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Keywords = measurements of deformations

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19 pages, 790 KB  
Review
Residual Stress in Epoxy-Based Insulators: Formation, Detection, and Reliability
by Jin Li, Siyuan Chen, Hucheng Liang and Boxue Du
Molecules 2026, 31(14), 2410; https://doi.org/10.3390/molecules31142410 (registering DOI) - 8 Jul 2026
Abstract
Gas-insulated switchgears (GISs) and gas-insulated transmission lines (GILs) are essential for large-capacity power transmission in demanding environments, such as high drops, large spans, and heavy pollution. As the core components providing both electrical insulation and mechanical support, ultra-high voltage (UHV) epoxy-based insulators often [...] Read more.
Gas-insulated switchgears (GISs) and gas-insulated transmission lines (GILs) are essential for large-capacity power transmission in demanding environments, such as high drops, large spans, and heavy pollution. As the core components providing both electrical insulation and mechanical support, ultra-high voltage (UHV) epoxy-based insulators often suffer from high internal residual stress. This issue, compounded by a lack of reliable detection methods, frequently results in equipment being commissioned with hidden defects. To address this, this review first examines the formation mechanisms of curing deformation and residual stress in oversized insulators based on cure kinetics and thermo-chemical coupling models. Subsequently, it provides a comprehensive summary of current residual stress measurement techniques, comparing the applicability and limitations of embedded sensors, direct mechanical measurements, and indirect non-destructive testing (NDT) methods. Finally, by coupling residual stress with filler sedimentation, the stress distribution patterns and mechanical reliability of epoxy-based insulators across different life-cycle stages are analyzed. These insights offer valuable theoretical references for the structural design, process optimization, and performance evaluation of oversized epoxy-based insulators, ultimately contributing to the intrinsic safety of UHV power equipment. Full article
28 pages, 559 KB  
Article
Geometry of Events in Deformed Cellular Spacetimes
by Shlomo Barak and George Salman
Mathematics 2026, 14(14), 2465; https://doi.org/10.3390/math14142465 (registering DOI) - 8 Jul 2026
Abstract
We develop the geometry of events in a deformable cellular spacetime, extending our earlier cellular-spaces framework from cellular complexes to cellular events complexes. The framework operates within the conformal class of Minkowski space; in four dimensions, this is the vanishing-Weyl-tensor sector, which excludes [...] Read more.
We develop the geometry of events in a deformable cellular spacetime, extending our earlier cellular-spaces framework from cellular complexes to cellular events complexes. The framework operates within the conformal class of Minkowski space; in four dimensions, this is the vanishing-Weyl-tensor sector, which excludes Schwarzschild, Kerr, and gravitational-wave spacetimes. The framework treats integer counts of cell crossings as the primitive geometric data: spatial separation between events is the shortest count of face-adjacent cells; temporal separation is the cell-crossing count of a reference light pulse. Newton’s universal clock is replaced by an operational one: the temporal count distance is the ratio of cell length to the speed of light through a cell, and because both quantities are invariants of the co-deformation, the temporal count is itself an invariant: temporal separation is operationally measured via light-pulse counts rather than posited as an external coordinate. Under the co-deformation principle, a single positive scalar field ρ (cell density) controls both the rod length and the clock period. We prove six results, all expressed in terms of counts on the cellular events complex, with a smooth conformally flat metric g˜=e2φη (φ=13lnρ) appearing only as the comparison/calibration object for convergence statements. First, the scalar curvature of the smooth comparison metric is the closed-form differential operator R˜=2ρ/ρ1/3(8/3)(ρ)2/ρ4/3. Second, the volume of a small Alexandrov interval admits an explicit asymptotic expansion in the interval height T, with leading correction Q(m,u)T2 involving an anisotropic invariant at the midpoint m. Third, Q is irreducible to scalar and Ricci-directional invariants alone; the explicit decomposition Q=145R˜+15R˜uu+12J exhibits a third independent invariant J(m,u)=(u·)2φ(m) as new structural content of the Lorentzian diagnostic. Fourth, the discrete-to-continuum convergence of counts on the cellular events complex yields a counts-only curvature estimator with rate O(a) at the joint scaling Ta. Fifth, the smooth comparison metric itself is reconstructible from counts on the discrete complex at rate O(a): the conformally flat Lorentzian geometry is uniquely determined, up to background Minkowski calibration, by the cellular events complex. Sixth, a finite collection of Alexandrov-interval volume measurements at a fixed midpoint suffices to recover the full local curvature data {R˜(m),R˜μν(m),J(m,u)} at rate O(a) (curvature spectroscopy); and the temporal light-tick count λ is essential in a precise sense—there exist conformally flat Lorentzian geometries indistinguishable on every spatial slice by the earlier spatial-only diagnostic but distinguished at the origin by the events-space directional invariant. The framework’s scope is the conformal class of Minkowski: flat FLRW in conformal time, leading-order weak-field gravity, and 2D gravity. This paper is a mathematical contribution to discrete-to-continuum geometry on cellular events complexes; it is not a physical theory of gravity. Full article
(This article belongs to the Section E4: Mathematical Physics)
17 pages, 5361 KB  
Article
A Wind-Aware 3D Spatiotemporal Forecasting Model for Ultra-Short-Term Cumulus Cloud Prediction
by Yuxuan Chen, Shujun Wu and Jinjin Gao
Appl. Sci. 2026, 16(14), 6856; https://doi.org/10.3390/app16146856 (registering DOI) - 8 Jul 2026
Abstract
Forecasting the deformation and movement of cumulus clouds provides an important basis for ultra-short-term solar irradiance nowcasting in photovoltaic (PV) power generation. Existing methods mainly use two-dimensional (2D) ground-based sky images for forecasting, which have limited ability to represent the three-dimensional (3D) spatial [...] Read more.
Forecasting the deformation and movement of cumulus clouds provides an important basis for ultra-short-term solar irradiance nowcasting in photovoltaic (PV) power generation. Existing methods mainly use two-dimensional (2D) ground-based sky images for forecasting, which have limited ability to represent the three-dimensional (3D) spatial structure of cumulus clouds and the influence of wind on cloud motion. In this study, we propose a wind-aware ultra-short-term spatiotemporal forecasting model for 3D cumulus clouds, termed three-dimensional Cloud Long Short-Term Memory with Wind Gate Recurrent Unit (3dCLSTM + WindGRU). The model uses 3dCLSTM to learn the spatial structure and temporal evolution of 3D voxel cumulus cloud sequences, and embeds a WindGRU unit between 3dCLSTM layers to introduce wind speed and wind direction information for wind-driven transient motion modeling. Experiments were conducted on 1-min and 10-min 3D cumulus cloud datasets reconstructed from ground-based sky image datasets collected at sites in California and Colorado, USA. All voxel sequences were resampled to 64 × 64 × 64, with five-step prediction for the 1-min dataset and three-step prediction for the 10-min dataset. The results show that 3dCLSTM achieved a structural similarity index measure (SSIM) of 0.7913 on the 1-min dataset, while 3dCLSTM + WindGRU achieved the best performance on the 10-min dataset, with an SSIM of 0.3512 and a peak signal-to-noise ratio (PSNR) of 18.3625. Compared with 3dCLSTM, introducing WindGRU improved the SSIM by 4.8% on the 10-min dataset, with a more evident improvement under relatively high wind-speed conditions. These results indicate that wind-aware volumetric spatiotemporal modeling can support ultra-short-term 3D cumulus cloud forecasting and provide a useful technical basis for solar irradiance nowcasting. Full article
24 pages, 10086 KB  
Article
Mechanistic Identification of Modal Softening and Self-Centering in a Full-Scale Mass-Timber Rocking-Wall Building Under Sequential Shake-Table Excitation
by Lin Ma, Pengfei Liu, Long Yan and Tenglong Rong
Buildings 2026, 16(14), 2706; https://doi.org/10.3390/buildings16142706 (registering DOI) - 8 Jul 2026
Abstract
Mass-timber rocking-wall systems are designed to limit residual deformation by concentrating lateral response in controlled uplift, recentering, and replaceable energy-dissipation mechanisms. Full-scale shake-table records provide a rare opportunity to evaluate this design concept using reproducible physical descriptors rather than isolated peak-response quantities. The [...] Read more.
Mass-timber rocking-wall systems are designed to limit residual deformation by concentrating lateral response in controlled uplift, recentering, and replaceable energy-dissipation mechanisms. Full-scale shake-table records provide a rare opportunity to evaluate this design concept using reproducible physical descriptors rather than isolated peak-response quantities. The public NHERI TallWood two-story mass-timber rocking-wall experiment is reanalyzed using fourteen sequential earthquake records, measured table accelerations, floor and roof accelerations, and instrumented deformation channels. A physics-informed workflow extracts input-intensity, transfer-function, coherence, modal-frequency, equivalent-damping, residual-deformation, self-centering, and deformation-weighted inertial-demand descriptors. An experiment-updated equivalent elastic Abaqus model converts selected identified states into three-dimensional displacement and stress-transfer fields. The identified dominant frequency decreases from approximately 2.11 Hz in the initial low-level event to approximately 0.70 Hz after the final maximum-level excitation, corresponding to a frequency-squared stiffness-loss index near 0.89. Despite this pronounced modal softening, measured residual deformation remains small in absolute terms, and the self-centering index remains moderate to high over most of the sequence. The results indicate that the tested system evolves mainly through changes in contact, uplift, diaphragm compatibility, and interface stiffness rather than through a conventional cumulative plastic-damage mechanism. The descriptor set and calibrated finite-element visualization provide a transferable basis for comparing future mass-timber shake-table datasets and for linking open experimental repositories, modal identification, and finite-element state visualization in performance-based seismic assessment of low-damage timber buildings. Full article
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12 pages, 638 KB  
Article
Proprioception and Balance in Young Adults with Pes Planus
by Fatma Betul Yardimci, Zeynep Yilmaz and Bahar Anaforoglu
J. Am. Podiatr. Med. Assoc. 2026, 116(4), 50; https://doi.org/10.3390/japma116040050 (registering DOI) - 8 Jul 2026
Abstract
Background: Pes planus is a common foot deformity that may lead to both structural and functional consequences. This alteration in foot morphology has been associated with changes in neurosensory mechanisms such as proprioception and balance. This study aims to evaluate proprioception and [...] Read more.
Background: Pes planus is a common foot deformity that may lead to both structural and functional consequences. This alteration in foot morphology has been associated with changes in neurosensory mechanisms such as proprioception and balance. This study aims to evaluate proprioception and balance parameters in young adults with pes planus by comparing them with healthy individuals. Methods: This case–control study, which had a quantitative and cross-sectional design, included a total of 90 volunteer university students aged 18–30. The presence of pes planus was assessed using the Navicular Drop Test. Proprioception assessment was performed using a digital goniometer to measure active and passive joint position sense, while balance assessment was performed using the Y Balance Test. Results: The groups were similar in terms of demographic and anthropometric characteristics (p > 0.05). In the proprioception assessment, a significant difference was observed in active joint position sense scores in individuals with pes planus (p = 0.032). In contrast, no significant difference was found between the two groups in terms of passive joint position sense (p = 0.769). According to the Y Balance Test results, no difference was observed in the anterior and posteromedial directions (p = 0.690 and p = 0.806). At the same time, the balance performance of individuals with pes planus was significantly lower in the posterolateral direction (p = 0.045). Conclusions: Young individuals with flexible pes planus showed differences in active joint position sense and balance performance in the posterolateral direction. This situation shows that pes planus may be associated with not only structural but also neurosensory functions. The findings highlight the importance of planning protective interventions early. In the future, there is a need for longitudinal studies conducted with larger and more heterogeneous samples, including rigid type pes planus. Full article
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11 pages, 1441 KB  
Article
Exercise-Induced ECG Abnormalities in Pediatric Pectus Excavatum: Evidence of Right Ventricular Compression Beyond the Haller Index
by Karine Guerrier, Aram Bejnood, Sharvari Shyam, Rebecca Ann Hyde, Benjamin Hendrickson, Trey Eubanks, Tim Jancelewicz and Ranjit Philip
Med. Sci. 2026, 14(3), 379; https://doi.org/10.3390/medsci14030379 (registering DOI) - 8 Jul 2026
Abstract
Background: Pectus excavatum (PEX) is the most common congenital chest wall deformity and may result in cardiac compression and arrhythmias. The relationship between structural severity and exercise-induced electrocardiographic (ECG) abnormalities in pediatric patients remains unclear. Methods: We performed a retrospective study of patients [...] Read more.
Background: Pectus excavatum (PEX) is the most common congenital chest wall deformity and may result in cardiac compression and arrhythmias. The relationship between structural severity and exercise-induced electrocardiographic (ECG) abnormalities in pediatric patients remains unclear. Methods: We performed a retrospective study of patients aged 10–19 years that underwent standardized preoperative evaluation for PEX between 2015 and 2021, including ECG, transthoracic echocardiography (TTE), computed tomography (CT), and cardiopulmonary exercise testing (CPET). PEX severity was assessed using the Haller index (HI), while right ventricular (RV) compression was evaluated on CT. Tricuspid valve annular size (TVAS) on TTE was used as a surrogate marker of RV compression. Exercise-induced ECG abnormalities, including premature ventricular complexes (PVCs), were analyzed and correlated with HI, RV compression, and TVAS. Results: Among 124 patients (85% male; median age 15 years), 33% exhibited exercise-induced ECG abnormalities, most commonly PVCs (24% overall). PVC occurrence was not associated with Haller index severity (p = 0.35) but was significantly associated with RV compression on CT (92.6% vs. 62.1%, OR 7.64, p = 0.02). Patients with ECG abnormalities had significantly smaller TVAS compared to those without (1.98 ± 0.31 cm vs. 2.09 ± 0.33 cm, p = 0.04). Although PVCs were more frequent in patients with TVAS z-score ≤ −2.0, this did not reach statistical significance. Conclusions: Exercise-induced ventricular ectopy in pediatric PEX is associated with right ventricular compression rather than structural severity as defined by HI. Echocardiographic measures such as TVAS may serve as noninvasive markers of clinically significant compression. These findings highlight the importance of cardiac–thoracic relationships in predicting arrhythmic risk and suggest a potential for reversibility with surgical correction. Full article
(This article belongs to the Section Cardiovascular Disease)
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26 pages, 13178 KB  
Article
Construction of a Dynamic Analysis and Monitoring–Early-Warning Model for Debris Flow Evolution Based on COMSOL Simulation
by Jianwei Cheng, Baocun Yang, Na He, Rui Xiang and Wenqi Lv
Water 2026, 18(14), 1656; https://doi.org/10.3390/w18141656 - 8 Jul 2026
Abstract
A frequent and sudden two-phase (solid–liquid) geological hazard in mountainous areas, the evolution of debris flows involves the coupling of multiple physical fields, making monitoring and early warning particularly challenging. To accurately reveal the dynamic patterns of debris flow evolution and improve early-warning [...] Read more.
A frequent and sudden two-phase (solid–liquid) geological hazard in mountainous areas, the evolution of debris flows involves the coupling of multiple physical fields, making monitoring and early warning particularly challenging. To accurately reveal the dynamic patterns of debris flow evolution and improve early-warning accuracy, this study focused on the Ni Chang Valley area in Shimian County, Ya’an City, Sichuan Province. Based on the COMSOL Multiphysics coupling simulation platform, a multiphysics bidirectionally strongly coupled numerical model was proposed and constructed, integrating the SPH (smoothed particle hydrodynamics) meshless particle method, FLO-2D shallow-water dynamics, and the MassFlow full-process simulation approach. Using COMSOL as a unified framework, this model employs MassFlow’s deep-integration, continuous medium method to simulate rainfall triggering and material source activation, FLO-2D’s shallow-water equations to describe macroscopic flow-deposition processes, and SPH’s mesh-free particle method to accurately capture large deformations and free-surface flow. The model fully reproduces the entire dynamic chain of debris flow processes, from rainfall triggering and soil mobilization to fluid transport and channel deposition. The reliability and accuracy of the model were verified by comparing it with field measurements from the 20 September 2022 historical debris flow event at Ni Chang Valley. Quantitative analysis indicates that when the viscosity coefficient increases from 0.1 Pa·s to 100 Pa·s, the flow velocity decreases by approximately 47% and the flow depth increases by approximately 62%. When the yield stress increases from 1 Pa to 100 Pa, the deposition area shrinks from 269,900 m2 to approximately 109,000 m2, a reduction of about 60%. Combining the results of the dynamic analysis, daily maximum temperature, daily precipitation, moisture content, mud-water level, and ground surface displacement were selected as core monitoring indicators. The analytic hierarchy process (AHP) was used to determine the weights of each indicator, and a data- and physics-driven weighted summation model for debris flow monitoring and early warning was constructed to achieve a five-level debris flow monitoring and early-warning system. Historical disaster cases demonstrate that this early-warning model can provide advance predictions of debris flow disasters up to 2 h and 40 min in advance. The warning lead time is sufficient, the grading logic is clear, and the model is capable of accurately capturing precursor information on disasters. Full article
(This article belongs to the Section Soil and Water)
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25 pages, 8719 KB  
Article
A Symmetry-Based Perspective Correction Method for High-Speed Deformation Analysis of Circular Blast-Loaded Plates
by Edison Shehu, Georgios Kechagiadakis, Bachir Belkassem, Andrea Manes, Frederik Coghe and David Lecompte
Materials 2026, 19(13), 2928; https://doi.org/10.3390/ma19132928 (registering DOI) - 7 Jul 2026
Abstract
The objective of this study is to recover the transient out-of-plane displacement field of clamped circular plates subjected to blast loading using a single high-speed camera, as a low-cost alternative to stereo Digital Image Correlation (DIC) for the specific class of axisymmetrical structural [...] Read more.
The objective of this study is to recover the transient out-of-plane displacement field of clamped circular plates subjected to blast loading using a single high-speed camera, as a low-cost alternative to stereo Digital Image Correlation (DIC) for the specific class of axisymmetrical structural responses of circular plates. The dynamic response of thin metal plates to blast loading is a fundamental problem in protective structural design, traditionally investigated through DIC. Although it provides full-field displacement measurements with high spatial resolution, it requires stereo camera arrangements, controlled illumination, speckle pattern preparation, and elaborate calibration procedures that significantly increase experimental cost and complexity. This study introduces a monocular optical method applicable to axisymmetrically defined material testing applications, such as the response of circularly supported isotropic plates under a uniform impulsive load, to recover the transient out-of-plane displacement field without using DIC. Clamped circular aluminum plates are subjected to blast loading generated by PG-3 charges of variable mass detonated at the closed end of a shock tube, with the exposed face matching the tube cross-section so as to enforce axisymmetric pressure load. A diametral reference line marked on the rear face of each specimen was recorded by a single high-speed camera, and a perspective correction derived from the axisymmetric deformed geometry was then applied to reconstruct the time-resolved displacement profile along the diameter. The permanent post-test deformed shape of each plate was subsequently digitized through 3D scanning and used as ground truth to validate the optical reconstruction. The reconstructed profiles closely matched the scans: for the conventional responses the root-mean-square error was 1.251 mm with a normalized mean residual of 6.57% (Case A) and 1.793 mm (9.20%, Case B), while for the anomalous counterintuitive response it was 1.043 mm (14.93%, Case C). Symmetry can thus be exploited as an active measurement principle to obtain quantitative blast-response data with substantially reduced experimental burden and without specialized stereo-optical instrumentation. Full article
27 pages, 8192 KB  
Article
Numerical Assessment of Safe Rock Pillar Thickness for Tunneling in High-Pressure CO2 Strata: A Case Study from a Deep Tunnel in Western China
by Chen Xue, Tong Lu, Hai Zhang, Guodong Wang, Fei Ye and Wenxi Fu
Appl. Sci. 2026, 16(13), 6817; https://doi.org/10.3390/app16136817 - 7 Jul 2026
Abstract
The expansion of deep-buried tunnels into complex geological settings has heightened the risk of encountering high-pressure gas strata. This study addresses a critical knowledge gap regarding safe rock-pillar thickness when tunneling through high-pressure CO2-bearing formations, motivated by a 2.3 MPa CO [...] Read more.
The expansion of deep-buried tunnels into complex geological settings has heightened the risk of encountering high-pressure gas strata. This study addresses a critical knowledge gap regarding safe rock-pillar thickness when tunneling through high-pressure CO2-bearing formations, motivated by a 2.3 MPa CO2 blowout event encountered during the geological investigation of a deep railway tunnel in western China. Numerical simulations were conducted using Phase2/RS2 (2D plane-strain models for the tunnel floor) and FLAC3D (3D models for the tunnel face) to evaluate plastic zone evolution and displacement responses under prescribed equivalent static CO2 pressure conditions and rock-mass degradation scenarios. The simulations represent a mechanical assessment under a prescribed pressure condition rather than a fully coupled gas-flow–mechanical analysis. Under the equivalent static CO2 pressure assumption, the calculated plastic zone depth increased from 10.2 m in the no-pressure case to 17.4 m under the 2.3 MPa pressure condition, while the maximum floor displacement increased from 0.4 cm to 11.0 cm. These results represent a conservative mechanical response under the adopted pore-pressure efficiency assumption and should not be interpreted as a direct simulation of gas compressibility, capillary effects, pressure diffusion, or gas–water two-phase behavior. Under the adopted parametric degradation scenarios, rock-mass strength reduction further increases the calculated plastic zone depth and displacement. In the strong degradation case, the plastic zone depth reaches 32.6 m and the maximum displacement reaches 19.0 cm. These values should be interpreted as sensitivity-analysis results for the assumed degraded rock-mass conditions, rather than as general predictions for all fractured or weathered rock masses. For face stability, the critical coalescence distance between excavation-disturbed and high-pressure-affected zones was identified as 15 m for intact rock, advancing to 20 m and 30 m under 10% and 20% strength reductions, respectively. Based on these findings, preliminary conservative reference values are proposed for risk identification when tunneling toward high-pressure CO2-bearing fractured zones. The calculated floor plastic zone depth of 17.4–32.6 m and the face coalescence distance of 15–30 m should be interpreted as mechanical warning indicators under the adopted equivalent static pressure assumption. These values have not yet been validated by construction-stage monitoring data and should therefore be updated using gas-pressure measurements, deformation monitoring, support response, drainage performance, and field back-analysis during tunnel construction. Full article
(This article belongs to the Section Civil Engineering)
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22 pages, 4669 KB  
Article
One-Dimensional Consolidation Characteristics and Mechanisms of Soft Soil Under Surcharge Preloading
by Pan Zhao, Junhao Tian, Yapeng Zhang, Zhe Wang, Jianhui Zhao, Wangjing Yao and Mingyuan Wang
Appl. Sci. 2026, 16(13), 6815; https://doi.org/10.3390/app16136815 - 7 Jul 2026
Abstract
This study investigates staged surcharge preloading at a coastal test section by integrating field monitoring (pore-water pressure, settlement/settlement rate, and layer-by-layer deformation) with laboratory consolidation tests and field vane shear measurements. Responses at the surcharge center and slope-toe margin are compared to quantify [...] Read more.
This study investigates staged surcharge preloading at a coastal test section by integrating field monitoring (pore-water pressure, settlement/settlement rate, and layer-by-layer deformation) with laboratory consolidation tests and field vane shear measurements. Responses at the surcharge center and slope-toe margin are compared to quantify spatial non-uniformity and pore-pressure–deformation coupling. Pronounced heterogeneity is observed (this field response represents three-dimensional deformation behavior that cannot be reproduced by 1D consolidation tests), with an empirical transition depth of ~24 m for this Wenzhou coastal soft soil site: above this depth, strains concentrate near the margin, whereas below it, compression at the center becomes dominant. The pore-pressure–settlement relationship is stage-dependent: during loading, pore pressure fluctuates markedly and settlement lags; during maintained consolidation, pore pressure dissipates, effective stress develops, and settlement is governed mainly by consolidation compression. After surcharging, water content decreases, and soil sensitivity reduces from 4.0 to 3.0 and stabilizes, indicating post-disturbance structural re-stabilization. These findings inform surcharge scheme design, monitoring layouts, and subsequent model calibration. Full article
(This article belongs to the Section Civil Engineering)
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55 pages, 9012 KB  
Article
Characteristics of Boundary and Focal Stress Loading of a Plastic Deformation Zone Under Conditions of Controlled Asymmetric Interaction
by Valeriy Chigirinsky, Abdrakhman Naizabekov, Sergey Lezhnev, Sergey Kuzmin, Evgeniy Panin, Olena Naumenko and Sergey Melentyev
Symmetry 2026, 18(7), 1150; https://doi.org/10.3390/sym18071150 - 6 Jul 2026
Abstract
Based on experimental studies, a model of the control effect on the plastic deformation process under boundary asymmetric loading conditions has been developed. The regulating factor of plastic deformation unevenness δ, which determines the stress–strain state of the entire deformation zone and [...] Read more.
Based on experimental studies, a model of the control effect on the plastic deformation process under boundary asymmetric loading conditions has been developed. The regulating factor of plastic deformation unevenness δ, which determines the stress–strain state of the entire deformation zone and the boundary conditions, is presented. The boundary conditions, determined by additional compressive and tensile stresses along the height, generate shear stresses and specific loading regimes at the edges and within the deformation zone itself. The confirmed reduction in interaction, which coincides with the effect of plastic deformation occurring under conditions of force unevenness, is one of the criteria for the controlling effect. A distinctive feature of this approach is the recognition and proof of the existence of a controlling additional effect under conditions of complex force and deformation loading. Theoretical and experimental studies have revealed such effects under various loading conditions. Based on a closed-form problem in plasticity theory and the method of argument functions of a complex variable, a mathematical model of the control process exerted by the metal’s plastic flow zone has been developed. A key feature of the solution to this theoretical problem was the consideration of the interaction between zones under different force loads, represented by a finite-difference scheme in the mathematical model. The decisive influence of deformation unevenness from the working rolls on the force and deformation parameters of the process was demonstrated, with the deformation unevenness factor δ serving as a quantitative measure of this influence. The result obtained through theoretical justification was confirmed by numerical simulation and a comparison of calculated data with experimental data, ensuring the reliability of the result. Full article
(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Solid Mechanics)
27 pages, 3386 KB  
Article
Symmetry-Restoring Profile Modification of Polyoxymethylene Gears Based on Cumulative Deformation Energy
by Jiaxin Shi, Peigang Jiao, Honghao Xu, Yiheng Zhang and Changhui Zheng
Symmetry 2026, 18(7), 1149; https://doi.org/10.3390/sym18071149 - 6 Jul 2026
Abstract
During the meshing process of plastic gears, inhomogeneous thermal deformation is prone to occur due to the coupling effect of frictional heat generation and material thermal sensitivity, leading to contact misalignment on tooth surfaces. Traditional modification designs mostly rely on empirical approaches or [...] Read more.
During the meshing process of plastic gears, inhomogeneous thermal deformation is prone to occur due to the coupling effect of frictional heat generation and material thermal sensitivity, leading to contact misalignment on tooth surfaces. Traditional modification designs mostly rely on empirical approaches or merely compensate for static elastic deformation, which cannot adequately address thermo-mechanical interactions. In this paper, an active modification method based on the identification of thermal deformation regions is proposed. First, a thermo-structural coupling finite element model of polyoxymethylene (POM) gears is established, taking into account the temperature-dependent modulus. The steady-state temperature field is obtained through ANSYS 2024 R1 simulations, and its accuracy is verified against experimental measurements. Subsequently, the thermal deformation distribution is acquired by coupling the structural field. The cumulative deformation energy function is introduced, and the modification length is objectively determined as L = 0.35 mm by adopting the extreme point of the second derivative of the normalized cumulative energy. Three modification strategies, namely linear modification, Walker curve modification, and Mingchuan curve modification, are designed. Simulation results demonstrate that all three strategies effectively reduce the thermal deformation, steady-state temperature, and contact pressure of the gears, among which the Walker curve modification exhibits the best performance. After modification, the maximum thermal deformation is reduced by 44.14%, the maximum contact pressure by 16.2%, and the maximum steady-state temperature by 9.5%. The proposed method transforms thermal deformation from a “passive response” into an “active design input”, verifies the feasibility of thermally driven modification, and thereby establishes a quantifiable thermally adaptive modification approach for plastic gears. Full article
(This article belongs to the Section Engineering and Materials)
17 pages, 2824 KB  
Article
Projection-Based Strain–Excitation Mapping Model for Beam Recovery of Arbitrarily Deformed Phased Array Antennas
by Bo Tang, Jinzhu Zhou, Le Kang, Xinrui Fang and Qingdong Zhang
Electronics 2026, 15(13), 2958; https://doi.org/10.3390/electronics15132958 - 6 Jul 2026
Abstract
Surface deformation of a phased array antenna (PAA) induced by external loads can degrade its radiation performance. To restore the beam of a deformed PAA, this paper proposes a new strain–excitation mapping model (SEMM) capable of rapidly calculating excitation adjustments based on measured [...] Read more.
Surface deformation of a phased array antenna (PAA) induced by external loads can degrade its radiation performance. To restore the beam of a deformed PAA, this paper proposes a new strain–excitation mapping model (SEMM) capable of rapidly calculating excitation adjustments based on measured structural strains. In the derivation of the SEMM, an analytical formula establishing the relationship between antenna excitations and the element positions and orientations for a PAA with an arbitrary surface shape is derived using the projection principle. Subsequently, the positions and orientations of the elements are expressed as functions of a limited number of strain measurements from the deformed antenna structure. An X-band PAA experimental system, equipped with a deformable mechanism and strain measurement capabilities, was developed. Two typical deformations were taken as examples to validate the proposed SEMM. Experimental results demonstrate that the SEMM can effectively recover the distorted pattern across the observation region. Compared with existing models, the proposed model achieves better sidelobe recovery. The rapid computation capability and analytical formulation of the SEMM make it highly suitable for developing an adaptive PAA that can autonomously preserve radiation beam quality under in-service deformations. Full article
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24 pages, 1288 KB  
Article
Spinopelvic Realignment and Clinical Outcomes After Surgical Management of Adult Degenerative Lumbar Deformity: A Multicenter Retrospective Cohort Study
by Sanubar Nazarli, Teoman Bircan, Doğan Güçlühan Güçlü and Altay Sencer
J. Clin. Med. 2026, 15(13), 5280; https://doi.org/10.3390/jcm15135280 - 6 Jul 2026
Abstract
Background/Objectives: Adult degenerative lumbar deformity is a heterogeneous condition in which outcome depends on radiographic correction, patient-related risk factors, and surgical burden. This study evaluated spinopelvic realignment, clinical outcomes, complications, and predictors of unfavorable postoperative course after surgical treatment of adult degenerative lumbar [...] Read more.
Background/Objectives: Adult degenerative lumbar deformity is a heterogeneous condition in which outcome depends on radiographic correction, patient-related risk factors, and surgical burden. This study evaluated spinopelvic realignment, clinical outcomes, complications, and predictors of unfavorable postoperative course after surgical treatment of adult degenerative lumbar deformity. Methods: This three-center retrospective cohort study included adult patients who underwent posterior decompression and instrumented fusion, with or without interbody fusion, for adult degenerative lumbar deformity between January 2021 and December 2024. Of 136 screened patients, 113 completed final follow-up and were included in the analysis. The mean follow-up duration was 31.0 ± 12.9 months. Radiographic parameters were assessed preoperatively, immediately postoperatively, and at final follow-up. Patient-reported outcome measures were analyzed using available paired data. Unfavorable postoperative course was defined as persistent or worsened pain with functional limitation, symptomatic mechanical complication, deep infection requiring surgical treatment, or revision/reoperation. Results: Surgery produced significant immediate improvement in coronal and sagittal alignment. Cobb angle improved from 29.8 ± 13.1° to 13.7 ± 6.7°, lumbar lordosis increased from 28.8 ± 15.5° to 40.3 ± 16.0°, PI–LL mismatch decreased from 21.7 ± 10.0° to 10.1 ± 11.5°, and SVA decreased from 58.8 ± 31.4 mm to 32.5 ± 36.0 mm. Partial loss of correction was observed at final follow-up, although alignment generally remained improved compared with baseline. ODI improved from 57.8 ± 12.6 to 34.7 ± 8.7 in patients with available paired data. Any postoperative complication occurred in 42.5% (n = 48) of patients, revision/reoperation in 23.9% (n = 27), and unfavorable postoperative course in 35.4% (n = 40). In multivariable analysis, osteoporosis, greater fusion length, and residual immediate postoperative PI–LL mismatch were independently associated with unfavorable postoperative course. Conclusions: In this three-center retrospective cohort, surgery for adult degenerative lumbar deformity was associated with significant radiographic correction and meaningful clinical improvement in patients with available paired outcome data. However, the substantial complication and revision/reoperation burden highlights the morbidity of adult degenerative lumbar deformity surgery. Osteoporosis, fusion length, and residual immediate postoperative PI–LL mismatch may help identify patients at higher risk for unfavorable postoperative course. Full article
(This article belongs to the Special Issue Advances in Diagnosis and Management of Scoliosis)
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Article
Numerical Investigation of Low-Velocity Impact Response of Nomex Honeycomb Sandwich Structures: Effects of Core Density, Face-Sheet Thickness, and Impactor Geometry
by Tarik Zarrouk, Mohammed Jeyar, Jamal-Eddine Salhi and Mohammed Barboucha
Appl. Mech. 2026, 7(3), 56; https://doi.org/10.3390/applmech7030056 - 6 Jul 2026
Abstract
This study examines the low-speed impact response of Nomex honeycomb-core sandwich structures using an approach combining experimental tests and three-dimensional numerical modeling. A finite element model was developed using Abaqus/Explicit to predict contact force, displacement, damage evolution, and absorbed energy under different impact [...] Read more.
This study examines the low-speed impact response of Nomex honeycomb-core sandwich structures using an approach combining experimental tests and three-dimensional numerical modeling. A finite element model was developed using Abaqus/Explicit to predict contact force, displacement, damage evolution, and absorbed energy under different impact configurations. The influence of core density, skin thickness, and impactor geometry was analyzed to identify the parameters governing impact resistance and energy dissipation mechanisms. The numerical results show good agreement with experimental measurements, with maximum relative differences between 7.3% and 8.3% for the maximum force and between 1.8% and 4.3% for the absorbed energy. Core density appears to be a determining factor: the D144 configuration reaches a maximum force of approximately 4400 N, compared to 2600 N for the D80 configuration, representing an increase of approximately 69%. However, sensitivity analysis indicates that skin thickness exerts the most dominant overall influence on load-bearing capacity; increasing this thickness from 0.2 mm to 1.2 mm leads to a fivefold increase in maximum force (from 1800 N to over 10,000 N) and a significant rise in absorbed energy (from 20 J to 105 J). The geometry of the impactor strongly controls the damage modes and stress distribution. A 60° conical impactor promotes localized deformation and rapid perforation, while a 70° angle offers a better compromise between local resistance and progressive energy absorption. At 80°, the stresses are distributed over a larger surface area, which delays perforation. The geometry of the impactor strongly controls the spatial distribution of damage modes. A sharper 60° conical impactor induces highly localized core crushing and rapid skin perforation, while a 70° angle offers a better compromise between local resistance and progressive energy absorption. At 80°, the stresses are distributed over a wider area, promoting diffuse damage and delaying perforation. These results show that the combined optimization of core density, skin thickness, and the impactor–structure interaction is an effective way to improve the impact tolerance of lightweight sandwich structures intended for aerospace, automotive, and marine applications. Full article
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