores according to pore size distribution. Real-time triaxial NMR tests were further conducted to reveal the coupled evolution of mechanical responses and PFS under different bedding orientations. Results show that bedding inclination controls pore distribution, connectivity, and structural complexity, while influencing coal strength, deformation, and failure through stress redistribution and bedding-plane activation. The mechanical response and PFS evolution exhibit strong anisotropic coupling during loading. A fractional-order porosity model was established by incorporating bedding orientation, anisotropy, and stress memory based on pore geometry and stress decomposition. Model verification confirms its effectiveness in describing anisotropic porosity and PFS evolution under varying bedding angles. This study provides theoretical support for permeability prediction, stability assessment, and hazard control in deep-bedded coal seams. Full article
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26 pages, 7730 KB  
Article
Numerical Analysis of Hydraulic Fracture Propagation Behaviors in Ultra-Deep Lattice-like Fractured Reservoirs
by Ju Liu, Hui Liu, Dengfeng Ren, Longcang Huang, Xin Qiao, Cheng Huang, Kun Li, Yaoyao Sun, Xiaoguang Wu and Zhongwei Huang
Appl. Sci. 2026, 16(16), 7950; https://doi.org/10.3390/app16167950 - 10 Aug 2026
Viewed by 166
Abstract
Ultra-deep lattice-like fractured carbonate reservoirs, formed by multi-period tectonic movements, feature strong heterogeneity, multi-scale fracture nesting, and anisotropic in situ stress. However, hydraulic fracture (HF) propagation behaviors within these complex formations remain poorly understood. In this study, using an unstructured fracture network approach, [...] Read more.
Ultra-deep lattice-like fractured carbonate reservoirs, formed by multi-period tectonic movements, feature strong heterogeneity, multi-scale fracture nesting, and anisotropic in situ stress. However, hydraulic fracture (HF) propagation behaviors within these complex formations remain poorly understood. In this study, using an unstructured fracture network approach, we simulated HF propagation in two typical fault-controlled lattice-like structures: compressive-torsion and pull-apart overlap zones. The performance of commingled, staged, and temporary plugging fracturing was evaluated, alongside sensitivity analyses of wellbore orientation, plugging timing, pump rate, and fluid viscosity. Results indicate that HFs in compressive-torsion zones exhibit long, straight geometries with local tensile activation points. Conversely, pull-apart overlap zones promote step-shaped, multi-branched fractures with superior lateral connectivity. The optimal timing for temporary plugging exhibits a delayed trend with increasing natural fracture density, ranging from 50% to 70% of the fracturing process in compressive-torsion zones, whereas an earlier implementation is preferred in pull-apart overlap zones, occurring at 33–65% of the fracturing process. Furthermore, HFs in compressive-torsion zones are less sensitive to viscosity and pump rate. To optimize stimulated volume, a moderate viscosity of 50–60 mPa·s is universally recommended. Regarding pump rates, 8–10 m3/min is ideal for balanced connectivity in pull-apart overlap zones, whereas >12 m3/min is required for compressive-torsion zones. These findings provide critical theoretical and engineering guidelines for differentiated fracturing strategies in ultra-deep reservoirs. Full article
(This article belongs to the Special Issue Petroleum Engineering: Advances and Prospects)
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33 pages, 38306 KB  
Article
A Physically Based Three-Dimensional Streamtube Model for Rapid Waterflood-Front Prediction and Sweep-Efficiency Evaluation in Ultra-Low-Permeability Reservoirs
by Tao Jiao, Jing Wang, Yanwei Wang, Zikuan Zhao, Wenjing Zhao, Junjian Li, Huan Zhao and Yan Lei
Energies 2026, 19(14), 3378; https://doi.org/10.3390/en19143378 - 17 Jul 2026
Viewed by 348
Abstract
Accurate and rapid prediction of waterflood front propagation and volumetric sweep efficiency remains challenging in ultra-low-permeability reservoirs because of strong heterogeneity, threshold pressure gradients, reservoir anisotropy, complex well-pattern geometry, and layer-dependent flow interference. In this study, an improved 3D streamtube model was developed [...] Read more.
Accurate and rapid prediction of waterflood front propagation and volumetric sweep efficiency remains challenging in ultra-low-permeability reservoirs because of strong heterogeneity, threshold pressure gradients, reservoir anisotropy, complex well-pattern geometry, and layer-dependent flow interference. In this study, an improved 3D streamtube model was developed for waterflood-front tracking and volumetric sweep evaluation in ultra-low-permeability reservoirs. The model incorporates experimentally constrained threshold pressure gradients, anisotropic coordinate transformation, dynamic streamtube flow-rate allocation, Buckley–Leverett-based non-piston displacement, interlayer interference correction, and irregular well-pattern adaptability. A unified calculation framework was established for both injector–producer and injector–fracture streamtube units, enabling 3D integration of layer-specific swept areas into volumetric sweep efficiency. The proposed model was validated against a commercial numerical simulator using a representative well group from Block A of the Changqing Oilfield. The predicted streamtube architecture and sweep-efficiency evolution agree well with numerical simulation results, with an average relative error of approximately 3.1%, while reducing the computational time from 1043 s to 1.42 s for a 30-year simulation. Sensitivity analysis demonstrates that threshold pressure gradient, well spacing, and inter-well connectivity are the dominant controls on sweep efficiency, whereas well-pattern type, interlayer heterogeneity, and reservoir anisotropy exert secondary but non-negligible effects. Field application further reveals a strongly layer-dependent waterflood behavior: the upper sand body preferentially propagates eastward, whereas the lower sand body advances mainly southward, producing a vertically asynchronous and laterally misaligned sweep pattern. These results show that the proposed model provides an efficient and physically interpretable tool for rapid waterflood-front prediction, refined waterflood optimization, and targeted production enhancement in heterogeneous ultra-low-permeability oil reservoirs. Full article
(This article belongs to the Special Issue Geological Sequestration and Resource Utilization of Carbon Dioxide)
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18 pages, 4863 KB  
Article
Deep-Learning Enabled Atomistic Understanding of Thermomechanical Behaviors and Fracture Mechanisms of High-Entropy Diboride (Hf0.2Zr0.2Ta0.2Ti0.2Nb0.2)B2
by Xu Zhang, Bei Li, Meng Wang, Bo Liu, Ji Zou and Jianjun Li
Materials 2026, 19(13), 2785; https://doi.org/10.3390/ma19132785 - 1 Jul 2026
Viewed by 467
Abstract
High-entropy transition-metal diborides represent a promising class of ultra-high temperature ceramics. However, atomic insights into their high-temperature elastic response, anisotropic deformation, and fracture mechanisms remain elusive. Herein, we perform molecular dynamic simulations to study the thermomechanical behaviors of (Hf0.2Zr0.2Ta [...] Read more.
High-entropy transition-metal diborides represent a promising class of ultra-high temperature ceramics. However, atomic insights into their high-temperature elastic response, anisotropic deformation, and fracture mechanisms remain elusive. Herein, we perform molecular dynamic simulations to study the thermomechanical behaviors of (Hf0.2Zr0.2Ta0.2Ti0.2Nb0.2)B2 from 900 to 3300 K by developing an ab initio accuracy deep-learning potential. The proposed potential accurately reproduces lattice parameters, equations of state, and elastic constants, in excellent agreement with density functional theory calculations and available experiments, and remains transferable under thermally expanded and compressed states. The simulations reveal anisotropic thermal expansion, with the out-of-plane expansion exceeding the in-plane expansion, together with progressive elastic softening while preserving C11 > C33 due to the dominant in-plane B-B bonding network. Furthermore, strain-rate- and temperature-dependent tensile and compressive responses show marked crystallographic anisotropy, tension–compression asymmetry, and severe thermomechanical degradation. Atomic structural evolution demonstrates that tensile fracture is dominated by bond stretching and progressive damage accumulation, whereas compressive failure is attributed to densification- and shear-mediated structural instability. These findings provide an atomistic understanding of the thermomechanical behavior and fracture mechanisms of the prototypical single-phase (Hf0.2Zr0.2Ta0.2Ti0.2Nb0.2)B2 high-entropy diboride, offering valuable insights into the design of ultra-high temperature ceramics under extreme service environments. Full article
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19 pages, 4062 KB  
Article
A Study on an Improved Fatigue Life Prediction Method for Type IV Cylinders
by Jinjie Lu and Chuanxiang Zheng
J. Compos. Sci. 2026, 10(6), 329; https://doi.org/10.3390/jcs10060329 - 22 Jun 2026
Viewed by 502
Abstract
With the rapid development of the hydrogen economy, Type IV composite pressure vessels have emerged as the core components of on-board hydrogen storage systems. However, accurate fatigue life prediction remains a critical bottleneck limiting their design optimization and safe operation. Existing methods often [...] Read more.
With the rapid development of the hydrogen economy, Type IV composite pressure vessels have emerged as the core components of on-board hydrogen storage systems. However, accurate fatigue life prediction remains a critical bottleneck limiting their design optimization and safe operation. Existing methods often exhibit prediction errors exceeding ±50% due to the inherent scatter, anisotropy, and complex service environments of composites. This study proposes an improved simulation method for fatigue life prediction of Type IV cylinders. Systematic tension–tension fatigue tests were conducted on carbon fiber-reinforced polymer (CFRP) laminates at four ply angles (0°, ±15°, ±30°, ±45°) and PA6 liner at three temperatures (−30 °C, 25 °C, 82 °C) to establish comprehensive S-N curve databases. The results reveal that ply angle is the predominant factor governing CFRP fatigue performance, while temperature significantly influences PA6 behavior, and failure mode transitions from fiber fracture to matrix-dominated damage as ply angle increases. A fatigue analysis model was developed in nCode, incorporating the ply fatigue Algorithm to characterize the anisotropic fatigue behavior of CFRP overwraps. Full-scale validation on Type IV cylinders under cyclic pressure (2–87.5 MPa) confirmed the method’s effectiveness, achieving prediction errors of 11.5% and 35.3% for the two failed specimens, with failure locations well predicted. This study provides a rapid and reliable engineering calculation method and data support for the anti-fatigue design, safety assessment, and life management of Type IV cylinders. Full article
(This article belongs to the Special Issue Composite Thin-Walled Structures: Stability and Damage)
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26 pages, 12952 KB  
Article
Modeling and Seismic Response of Stress-Fracture Coupled Anisotropy Under Triaxial Stress
by Haiyu Li, Guangtan Huang, Xilin Qin, Zhennan Yu, Mingliao Wu and Lujia Ma
Processes 2026, 14(11), 1826; https://doi.org/10.3390/pr14111826 - 4 Jun 2026
Viewed by 358
Abstract
In shale reservoirs, where stress heterogeneity and fracture systems commonly coexist, elastic anisotropy is jointly controlled by in situ stress and fractures, resulting in pronounced azimuthal dependence in wide-azimuth AVO/AVAZ responses. This behavior directly affects fracture characterization and hydraulic fracturing design. However, existing [...] Read more.
In shale reservoirs, where stress heterogeneity and fracture systems commonly coexist, elastic anisotropy is jointly controlled by in situ stress and fractures, resulting in pronounced azimuthal dependence in wide-azimuth AVO/AVAZ responses. This behavior directly affects fracture characterization and hydraulic fracturing design. However, existing studies commonly attribute anisotropy to either fractures or uniaxial stress perturbations in isolation, and a systematic equivalent-medium formulation that unifies stress-driven stiffness evolution with fracture-weakness effects remains insufficient. To address this gap, we derive an acoustoelastic expression under the weak-stress perturbation assumption, combining background stiffness with third-order stress effects. By incorporating linear-slip fracture weakness, we construct a coupled stress–fracture equivalent stiffness matrix. Using Christoffel eigenanalysis and a welded-interface operator, we then compute anisotropic parameters and AVAZ responses under different stress paths. Numerical simulations show that the principal stress difference dominates both the splitting of reflection curves and azimuthal fluctuations, with an approximately linear sensitivity within the weak-stress regime. Unlike conventional descriptions of fracture-induced anisotropy, in which fracture parameters are commonly prescribed, the proposed framework constructs a physically traceable modeling chain from triaxial stress perturbations to stress-dependent fracture weakness, equivalent orthorhombic stiffness, Christoffel-equation-based wave propagation, and AVAZ responses. This provides a forward-modeling foundation for interpreting coupled stress–fracture anisotropy and for designing future inversion constraints under weak-perturbation conditions. Full article
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23 pages, 7336 KB  
Article
Biomechanical Behavior of Composite Bone–Osteosynthesis Constructs in Complex Proximal Humerus Fractures: A Synergistic Experimental and Finite Element Approach
by Andrei Scripcaru, Vasile Iulian Antoniac, Mădălina Maria Diac, Mihnea Theodor Sîrbu, Tatiana Iov, Veronica Scripcaru, Simona Irina Damian, Diana Bulgaru Iliescu, Norin Forna and Paul-Dan Sîrbu
Bioengineering 2026, 13(6), 625; https://doi.org/10.3390/bioengineering13060625 - 27 May 2026
Viewed by 853
Abstract
This study evaluates the mechanical behavior of bone-implant assemblies used in treating complex proximal humerus fractures, a clinical challenge due to the anisotropic nature of bone and variability in patient-specific conditions. The aim of this study was to compare the stability and stress [...] Read more.
This study evaluates the mechanical behavior of bone-implant assemblies used in treating complex proximal humerus fractures, a clinical challenge due to the anisotropic nature of bone and variability in patient-specific conditions. The aim of this study was to compare the stability and stress distribution of three fixation methods: polyaxial locking plates, monoaxial locking plates, and intramedullary nails. Using 4th-generation composite humerus models, a four-part fracture (Neer IV) was simulated. The assemblies underwent axial compression testing using a universal testing machine, complemented by finite element analysis (FEA) and stereomicroscopy. The results indicate that while both plate types exhibited similar mechanical behavior—with stiffness values around 113–115 N/mm and failure initiated by plastic deformation of the implant—the intramedullary nail configuration demonstrated higher stiffness values under the tested experimental conditions (1084 N/mm), approximately 9.5 times higher than that of the plates. However, the nail assembly failed through brittle fracture of the bone rather than implant deformation. We conclude that while the intramedullary nail configuration demonstrated higher stiffness under the tested experimental conditions, its performance is heavily dependent on bone quality. In contrast, locking plates may provide a more gradual load-transfer behavior by transferring a greater proportion of the mechanical load to the implant, potentially making them more suitable for osteoporotic bone conditions, where reducing excessive stress concentration within the bone tissue may be beneficial. Full article
(This article belongs to the Special Issue Orthopedic and Trauma Biomechanics)
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15 pages, 3075 KB  
Article
Deformation and Constitutive Behaviors of Ferrite Steel Under Tension Condition
by Hui Lin, Lin Lv, Xueli Ge and Tao Jin
Materials 2026, 19(9), 1889; https://doi.org/10.3390/ma19091889 - 3 May 2026
Cited by 1 | Viewed by 565
Abstract
This study systematically investigates the tensile anisotropic mechanical behavior of ferritic steel under different orientations through an integrated experimental, theoretical modeling, and simulation approach employing advanced characterization techniques including electron backscatter diffraction (EBSD), digital image correlation (DIC), scanning electron microscopy (SEM), and finite [...] Read more.
This study systematically investigates the tensile anisotropic mechanical behavior of ferritic steel under different orientations through an integrated experimental, theoretical modeling, and simulation approach employing advanced characterization techniques including electron backscatter diffraction (EBSD), digital image correlation (DIC), scanning electron microscopy (SEM), and finite element analysis. The results demonstrate pronounced orientation dependence in mechanical response, with initial yield strengths of 391, 391, and 405 MPa and fracture strains of 0.237, 0.220, and 0.212 observed for 0°, 45°, and 90° orientations, respectively, corresponding to orientation-induced variations of 3.6% in yield strength and 11.8% in fracture strain. These anisotropic characteristics are primarily attributed to the predominant α-fiber texture <110>||RD, which accounts for 59.8% of the texture components. Furthermore, crystallographic texture significantly influences fracture behavior, as evidenced by the distinct orientation-dependent macroscopic contraction characteristics and morphological features of fracture surfaces. Full article
(This article belongs to the Section Metals and Alloys)
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19 pages, 4487 KB  
Article
An Anisotropic Bilinear Cohesive Zone-Based Damage Evolution Model with Experimentally Calibrated Parameters for Mode I Cracking in Chinese Fir
by Juncheng Tu, Zhongquan Tao, Dong Zhao and Zhenqing Gao
Forests 2026, 17(3), 351; https://doi.org/10.3390/f17030351 - 11 Mar 2026
Viewed by 662
Abstract
This study investigates the crack damage evolution in Chinese fir using an anisotropic bilinear cohesive zone-based constitutive model. The crack initiation and propagation processes were numerically modeled and simulated, and the results were validated through double cantilever beam (DCB) fracture tests. By exploiting [...] Read more.
This study investigates the crack damage evolution in Chinese fir using an anisotropic bilinear cohesive zone-based constitutive model. The crack initiation and propagation processes were numerically modeled and simulated, and the results were validated through double cantilever beam (DCB) fracture tests. By exploiting the bijective relationship between the equivalent linear elastic fracture mechanics (LEFM) resistance curve (R-curve) and the cohesive softening law, the bilinear cohesive parameters were inversely identified from experimental data. The simulation results show good agreement with experimental observations in terms of crack path, propagation rate, and failure mode. The accuracy of the maximum load simulation results for mode I fracture of wood beams is 96.8%. These results further demonstrate the accuracy and applicability of the proposed cohesive zone model in describing crack propagation behavior in Chinese fir and provide a reliable theoretical and numerical framework for predicting fracture performance in timber structures. Full article
(This article belongs to the Section Wood Science and Forest Products)
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30 pages, 9483 KB  
Article
Anisotropic Mechanical Parameter Testing of Bedded Shale and Its Influence Mechanisms on Hydraulic Fracture Propagation
by Zhihao Zhao, Yuan Liu, Litao Shang, Jinliang Song, Man Li, Dawei Hu and Fujian Yang
Appl. Sci. 2026, 16(5), 2534; https://doi.org/10.3390/app16052534 - 6 Mar 2026
Viewed by 656
Abstract
The development and utilization of unconventional shale oil and gas have enhanced the resilience of global energy security. Hydraulic fracturing is the primary method for enhancing unconventional shale oil and gas extraction. Previous studies have predominantly employed homogenized geomechanical models to simulate fracture [...] Read more.
The development and utilization of unconventional shale oil and gas have enhanced the resilience of global energy security. Hydraulic fracturing is the primary method for enhancing unconventional shale oil and gas extraction. Previous studies have predominantly employed homogenized geomechanical models to simulate fracture propagation in rock masses. However, bedding planes and inhomogeneous mineral distributions introduce mechanical anisotropy in shale, rendering conventional homogenized models insufficient for accurately representing hydraulic fracturing in real reservoirs. For this, millimeter-scale indentation testing was employed to systematically quantify the depth-dependent distribution of mechanical parameters across varying bedding orientations, using fragmented shale samples obtained from the Qingshankou Formation of the Songliao Basin, northern China. Then, hydraulic fracturing simulations were performed using the mechanical properties derived from the indentation tests. The key findings include: (1) The elastic modulus of the Qingshankou Formation shale reservoir exhibits significant anisotropic properties in both the depth and bedding orientations. The elastic modulus measured parallel to bedding (10.23–65.08 GPa) is 28% higher than that measured perpendicular to bedding (9.60–47.24 GPa) due to shale bedding anisotropy. The mineralogical composition predominantly governs the depth-dependent anisotropy, with an elevated brittle mineral content increasing the elastic modulus and a higher clay content reducing it. (2) The simulation results reveal that the depth-dependent anisotropy of elastic modulus induces asymmetric hydraulic fracture propagation, with the fractures preferentially extending along the orientations exhibiting a higher elastic modulus. This behavior arises due to the enhanced brittleness and reduced deformation resistance of high-modulus rocks, facilitating fracture advancement. The study offers critical insights for hydraulic fracturing design and operational implementation in bedded shale reservoirs. Full article
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31 pages, 2746 KB  
Article
Metaheuristic-Driven Ensemble Learning for Robust Fracture Energy Prediction in FDM-Fabricated PLA Components
by Volkan Ates, Mehmet Eker, Ramazan Gungunes and Demet Zalaoglu
Polymers 2026, 18(4), 470; https://doi.org/10.3390/polym18040470 - 12 Feb 2026
Viewed by 798
Abstract
Additive manufacturing (AM) has reshaped production methodologies by enabling the fabrication of complex geometries for high-performance applications. As a leading AM technique, Fused Deposition Modeling (FDM) is widely used for its versatility. However, the structural reliability of FDM-printed parts is fundamentally dictated by [...] Read more.
Additive manufacturing (AM) has reshaped production methodologies by enabling the fabrication of complex geometries for high-performance applications. As a leading AM technique, Fused Deposition Modeling (FDM) is widely used for its versatility. However, the structural reliability of FDM-printed parts is fundamentally dictated by their mechanical performance, where impact toughness functions as a critical benchmark across demanding industrial environments. Polylactic acid (PLA) has distinguished itself as a premier biodegradable polymer, favored for its superior stiffness and processability. Nevertheless, the inherent brittleness and anisotropic behavior of FDM-printed PLA pose significant challenges, necessitating investigation of their fracture mechanics. This study firstly evaluates the impact toughness of FDM-processed PLA Izod specimens using impact tests, structured within a Taguchi design of experiments (DoE) methodology. An L27 orthogonal array was employed to investigate the influence of manufacturing parameters on impact behavior and fracture energy. Then, to achieve high-fidelity predictions from experimental data, the parametric effects were systematically investigated through an advanced machine learning framework. In the first stage, optimal prediction models were identified by evaluating five mathematical formulations hybridized with five nature-inspired optimization algorithms (GWO, SMA, GSA, FPA, and KH) across nine dataset combinations. In the second stage, these best-performing models were integrated into a metaheuristic ensemble using the GWO to perform a weighted aggregation. This hybrid ensemble methodology significantly enhanced predictive accuracy, achieving a Mean Absolute Percentage Error (MAPE) of 5.0847%, which represents a 37.3% relative improvement over the best individual base model. Full article
(This article belongs to the Special Issue Polymer Composites: Mechanical Characterization)
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22 pages, 6340 KB  
Article
Creep Instability and Acoustic Emission Responses of Bedded Coal Subjected to Compressive Loads and Acidic Water Saturation
by Zhenhua Zhao, Lin Han, Hongjie Sun, Hongtao Li, Rui Zhang, Xinyu Bai and Yu Wang
Appl. Sci. 2026, 16(2), 1005; https://doi.org/10.3390/app16021005 - 19 Jan 2026
Cited by 2 | Viewed by 403
Abstract
This study investigates the creep behavior and acoustic emission (AE) characteristics of bedded coal samples under acidic water environments. Uniaxial graded creep tests coupled with AE monitoring were conducted on samples with bedding angles of 0°, 30°, 60°, and 90°, respectively. The anisotropic [...] Read more.
This study investigates the creep behavior and acoustic emission (AE) characteristics of bedded coal samples under acidic water environments. Uniaxial graded creep tests coupled with AE monitoring were conducted on samples with bedding angles of 0°, 30°, 60°, and 90°, respectively. The anisotropic mechanical behavior and acoustic emission characteristics in terms of stress–strain, deformation, AE count, AE energy, and spectrum characteristics were revealed. The experimental results show that the strength of the coal samples gradually decreases as the saturation duration increases. At the same axial stress level, the axial deformation of the coal samples becomes larger with increasing saturation duration. The mechanical strength exhibits a distinct “U-shaped” relationship with the bedding angle, initially decreasing and then increasing. Correspondingly, axial deformation at a given stress level first increases and then decreases as the bedding angle increases. AE activity, particularly the AE ring count and energy, peaks at specimen failure, indicating significant fracture development. Spectral analysis revealed that under conditions of severe strength degradation (e.g., 0° bedding after 60-day saturation or 60° bedding after 30-day saturation), high-frequency, high-amplitude AE signals were absent. This suggests a shift in the dominant fracture mechanism from small-scale cracking to larger-scale fracture propagation in weakened samples. These findings offer valuable theoretical insights for the prevention and early warning of coal mine disasters. Full article
(This article belongs to the Topic Failure Characteristics of Deep Rocks, 3rd Edition)
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22 pages, 12152 KB  
Article
Printing-Path-Dominated Anisotropy in FDM-PEEK: Modulation by Build Orientation for Tensile and Shear Performance
by Kui Liu, Wei Chen, Feihu Shan, Hairui Wang and Kai Li
Polymers 2026, 18(1), 41; https://doi.org/10.3390/polym18010041 - 23 Dec 2025
Cited by 5 | Viewed by 1437
Abstract
Fused deposition modeling of polyether ether ketone offers distinct advantages for fabricating complex and lightweight structures. Although three principal build orientations theoretically exist for practical 3D engineering components, research on their effects remains limited, especially regarding the influence of the interaction between build [...] Read more.
Fused deposition modeling of polyether ether ketone offers distinct advantages for fabricating complex and lightweight structures. Although three principal build orientations theoretically exist for practical 3D engineering components, research on their effects remains limited, especially regarding the influence of the interaction between build orientation and printing path on mechanical performance. This study investigated the tensile and shear properties, as well as the failure mechanisms, of FDM-fabricated PEEK under the coupled effects of build orientation and printing path through mechanical testing, fracture morphology analysis, and statistical methods. The results indicate that the printing path exerts a dominant influence on anisotropic behavior, while the interaction between printing path and build orientation jointly governs the shear failure modes. Under identical printing paths, the elongation at break varied by up to twofold across different build orientations, reaching a maximum of 96%, whereas samples printed with W or T paths exhibited elongations at break below 5%. Although shear and tensile moduli remained largely consistent across build orientations, other mechanical properties demonstrated significant differences. Variations in cross-sectional dimensions induced by build orientation markedly affected tensile performance: the coupled effect of build orientation and printing path was found to render the path repetition frequency a critical factor in determining temperature uniformity within the printed region and the quality of interlayer interfaces, thereby constituting the core mechanism underlying anisotropic behavior. Furthermore, larger cross-sections re-duced tensile modulus but enhanced yield strength and elongation at break, highlight-ing the regulatory role of cross-sectional geometry on mechanical response. Based on these findings, a synergistic optimization strategy integrating printing path, build orientation, and tensile–shear performance is proposed to achieve tailored mechanical properties in FDM-fabricated PEEK components. This approach enables controlled enhancement of structural performance to meet diverse application requirements. Full article
(This article belongs to the Section Polymer Processing and Engineering)
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22 pages, 4729 KB  
Article
Unidirectional Ligament Orientation Enables Enhanced Out-of-Plane Mechanical Properties in Anisotropic Nanoporous Gold
by Yuhang Zhang, Xiuming Liu, Yiqun Hu, Suhang Ding and Feixiang Tang
Nanomaterials 2025, 15(21), 1675; https://doi.org/10.3390/nano15211675 - 4 Nov 2025
Cited by 1 | Viewed by 1005
Abstract
Nanoporous gold (NPG), characterized by a bicontinuous network of nanoscale solid ligaments and pore channels, exhibits exceptional physical and chemical properties. However, the limited strength and stiffness of traditional isotropic NPG (INPG) have constrained its engineering applications. To effectively enhance the mechanical properties [...] Read more.
Nanoporous gold (NPG), characterized by a bicontinuous network of nanoscale solid ligaments and pore channels, exhibits exceptional physical and chemical properties. However, the limited strength and stiffness of traditional isotropic NPG (INPG) have constrained its engineering applications. To effectively enhance the mechanical properties of NPG, this work proposes an innovative anisotropic NPG (ANPG) architecture featuring unidirectional ligament orientation. By controlling spinodal decomposition parameters, ANPG models with preferentially aligned ligaments and INPG with random ligament orientation are constructed, spanning relative densities from 0.30 to 0.50. The ligament length and diameter of ANPG along the out-of-plane direction are twice those along other directions. Molecular dynamics simulations of tensile tests show that ANPG exhibits superior out-of-plane Young’s modulus and yield strength but reduced fracture strain compared to INPG. Crucially, ANPG maintains toughness comparable to INPG at relative densities below 0.4, offering an optimal strength-toughness balance for practical applications. Scaling law analysis demonstrates INPG follows classical bending-dominated Gibson-Ashby behavior, while ANPG exhibits a hybrid deformation mechanism with significant ligament stretching contribution. Atomic-scale analysis reveals that both structures develop dislocation-mediated plasticity initially, but ANPG transitions to localized ligament necking and fractures more rapidly, explaining its reduced ductility. Strain localization quantification, measured by atomic shear strain standard deviation, confirms the intensifier deformation concentration in ANPG at large plastic strain. These findings suggest anisotropic design as a powerful strategy for developing high-performance NPG for actuators, sensors, and catalytic systems where simultaneous mechanical robustness and functional performance are required. Full article
(This article belongs to the Special Issue Advances in Nanoindentation and Nanomechanics)
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26 pages, 5224 KB  
Article
Modeling Anisotropic Permeability of Coal and Shale with Gas Rarefaction Effects, Matrix–Fracture Interaction, and Adsorption Hysteresis
by Lilong Wang, Zongyuan Li, Jie Zeng, Biwu Chen, Jiafeng Li, Huimin Jia, Wenhou Wang, Jinwen Zhang, Yiqun Wang and Zhihong Zhao
Processes 2025, 13(10), 3304; https://doi.org/10.3390/pr13103304 - 15 Oct 2025
Cited by 3 | Viewed by 940
Abstract
Permeability of fissured sorbing rocks, such as coal and shale, controls gas transport and is relevant to a variety of scientific problems and industrial processes. Multiple gas transport and rock deformation mechanisms affect permeability evolution, including gas rarefaction effects, gas-sorption-induced anisotropic matrix–fracture interaction, [...] Read more.
Permeability of fissured sorbing rocks, such as coal and shale, controls gas transport and is relevant to a variety of scientific problems and industrial processes. Multiple gas transport and rock deformation mechanisms affect permeability evolution, including gas rarefaction effects, gas-sorption-induced anisotropic matrix–fracture interaction, and anisotropic deformation induced by effective stress variation. In this paper, a generic anisotropic permeability model is proposed to address the impacts of the above mechanisms and effects. Specifically, the influence of matrix–fracture interactions on permeability evolution is depicted through the nonuniform matrix swelling caused by the gas diffusion process from fracture walls into the matrix. The following characteristics are also incorporated in this model: (1) anisotropic mechanical and swelling properties, (2) arbitrary box-shaped matrix blocks due to the anisotropic rock structure, (3) adsorbability variation of different matrix blocks because of complex rock compositions, (4) adsorption hysteresis, and (5) dynamic tortuosity. The directional permeability models are derived based on the anisotropic poroelasticity theory and anisotropic swelling equations considering adsorption hysteresis. We use a gas-invaded-volume ratio to describe the nonuniform swelling of matrix blocks. Additionally, swelling of blocks with different adsorption and mechanical properties are characterized by a volume-weighted function. Finally, the anisotropic tortuosity is defined as a power law function of effective porosity. The model is verified against experimental data. Results show that four-stage permeability evolution with time can be observed. Permeability evolution in different directions follows its own ways and depends on anisotropic swelling, mechanical properties, and structures, even when the boundary conditions are identical. Adsorption hysteresis controls the local shrinkage region. Tortuosity variation significantly affects permeability but has the smallest influence on the local swelling region. The existence of multiple matrix types complicates the permeability evolution behavior. Full article
(This article belongs to the Special Issue Advances in Enhancing Unconventional Oil/Gas Recovery, 2nd Edition)
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