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Keywords = bending elasticity

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14 pages, 4677 KB  
Article
Barkhausen Noise in 100Cr6 Bearing Steel as a Function of Microstructure and Stress State
by Martin Pitoňák, Anna Mičietová, Ján Moravec, Miroslav Neslušan, Štefan Toth and Branislav Mičieta
Materials 2026, 19(14), 3135; https://doi.org/10.3390/ma19143135 - 21 Jul 2026
Abstract
This study is focused on the unwrapping contribution of microstructure (mainly expressed in terms of dislocation density) and stress state in the quenched bearing steel 100Cr6. Microstructure as well as residual stress state alterations are developed only as a function of variable infeed [...] Read more.
This study is focused on the unwrapping contribution of microstructure (mainly expressed in terms of dislocation density) and stress state in the quenched bearing steel 100Cr6. Microstructure as well as residual stress state alterations are developed only as a function of variable infeed rates in the flat plunge grinding (other grinding conditions are kept constant). The study is also dealing with the synergistic contribution of residual stress state and the superimposing elastic external stress developed during bending. It was found that the Barkhausen noise after grinding is mostly a function of the thermal softening, whereas the role of residual stress state is only minor. The growing Barkhausen noise emission at the lower infeed rates is connected with the compressive stress, and the tensile stresses are developed at the higher removal rates only. The study also demonstrates good sensitivity of Barkhausen noise when this emission is descending along the compressive external stresses and the ascending evolution along the tensile stresses when the magnetic field is altering along the direction of exerted stress. On the other hand, this evolution is reversed when the altering magnetic field is altered along the transversal direction. Full article
(This article belongs to the Section Advanced Materials Characterization)
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25 pages, 11460 KB  
Article
Pilot Study on the Mechanical Stress and Vibrational Response of Gymnastics Springboard Support System
by Paula Tudor, Gheorghe Voicu, Daniel-Mirel Dumitrescu, Gabriel-Alexandru Constantin, Andrei Craifaleanu and Elena-Madalina Stefan
Appl. Sci. 2026, 16(14), 7284; https://doi.org/10.3390/app16147284 - 21 Jul 2026
Abstract
The analysis of displacements and stresses in the bottom plates (base) of a gymnastic springboard is essential for the safety of the athlete and for obtaining an optimal energy transfer. In a modern springboard, the system works as an elastic assembly composed of [...] Read more.
The analysis of displacements and stresses in the bottom plates (base) of a gymnastic springboard is essential for the safety of the athlete and for obtaining an optimal energy transfer. In a modern springboard, the system works as an elastic assembly composed of layers of laminated plywood and steel springs. The bottom plates act as a rigid or semi-rigid support for the springs. They are subjected to both localized compression at the contact points where the spring bases are fixed, the material being strongly compressed, and are bending, undergoing elastic deformation, or shear and fatigue. Since a springboard is used for thousands of loading–unloading cycles, micro-cracks can appear in the fibrous structure of the wood (usually birch or maple). The paper presents data on the vibration behavior of the support plates arranged under the main plate of the springboard, when gymnasts weighing 40 and 58.5 kg jumped from 60 and 35 cm, respectively, or from running from 3 m. The data were taken with accelerometers mounted on these plates, the accelerations being then transformed into displacements. The basic conclusion is that for testing the resistance of the plates to breakage, the most relevant test point is at the end of the springboard, while for checking the resistance over time of the fastenings with the other component elements, the critical point is at the middle of the springboard. Full article
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18 pages, 12941 KB  
Article
Physics-Guided CNN Detection of Crack-Associated Events from Embedded Fiber Bragg Grating Sensors
by Yagiz Uğurveren, Alexander Gros, Enes Nohutcuoğlu, Tarik Tekoğlu, Kivilcim Yüksel, Karima Chah and Christophe Caucheteur
Sensors 2026, 26(14), 4556; https://doi.org/10.3390/s26144556 - 17 Jul 2026
Viewed by 367
Abstract
Crack detection in composite structures remains a central challenge in structural health monitoring, particularly when sensing must rely on a small number of embedded multiplexed fiber Bragg gratings (FBGs). Here, we present a physics-guided convolutional neural network (CNN) framework for crack-associated event detection [...] Read more.
Crack detection in composite structures remains a central challenge in structural health monitoring, particularly when sensing must rely on a small number of embedded multiplexed fiber Bragg gratings (FBGs). Here, we present a physics-guided convolutional neural network (CNN) framework for crack-associated event detection from multiplexed FBG interrogator signals acquired during the three-point bending of glass-fiber-reinforced polymer (GFRP) beams. The dataset was constructed from raw interrogator recordings and synchronized force–displacement metadata while preserving the cracked and non-cracked loading stages present in the experiments. Each candidate response was encoded by 13 synchronized optical, loading, and mechanics-guided descriptors, including Euler–Bernoulli expected strain and residual terms, where the residual denotes the difference between the measured response and the elastic response predicted by beam theory. A compact one-dimensional CNN operating on 30-response sequences was evaluated on 64 experimental runs under strict leave-one-run-out validation. At the selected operating point, the model reached window-level precision of 0.900, recall of 0.910, F1 score of 0.905, and balanced accuracy of 0.942, while the corresponding run-level decision reached a precision of 0.833, a recall of 1.000, an F1 score of 0.909, and a balanced accuracy of 0.969. Bootstrap resampling over runs yielded 95% confidence intervals of 0.787–0.978 for window-level F1 and 0.769–1.000 for run-level F1. To probe generalization beyond the initial fabrication batch, the final frozen pipeline was also tested once on seven later-batch runs from two newly manufactured specimens, where it reached a window-level precision of 0.908, a recall of 1.000, an F1 score of 0.952, a balanced accuracy of 0.969, an ROC-AUC of 0.979, a PR-AUC of 0.955, and perfect run-level classification. These results show that a compact sequence CNN, enriched with mechanics-guided strain interpretation, can extract robust crack-event signatures from multiplexed FBG measurements while preserving a simple and reproducible modeling pipeline. Full article
(This article belongs to the Section Optical Sensors)
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21 pages, 6349 KB  
Article
Mechanical Behavior of Conventional and Subtractively Manufactured Dental Resin Composites After Water Degradation
by Georgiana Osiceanu, Roxana Diana Vasiliu, Flavia Roxana Bejan, Radu Negru, Nicușor Alin Sîrbu, Raluca Faur and Liliana Porojan
Bioengineering 2026, 13(7), 829; https://doi.org/10.3390/bioengineering13070829 - 17 Jul 2026
Viewed by 226
Abstract
The ongoing development of subtractive options for indirect restorations places clinicians in a position that requires adaptation, understanding and choosing of the most suitable option for the long-term survival of the restoration. Mechanical parameters represent important indicators of long-term success. Consequently, this research [...] Read more.
The ongoing development of subtractive options for indirect restorations places clinicians in a position that requires adaptation, understanding and choosing of the most suitable option for the long-term survival of the restoration. Mechanical parameters represent important indicators of long-term success. Consequently, this research aimed to assess the impact of water sorption on the mechanical properties of two direct resin composites, Gradia Direct Anterior A2 and Filtek Z550 A2 and three CAD/CAM subtractively manufactured dental resin composites, Vita Enamic, Brilliant and Cerasmart. A total of one hundred specimens (50 control, 50 underwent this protocol: dehydration, immersion in distilled water for 30 days and then re-desiccation), standardized to the dimensions of 14 mm × 4 mm × 1.2 mm were subjected to three-point bending test (based on ISO 4049:2019 and ISO 6872:2015), in order to find out the flexural strength and the elastic modulus of the material at the breaking point. Then, the fractured sample surfaces were fractographical analyzed. Using the two-parameter Weibull approach, the Weibull modulus (m) and the characteristic strength (σ0) were evaluated. In this investigation, the elastic modulus varied from 5.8 (Gradia Control) to 20.31 (Vita Degraded) GPa, with the upper limit close to the values of natural dentin (17.7–29.8 GPa). The values of flexural strength ranged from 174.47 (Brilliant Control) to 79.2 (Gradia Control), subtractively processed materials demonstrating higher flexural strength and elastic modulus values than the direct resin composites, which is related to their high inorganic filler content. All material groups, except for Gradia Control, had a flexural strength more than the 80 MPa minimum value needed to sustain masticatory force. The dehydration and hydration cycles did not have a statistically significant influence on the mechanical properties of the material. The fractographic analysis revealed fracture patterns and features associated with the microstructure, with the PICN category material being particularly notable. Weibull analysis revealed that the direct resin composite materials exhibited higher reliability, lower data scatter and CAD-CAM materials showed greater characteristic strength, with a notably high performance of the nano-hybrid direct resin composite. Full article
(This article belongs to the Section Biomedical Engineering and Biomaterials)
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26 pages, 16089 KB  
Article
Research on Parameter Formulation Strategy of Asymmetric Four-Point Bending Progressive Process for LSAW Pipes
by Zhiyuan Zhang, Junchao An, Junfang Shen, Yi Liu and Yan Gao
Metals 2026, 16(7), 803; https://doi.org/10.3390/met16070803 - 17 Jul 2026
Viewed by 106
Abstract
The current progressive forming process for large-scale longitudinally submerged arc-welded (LSAW) pipes is continuously losing competitiveness in terms of manufacturing quality and production efficiency. Based on the asymmetric four-point bending (AFB) mechanical model and classical elastic–plastic bending theory, in this paper, we investigate [...] Read more.
The current progressive forming process for large-scale longitudinally submerged arc-welded (LSAW) pipes is continuously losing competitiveness in terms of manufacturing quality and production efficiency. Based on the asymmetric four-point bending (AFB) mechanical model and classical elastic–plastic bending theory, in this paper, we investigate sheet bending behavior during the four-point bending stage. Analytical expressions are derived for the main influencing factors during the forming and springback process. Finite element simulation and experimental research into the mechanical model are conducted to analyze the effects of various process parameters on the forming results. On this basis, an AFB progressive forming process parameter formulation strategy is established and programmed. Experiments and simulations were conducted using the process parameters formulated by this strategy. The results showed that pipes could complete the progressive forming process in fewer passes, thereby improving production efficiency. The ovality of most experimental pipes was less than 1.5% and consistently below 0.7% in simulations—significantly lower than the engineering requirement of 2%. These results demonstrate the feasibility and reliability of the strategy, highlight the significant improvement in pipe quality achieved through the AFB process, and lay a solid foundation for the development and intelligentization of future progressive forming processes for LSAW pipes. Full article
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20 pages, 7673 KB  
Article
Experimental and Numerical Investigation into Active–Passive Behavior and Shear Resistance of Anchored Rock Joints
by Yinfeng Tang, Tongxu Wang, Yuxiang Ma and Yaling Wang
Geotechnics 2026, 6(3), 65; https://doi.org/10.3390/geotechnics6030065 - 17 Jul 2026
Viewed by 108
Abstract
To elucidate the active–passive reinforcement mechanisms of rock bolts and the evolution of shear strength in anchored rock joints, this study integrates theoretical analysis, laboratory direct shear tests, and numerical simulations to investigate the deformation and failure characteristics of fully grouted, end-anchored, and [...] Read more.
To elucidate the active–passive reinforcement mechanisms of rock bolts and the evolution of shear strength in anchored rock joints, this study integrates theoretical analysis, laboratory direct shear tests, and numerical simulations to investigate the deformation and failure characteristics of fully grouted, end-anchored, and prestressed bolted specimens. The results show that bolt reinforcement can be classified into prestress-dominated active action and dislocation-induced passive action. The shear strength curve of anchored rock joints exhibits four distinct stages with increasing shear displacement: initial slip, elasticity, yielding, and softening. Fully grouted bolts fail primarily by tensile–shear fracture, enabling a rapid increase in shear strength at small displacements. In contrast, end-anchored bolts undergo S-shaped bending and form symmetrical plastic hinges on both sides of the joint, sustaining resistance under large displacements albeit with lower peak strength. While the laboratory tests experimentally clarified the distinct failure modes and passive shear resistance mechanisms of fully grouted and end-anchored bolts, the quantitative partitioning between active and passive contributions was derived from a numerically simulated prestressed bolt model. The simulations indicate that for prestressed bolts, the active contribution accounts for approximately 69.6% of the total shear strength enhancement, while the passive contribution is about 30.4%. These findings yield actionable design criteria: end-anchored or yielding bolts are recommended for high-geostress environments or scenarios involving large potential deformations to exploit the large-deformation bearing capacity of passive action; conversely, prestressed bolts should be prioritized where strict control of early-stage deformation is required to maximize active support efficiency. Full article
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25 pages, 5025 KB  
Article
Generalized Strength Prediction Model for Timber Beams Strengthened Using NSM FRP Bars and FRP Sheets
by Husain Abbas, Nadeem A. Siddiqui, Mohammed S. Shaik, Tarek Almusallam and Yousef Al-Salloum
Polymers 2026, 18(14), 1705; https://doi.org/10.3390/polym18141705 - 10 Jul 2026
Viewed by 347
Abstract
Existing analytical models for Fiber-Reinforced Polymer (FRP)-strengthened timber beams are generally limited to individual strengthening techniques and cannot readily accommodate hybrid reinforcement systems. This study develops a generalized analytical model to predict the flexural capacity of timber beams strengthened with near-surface-mounted (NSM) FRP [...] Read more.
Existing analytical models for Fiber-Reinforced Polymer (FRP)-strengthened timber beams are generally limited to individual strengthening techniques and cannot readily accommodate hybrid reinforcement systems. This study develops a generalized analytical model to predict the flexural capacity of timber beams strengthened with near-surface-mounted (NSM) FRP bars, externally bonded FRP sheets, or their hybrid combination within a unified theoretical framework. The model is formulated based on internal force equilibrium and strain compatibility, incorporating a constitutive model for timber with linear elastic tensile behavior and a bilinear compressive stress–strain relationship including post-peak softening. The generalized formulation can be readily adapted to different strengthening configurations through appropriate simplifications. The proposed model was validated against experimental results obtained from four-point bending tests on small-scale timber beams strengthened with NSM GFRP bars and externally bonded GFRP sheets. The analytical predictions showed good agreement with the experimental results, with differences generally ranging from 2% to 23%, demonstrating satisfactory predictive accuracy. The experimental results further showed that the hybrid strengthening system increased the flexural capacity of the timber beams by up to 84% compared with the unstrengthened control beams, while also improving stiffness, ductility, and overall structural response. Failure was primarily due to timber tensile rupture and longitudinal splitting, whereas the GFRP reinforcement remained effective without rupture, indicating efficient utilization of the strengthening system. The proposed generalized analytical model provides a practical and reliable design tool for predicting the flexural strength of timber beams strengthened with various FRP reinforcement configurations, thereby supporting the structural rehabilitation and sustainable retrofitting of timber structures. Full article
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31 pages, 9920 KB  
Article
Structure–Property–Transport Relationship in Hyaluronic Acid/ZnO Nanocomposite Dissolving Microneedles for Transdermal Ciprofloxacin Delivery
by Kolawole S. Dada, Roman O. Olekhnovich, Falia F. Zaripova, Vladimir D. Kalganov and Oleg N. Petrovich
Macromol 2026, 6(3), 46; https://doi.org/10.3390/macromol6030046 - 10 Jul 2026
Viewed by 256
Abstract
Polymeric microneedles are introduced as a promising platform for minimally invasive drug delivery and molecular transport control. In the present study, hollow dissolving nanocomposite microneedles based on a mixture of high- and low-molecular-weight hyaluronic acid (HA) in a 40:60 ratio, including zinc oxide [...] Read more.
Polymeric microneedles are introduced as a promising platform for minimally invasive drug delivery and molecular transport control. In the present study, hollow dissolving nanocomposite microneedles based on a mixture of high- and low-molecular-weight hyaluronic acid (HA) in a 40:60 ratio, including zinc oxide nanoparticles (ZnO NPs), have been created and evaluated as hydrated polymer transport matrices. Surface modification of ZnO nanoparticles using citric acid was proposed to improve dispersion by reducing agglomeration of nanoparticles in the polymer matrix. ZnO nanoparticles in concentrations ranging from 1 to 10% (w/w) were used to study the effects of the loading level of nanoparticles on the structure, mechanical response, and controlled diffusion behavior of hydrated polymer matrices. The created nanocomposites exhibited clear hollow structures with tip radius of 18–23 μm, height of 1500 μm, and aspect ratio of 5.7. Nanoscale surface organization and particle dispersion in the polymer matrix were studied by scanning electron microscope (SEM) and atomic force microscope (AFM). Low nanoparticle concentrations were favorable for maintaining high matrix homogeneity, while high concentrations resulted in increased surface roughness and nanoparticle agglomeration. Mechanical compression testing confirmed that hydrated HA/ZnO microneedles were characterized by elastic bending behavior until fracture. Diffusion experiments performed in Franz diffusion cells showed that nanoparticle concentration significantly impacted the cumulative transport and flux of molecules through the hydrated microneedle matrix. Formulations with 5% and 7% ZnO nanoparticles were characterized by a prolonged diffusion behavior attributed to ZnO-induced tortuous transport channels in the polymer matrix. In contrast, formulations with 10% ZnO nanoparticles exhibited accelerated heterogeneous transport due to ZnO-induced changes in structure and morphology. The experimental diffusion data correlated well with the Higuchi kinetic model, and anomalous transport was detected using the Korsmeyer–Peppas model, which indicated a synergistic effect of diffusion and polymer relaxation on molecular transport. As compared to coating and tip-loaded microneedle designs, the obtained HA/ZnO nanocomposite microneedles offered a simple approach for embedding Ciprofloxacin in the hydrated polymer matrix. This was achieved due to the direct creation of microneedles containing dissolved particles. Full article
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39 pages, 25210 KB  
Article
Theoretical and Numerical Study of the Buckling of Axially Compressed Bimodular Thin Cylindrical Shells
by Jun-Song Ran, Xiao-Ting He and Jun-Yi Sun
Materials 2026, 19(14), 2964; https://doi.org/10.3390/ma19142964 - 9 Jul 2026
Viewed by 203
Abstract
Bimodular materials refer to materials that exhibit distinct elastic properties under tensile and compressive loading conditions. This study aims to analyze the buckling problem of bimodular thin cylindrical shells under axial compressive loading. In existing studies on the buckling behavior of thin shells, [...] Read more.
Bimodular materials refer to materials that exhibit distinct elastic properties under tensile and compressive loading conditions. This study aims to analyze the buckling problem of bimodular thin cylindrical shells under axial compressive loading. In existing studies on the buckling behavior of thin shells, the bimodular effect of materials is rarely considered due to the complexity of the analysis. Therefore, based on the elasticity theory of different moduli, this paper presents a theoretical and numerical study on the buckling problem of thin cylindrical shells with bimodular effect under axial compression. Based on the deformation characteristics of thin cylindrical shells under axial compression before and after buckling, a simplified mechanical model suitable for the buckling analysis of bimodular axially compressed thin cylindrical shells is established. The simplified mechanical model proposed in this paper decouples the membrane effect and bending effect during shell buckling by introducing the concept of the physical neutral layer. It divides the shell cross-section into tensile and compressive regions according to the bending effect component, thereby fully accounting for the influence of the bimodular effect of materials on the lateral bending stiffness of the shell. Subsequently, through this simplified mechanical model, the analytical expression for the linear critical load of bimodular thin cylindrical shells under axial compression is obtained. Eigen Value buckling analysis of bimodular axially compressed thin cylindrical shells based on ABAQUS is carried out to validate the correctness of the analytical solution. The results indicate that the shell height L, the radius-to-thickness ratio R/t, and the tension-to-compression modulus ratio E+/E have significant influences on their linear critical load. Moreover, the larger the tensile to compressive modulus ratio, the more sensitive the linear critical load of the shell is to the bimodular effect of materials. Specifically, when the E+/E ratio of the shell equals 1/2, the corresponding linear critical load is approximately 10% higher than that predicted by the classical solution. Meanwhile, when the E+/E ratio equals 2, the linear critical load of the shell is approximately 21% lower than that predicted by the classical solution. The novelty of this study lies in that, for the first time, based on the simplified mechanical model of tension-compression subarea, the influence of bimodular effect of materials is considered in the buckling analysis of thin cylindrical shells under axial compression, which provides a new analytical idea for the refined analysis and optimal design on it. Full article
(This article belongs to the Section Construction and Building Materials)
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19 pages, 1536 KB  
Article
Study on Rheological Properties of SBS/Crumb Rubber Modified Direct Coal Liquefaction Residue Asphalt Prepared Through an Extraction–Blending Process
by Yongxiang Li, Shizhong Mi, Chaoyang Guo, Jian Gao, Qi Qi, Yongjie Jia and Jing Li
Materials 2026, 19(14), 2940; https://doi.org/10.3390/ma19142940 - 8 Jul 2026
Viewed by 224
Abstract
To address the insufficient low-temperature performance of asphalt modified with direct coal liquefaction residue (DCLR), this study proposed a composite modification strategy based on an extraction–blending process using styrene–butadiene–styrene (SBS) and crumb rubber (CR). The high- and low-temperature rheological properties, phase morphology, and [...] Read more.
To address the insufficient low-temperature performance of asphalt modified with direct coal liquefaction residue (DCLR), this study proposed a composite modification strategy based on an extraction–blending process using styrene–butadiene–styrene (SBS) and crumb rubber (CR). The high- and low-temperature rheological properties, phase morphology, and functional-group characteristics of DCLR-blended asphalt with different formulations were systematically evaluated using a dynamic shear rheometer (DSR), a bending beam rheometer (BBR), fluorescence microscopy (FM), and Fourier transform infrared spectroscopy (FTIR). The results demonstrate that the combined addition of SBS and crumb rubber significantly enhances the high-temperature stability and elastic response of the asphalt. Specifically, formulation 5# (8 wt.% SBS and 10 wt.% CR) maintained a rutting factor of 1.007 kPa at 82 °C, indicating superior high-temperature rutting resistance. Meanwhile, this formulation satisfied the Superpave low-temperature requirements at −18 °C, achieving a balanced improvement in both high- and low-temperature performance. Microstructural analysis suggests that an appropriate SBS/CR ratio contributes to the formation of a relatively continuous and uniformly distributed polymer-rich phase, whereas excessive modifier contents may lead to rubber agglomeration and phase-structure imbalance. FTIR results showed that the characteristic absorption peaks of the modified binders were generally consistent with those of the base asphalt, and no obvious new absorption bands were observed. This indicates that the extraction–blending process mainly involved physical blending, swelling, and phase interaction rather than the formation of new covalent functional groups. This study provides a technical reference for the high-value utilization of DCLR and the development of high-performance modified asphalt. Full article
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46 pages, 12180 KB  
Article
Micropolar Prismatic Body in the First Approximation: Field Reconstruction, Cutoff Resonances, and a Spectroscopic Damage Indicator
by Armine Ulukhanyan
Appl. Mech. 2026, 7(3), 57; https://doi.org/10.3390/applmech7030057 - 8 Jul 2026
Viewed by 181
Abstract
The first approximation (N=1) of a three-dimensional micropolar elastic prismatic body in moments of displacement and rotation, obtained via Legendre polynomial expansion, is applied to two related problems: field reconstruction and damage identification. In the first problem, two- and [...] Read more.
The first approximation (N=1) of a three-dimensional micropolar elastic prismatic body in moments of displacement and rotation, obtained via Legendre polynomial expansion, is applied to two related problems: field reconstruction and damage identification. In the first problem, two- and three-dimensional field distributions are reconstructed for a simply supported square prismatic body under three loading configurations, with first-order moment loading as the primary case. Two distinct resonances are identified within the N=1 framework. At the material cutoff ωc=4α/J, micro-rotation amplitudes are amplified while translational amplitudes are suppressed (displacement locking). At the geometric cutoff ωgeoh1, the bending mode is resonantly excited while micro-rotation remains near its quasi-static level. In the second problem, a scalar damage model αeff=α(1D) is introduced. The material cutoff follows ωc(D)=ωoc1D, confirmed numerically for all four decoupled subsystems and different prismatic body thicknesses. Geometric branches remain insensitive to damage, producing a spectral separation that may serve as a damage indicator. A critical thickness h* is identified where ωgeo=ωoc, leading to role reversal between material and geometric branches. Numerical results are presented for the polyurethane foam of Lakes. Full article
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27 pages, 43695 KB  
Article
Research on Rational Structural Parameters and Flexural Performance of Hybrid Fiber Concrete Joints in Prefabricated Steel Grid–Hybrid Fiber Concrete Composite Bridge Deck
by Jianyong Ma, Yongli Zhang, Haoyun Yuan, Zuolong Luo, Junhao Duan and Pengfei Ren
Buildings 2026, 16(13), 2696; https://doi.org/10.3390/buildings16132696 - 7 Jul 2026
Viewed by 256
Abstract
Prefabricated steel–concrete composite bridge decks are widely used in the construction of long-span bridges due to their excellent mechanical performance and rapid construction speed. However, the joints in these decks are prone to tensile failure under negative bending moments, which limits the overall [...] Read more.
Prefabricated steel–concrete composite bridge decks are widely used in the construction of long-span bridges due to their excellent mechanical performance and rapid construction speed. However, the joints in these decks are prone to tensile failure under negative bending moments, which limits the overall mechanical behavior of the structure. To improve the flexural–tensile performance of joints in prefabricated steel–concrete composite bridge decks under negative bending moments, a novel prefabricated steel grid–hybrid fiber concrete (PSG-HFC) composite bridge deck with closed-loop steel bar joints is proposed. Basic unit specimens of the composite bridge deck with closed-loop steel bar joints were designed and fabricated. Both physical and numerical experiments, including finite element modeling and model refinement, were conducted to clarify the mechanical response and failure mode of closed-loop steel bar joints under negative bending moments and to identify their rational structural parameters. Theoretical formula for calculating the flexural capacity of the closed-loop steel bar joints based on the strut-and-tie model theory was derived and verified. The results indicate that the failure mode of the novel PSG-HFC composite bridge deck under negative bending moments is typical plastic failure, with the ultimate failure mode being flexural–tensile failure at the joint section. The loading process includes elastic, elastoplastic, and plastic stages. From the perspectives of improving flexural capacity and fully utilizing high-strength materials, the rational structural parameters for the closed-loop steel bar joints are as follows: lap length of closed-loop steel bars of 230~250 mm, spacing of closed-loop steel bars of 130~150 mm, and bending radius of closed-loop steel bars of 70~90 mm. The maximum deviation between the theoretical formula results and the experimental and finite element numerical simulation results is 8.21%, indicating that the proposed formula is suitable for calculating and analyzing the flexural capacity of the joints in this novel composite bridge deck. This study reveals that the proposed closed-loop steel bar joint enables a ductile flexural–tensile failure mode in PSG-HFC composite deck under negative bending moments, and provides a validated theoretical formula for advancing the understanding of joint design in fiber-reinforced concrete structures. Full article
(This article belongs to the Special Issue Advanced Research on Cementitious Composites for Construction)
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25 pages, 9304 KB  
Article
Long-Term Bending Behavior of Laminated Glass Plate with Temperature-Dependent Viscoelastic Interlayer
by Xia Zhu, Kangyu Ni, Changkuo Xu, Aiguo Zhao and Peng Wu
Materials 2026, 19(13), 2925; https://doi.org/10.3390/ma19132925 - 7 Jul 2026
Viewed by 173
Abstract
This study presents an analytical model for the long-term bending behavior of simply supported laminated glass (LG) plates with temperature-dependent viscoelastic interlayers. The glass layers are described based on three-dimensional elasticity theory, and the governing stress and displacement equations are formulated using the [...] Read more.
This study presents an analytical model for the long-term bending behavior of simply supported laminated glass (LG) plates with temperature-dependent viscoelastic interlayers. The glass layers are described based on three-dimensional elasticity theory, and the governing stress and displacement equations are formulated using the state-space method. The polymer interlayer is characterized by the generalized Maxwell model and the Williams–Landel–Ferry equation, while its time-dependent response is described through the Boltzmann convolution principle. By combining double Fourier series expansions with the Laplace-transform technique, analytical solutions for the stresses and displacements of multilayer LG plates are derived. The comparison shows that Kirchhoff–Love plate theory gives results close to the present solution for relatively thin LG plates, whereas the discrepancy becomes increasingly pronounced as the plate thickness increases. The finite element results agree well with those obtained from the proposed model; however, for the representative benchmark case, the present solution is approximately 1.13 × 103 times faster than the FE simulation, and its memory usage is only about 10.88% of that required by the FE model. Parametric studies further reveal the effects of temperature, interlayer thickness, interlayer material, number of glass layers, and aspect ratio on the stress redistribution and deflection development of LG plates. Full article
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48 pages, 28313 KB  
Article
Development of an Engineering Methodology for Designing Overpasses of Different Scales Based on Establishing Dimensionless Similarity Criteria
by Aliya Kukesheva, Alexandr Ganyukov, Adil Kadyrov, Kirill Sinelnikov, Aidar Zhumabekov, Anel Akhmetova and Oxana Privalova
Appl. Sci. 2026, 16(13), 6784; https://doi.org/10.3390/app16136784 - 6 Jul 2026
Viewed by 198
Abstract
This article discusses the relevant problem of ensuring transport connectivity under the conditions of temporal restrictions of the road network, which arise during repair, communal and emergency operations. It is established that the existing organizational and intellectual methods of traffic management do not [...] Read more.
This article discusses the relevant problem of ensuring transport connectivity under the conditions of temporal restrictions of the road network, which arise during repair, communal and emergency operations. It is established that the existing organizational and intellectual methods of traffic management do not eliminate physical decrease in road capacity, while construction of stationary structures with different levels is limited by high costs and long terms of implementation. The above substantiates the need for the development of mobile overpasses as adaptive engineering solutions ensuring continuity of the traffic flows. The purpose of the research is to develop a scientifically substantiated theoretical and experimental methodology for designing a mobile overpass as an integrated system “structure-moving load”, taking into account its dynamic behavior. The paper proposes an integrated approach based on the use of physical similarity theory and dimensionless analysis. A differential equation of dynamic bending of a beam on an elastic foundation is formulated taking into account inertia, damping, base reaction and the effect of a moving mass, and then its nondimensionalization is performed to obtain a similarity criteria system. The scientific novelty of the research consists in developing a system of dimensionless criteria to describe the relationship between the structural, dynamic and operational parameters of a mobile overpass, as well as in the formation of a criterion base for large-scale modeling and transfer of the results to full-scale structures. The proposed methodology describes the mobile overpass as an integrated transport-engineering system accounting for the coupled interaction between the deformable structure, moving traffic load, elastic foundation, and damping effects. Experimental verification was performed on a specially designed stand in the scale 1:4. The results obtained showed the quasi-static nature of the structure performance with moderate damping and rigid base. It is established that the distribution of engineering stresses along the span length has a regular character and retains its shape when the load level changes, which confirms fulfillment of similarity conditions. Regression analysis revealed a close to linear dependence of stresses on the load mass with a high degree of confidence (R20.995). The practical significance of the research consists in creating an engineering method for express design of mobile overpasses, which allows for assessing their stress–strain state, stability and serviceability without expensive full-scale tests. The proposed approach can be used in designing temporary transportation structures under the conditions of urban area, and in operation in areas of road operations and emergency situations. Full article
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Article
Adaptive Phase-Field Fracture Modeling Using C1 PHT-Splines: A Consistent High-Order Isogeometric Formulation
by Abdel Ahad El Mahmi, Ahmed El Khalfi, Abdeslam El Akkad, Maria Luminița Scutaru and Sorin Vlase
Axioms 2026, 15(7), 503; https://doi.org/10.3390/axioms15070503 - 3 Jul 2026
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Abstract
This work develops a locally adaptive isogeometric phase-field framework for two-dimensional quasi-static brittle fracture using cubic C1 polynomial splines over hierarchical T-meshes (PHT-splines). The aim is not to introduce a new crack-density functional or a new degradation law, but to provide a [...] Read more.
This work develops a locally adaptive isogeometric phase-field framework for two-dimensional quasi-static brittle fracture using cubic C1 polynomial splines over hierarchical T-meshes (PHT-splines). The aim is not to introduce a new crack-density functional or a new degradation law, but to provide a consistent variational-to-discrete setting in which second- and fourth-order phase-field regularizations can be treated within the same locally refined spline framework. Starting from the energy functional, the formulation is carried through admissible weak forms to the corresponding discrete residual equations. The second-order formulation is posed in an H1(Ω) setting, whereas the fourth-order model is treated directly through a Laplacian-based H2(Ω)-compatible approximation without auxiliary phase-field variables. The formulation combines history-field irreversibility, the tension–compression split of the elastic energy, and an adopted cubic degradation law with s=104, whose nonlinear tangent contribution is handled by a Taylor-stabilized staggered Newton scheme. Numerical tests on a single-edge notched tensile benchmark and a notched perforated beam under asymmetric bending show that local refinement captures the fracture zone while maintaining critical-load deviations of about 0.8% and 0.3%, respectively, relative to the reference critical loads used for the two benchmark problems. The contribution therefore lies in the coherent coupling of higher-order regularity, admissible weak forms, local PHT-spline adaptivity, and stabilized nonlinear degradation treatment within a spline-based phase-field fracture implementation. Full article
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