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Search Results (1,259)

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Keywords = nonlinear material properties

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18 pages, 1962 KB  
Article
Mechanical Signatures of Tibiofemoral Cartilage Degeneration Identified by Unconfined Compression Testing: Implications for Early Osteoarthritis Risk in Athletes
by Saida Benhmida, Ismail Dergaa, Halil İbrahim Ceylan, Nicola Luigi Bragazzi, Andrea de Giorgio, Hanene Boussi and Hedi Trabelsi
Medicina 2026, 62(4), 720; https://doi.org/10.3390/medicina62040720 - 9 Apr 2026
Viewed by 102
Abstract
Background and objectives: Articular cartilage provides low-friction articulation across joint surfaces, distributes loads, and absorbs stress, all of which are crucial mechanical functions of joints. Changes in the mechanical characteristics of cartilage are among the first signs of degenerative joint disease, and [...] Read more.
Background and objectives: Articular cartilage provides low-friction articulation across joint surfaces, distributes loads, and absorbs stress, all of which are crucial mechanical functions of joints. Changes in the mechanical characteristics of cartilage are among the first signs of degenerative joint disease, and they are especially important for athletes who are subjected to high-impact, high-magnitude loading on a regular basis. The objective of this study was to: (i) compare the mechanical characteristics of tibiofemoral cartilage in healthy and osteoarthritic conditions across medial and lateral anatomical compartments; and (ii) use nonlinear phenomenological viscoelastic modeling in conjunction with unconfined compression testing to characterize compartment-specific viscoelastic behavior. Materials and Methods: Forty-six human tibiofemoral cartilage samples were collected during knee surgeries and classified as healthy (n = 17) or osteoarthritic (n = 29) and as medial (n = 26) or lateral (n = 20). Quasi-static unconfined compression tests were performed at 1 mm/min to obtain stress–strain responses, Young’s modulus, maximum compressive stress, and energy absorption. Viscoelastic behavior was analyzed using a nonlinear phenomenological viscoelastic model. Appropriate parametric or non-parametric statistical tests and effect size measures were applied. Results: Osteoarthritic cartilage’s stiffness and energy absorption were significantly higher than those of healthy tissue (p < 0.05). Medial cartilage exhibited significantly greater stiffness and stress than lateral cartilage (p < 0.001). The nonlinear phenomenological viscoelastic model provided an excellent fit (R2 > 0.999). Conclusions: The mechanical profile of osteoarthritic tibiofemoral cartilage is characterized by pathological mechanical remodeling and increased stiffness. Greater mechanical susceptibility in the medial compartment supports the significance of cartilage biomechanical properties as sensitive indicators of early degeneration and osteoarthritis risk in athletic populations. Full article
(This article belongs to the Section Sports Medicine and Sports Traumatology)
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20 pages, 6734 KB  
Article
Time-Scale Mismatch as a Fundamental Constraint in Quantum Beam–Matter Interactions
by Abbas Alshehabi
Quantum Beam Sci. 2026, 10(2), 10; https://doi.org/10.3390/qubs10020010 - 8 Apr 2026
Viewed by 170
Abstract
Quantum beams-including X-rays, synchrotron radiation, electrons, neutrons, ions, and ultrafast photon sources-are indispensable tools for probing the structure, dynamics, and electronic properties of matter. The excitation time scale τexc is defined operationally as the characteristic temporal interval governing externally imposed [...] Read more.
Quantum beams-including X-rays, synchrotron radiation, electrons, neutrons, ions, and ultrafast photon sources-are indispensable tools for probing the structure, dynamics, and electronic properties of matter. The excitation time scale τexc is defined operationally as the characteristic temporal interval governing externally imposed energy deposition events within the interaction volume, such as pulse duration, bunch spacing, or beam dwell time. Interpretation of beam–matter interactions has traditionally relied on steady-state or quasi-equilibrium assumptions, implicitly presuming that intrinsic material relaxation processes can accommodate externally imposed excitation. Recent advances in high-brightness synchrotron sources, X-ray free-electron lasers (XFELs), and pulsed electron beams increasingly operate in regimes where this assumption is strained, and systematic nonequilibrium effects, radiation damage, and irreversible transformations are reported even under routine experimental conditions. This work examines the role of time-scale mismatch between beam-driven energy deposition and intrinsic material relaxation as a governing constraint in beam–matter interactions. Analyzing the hierarchy of excitation, electronic relaxation, phonon coupling, and thermal diffusion time scales, the analysis introduces a dimensionless mismatch parameter Λ=τrelτexc, which quantifies the competition between externally imposed excitation and intrinsic relaxation processes in beam–matter interactions. The resulting framework provides a unified physical interpretation of beam-induced damage, signal distortion, dose dependence, and nonlinear response across quantum beam modalities, framing these effects as consequences of forced nonequilibrium dynamics rather than technique-specific artifacts. Full article
(This article belongs to the Section Radiation Scattering Fundamentals and Theory)
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29 pages, 4375 KB  
Article
Application of AI in Tablet Development: An Integrated Machine Learning Framework for Pre-Formulation Property Prediction
by Masugu Hamaguchi, Tomoki Adachi and Noriyoshi Arai
Pharmaceutics 2026, 18(4), 452; https://doi.org/10.3390/pharmaceutics18040452 - 8 Apr 2026
Viewed by 150
Abstract
Background/Objectives: Tablet development requires simultaneous optimization of multiple quality attributes under limited experimental budgets, yet formulation–property relationships are highly nonlinear in mixture systems. To support pre-formulation decision-making prior to extensive tablet prototyping, this study proposes an AI framework that organizes formulation and process [...] Read more.
Background/Objectives: Tablet development requires simultaneous optimization of multiple quality attributes under limited experimental budgets, yet formulation–property relationships are highly nonlinear in mixture systems. To support pre-formulation decision-making prior to extensive tablet prototyping, this study proposes an AI framework that organizes formulation and process data together with raw-material property records into a reusable database, and enriches conventional composition/process features with physically motivated mixture descriptors derived from raw-material properties and formulation/process settings. Methods: Mixture-level scalar descriptors are constructed by composition-weighted aggregation of material properties, and particle size distribution (PSD) is incorporated via a compact set of summary statistics computed from composition-weighted mixture PSDs. Three feature sets are compared: (i) Materials + Processes (MP), (ii) MP with scalar Descriptors (MPD), and (iii) MPD with PSD summaries (MPDD). Five target properties are modeled: hardness, disintegration time, flow function, cohesion, and thickness. We train and evaluate Random Forest, Extra Trees Regressor, Lasso, Partial Least Squares, Support Vector Regression, and a multi-branch neural network that processes the three feature blocks separately and concatenates them for prediction. For interpolation assessment, repeated Train/Dev/Test splitting (5:3:2) across multiple random seeds is used, and the effect of feature augmentation is quantified by paired RMSE improvements with bootstrap confidence intervals and paired Wilcoxon signed-rank tests. To assess robustness under practical formulation updates, rolling-origin time-series splits are employed and Applicability Domain indicators are computed to characterize out-of-distribution coverage. Results: Across interpolation evaluations, mixture-descriptor augmentation (MPD/MPDD) improves hardness and disintegration time in most settings, whereas gains for flow function are smaller and cohesion/thickness show mixed effects under limited sample sizes. Conclusions: Under extrapolation-oriented evaluation, the descriptors can improve hardness but may degrade disintegration-time prediction under covariate shift, emphasizing the need for careful descriptor selection and dimensionality control when deploying pre-formulation predictors. Full article
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18 pages, 4332 KB  
Article
Skew Angle Optimization for Cogging Torque Reduction in 12-Pole/15-Slot Axial Flux PMSMs
by Ice Poonphol and Padej Pao-la-or
World Electr. Veh. J. 2026, 17(4), 192; https://doi.org/10.3390/wevj17040192 - 6 Apr 2026
Viewed by 258
Abstract
Axial Flux Permanent Magnet Synchronous Motors (AFPMSMs) are gaining increasing attention for their application in electric vehicle (EV) drive systems. Their high torque density and compact axial geometry make them attractive for high-performance EV drive systems. However, cogging torque remains a major challenge, [...] Read more.
Axial Flux Permanent Magnet Synchronous Motors (AFPMSMs) are gaining increasing attention for their application in electric vehicle (EV) drive systems. Their high torque density and compact axial geometry make them attractive for high-performance EV drive systems. However, cogging torque remains a major challenge, degrading low-speed drivability, noise performance, and control stability. This article proposes a magnet skew on rotor modulation structure using a genetic algorithm (GA) to reduce cogging torque in AFPMSMs utilizing a 12/15 non-integer pole/slot arrangement. The objective of optimization is to simultaneously reduce cogging torque under identical electromagnetic constraints. A complete three-dimensional finite element model (3D-FEM) incorporating nonlinear magnetic material properties has been developed to evaluate the electromagnetic field distribution and torque components. The results indicate that a 12/15 non-integer pole/slot arrangement improves harmonic distribution and extends the operating range with lower cogging torque compared to integer pole/slot designs. Combined with GA-optimized skew angles, this reduces peak-to-peak cogging torque to less than 50%. This design is ideally suited for the traction requirements of electric vehicles, including premium electric vehicles where smooth operation at low speeds is critical. Full article
(This article belongs to the Section Propulsion Systems and Components)
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18 pages, 2678 KB  
Article
Multi-Objective Optimization of Ultrasonic Surface Rolling Process Parameters for TC4 Titanium Alloy with IWOA–RBF and MOGWO Algorithms
by Yeshen Lan, Chuchu Rao and Yunpeng Lyu
Micromachines 2026, 17(4), 451; https://doi.org/10.3390/mi17040451 - 6 Apr 2026
Viewed by 276
Abstract
A structured optimization approach was applied to ultrasonic surface rolling process (USRP) parameters, aiming to enhance the material surface characteristics of TC4 titanium alloy. To overcome the premature convergence and limited exploration capability of the standard Whale Optimization Algorithm (WOA), three enhancement strategies [...] Read more.
A structured optimization approach was applied to ultrasonic surface rolling process (USRP) parameters, aiming to enhance the material surface characteristics of TC4 titanium alloy. To overcome the premature convergence and limited exploration capability of the standard Whale Optimization Algorithm (WOA), three enhancement strategies were introduced, including population initialization based on an optimal point set, a sinusoidal nonlinear convergence factor, and an adaptive inertia-based position update strategy. By optimizing the structural parameters of the RBF neural network with the improved WOA, an IWOA–RBF predictive model for surface performance evaluation was developed and rigorously validated in terms of prediction accuracy. Using the developed IWOA–RBF model, a multi-criteria decision-making framework integrating the CRITIC weighting method and the TOPSIS ranking approach was constructed to evaluate surface quality. This framework was further combined with a multi-objective Grey Wolf Optimization (MOGWO) algorithm to perform Pareto-based optimization and determine the optimal USRP parameter set. Experimental validation showed that the optimized parameters resulted in a significant reduction in surface roughness, while enhancing both surface hardness and residual compressive stress. The results confirm the robustness and effectiveness of the proposed IWOA–RBF and MOGWO optimization framework, providing a reliable strategy for high-precision parameter optimization and coordinated enhancement of surface properties in the TC4 titanium alloy USRP. Full article
(This article belongs to the Section D:Materials and Processing)
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21 pages, 4221 KB  
Article
Linear and Nonlinear Optical Properties of SiO2/TiO2 Heterostructures Grown by Plasma-Enhanced Atomic Layer Deposition
by Jinsong Liu, Martin Mičulka, Raihan Rafi, Sebastian Beer, Denys Sevriukov, Stefan Nolte, Sven Schröder, Andreas Tünnermann, Isabelle Staude and Adriana Szeghalmi
Coatings 2026, 16(4), 424; https://doi.org/10.3390/coatings16040424 - 2 Apr 2026
Viewed by 280
Abstract
Second harmonic (SH) radiation can only be generated in non-centrosymmetric bulk crystals under electric dipole approximation. Nonlinear thin films made from bulk crystals are technologically challenging because of complex and high-temperature fabrication processes. In this work, heterostructures made of two distinct amorphous materials, [...] Read more.
Second harmonic (SH) radiation can only be generated in non-centrosymmetric bulk crystals under electric dipole approximation. Nonlinear thin films made from bulk crystals are technologically challenging because of complex and high-temperature fabrication processes. In this work, heterostructures made of two distinct amorphous materials, namely SiO2 and TiO2, were prepared through plasma-enhanced atomic layer deposition (PEALD) with deposition temperature of 100 °C. By using the uniaxial dispersion model, we characterized the form birefringence of the deposited films, which can play a crucial role for the phase-matching condition in nonlinear waveguides or other nonlinear optical applications. By applying a fringe-based technique, we determined the largest diagonal component of the effective bulk second-order susceptibility, χzzz(2) = 1.30 ± 0.13 pm/V, at a wavelength of 1032 nm. Noteworthy, we observed strong SHG signals from two-component nanolaminates, which are several orders of magnitude larger than those from single layers. The SHG signals from our samples only require the broken inversion symmetry at the interface. Here, optical properties of nanocomposites can be precisely engineered using the promising PEALD technology. Full article
(This article belongs to the Collection Advanced Optical Films and Coatings)
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19 pages, 6836 KB  
Article
Thermoelastic Vibration of Functionally Graded Porous Euler–Bernoulli Beams Using the Differential Transformation Method
by Selin Kaptan and İbrahim Özkol
Appl. Sci. 2026, 16(7), 3271; https://doi.org/10.3390/app16073271 - 27 Mar 2026
Viewed by 235
Abstract
Functionally graded porous beams are increasingly used in lightweight engineering structures, where thermal effects and material inhomogeneity significantly influence vibration behavior. In this study, the thermoelastic free vibration of functionally graded porous Euler–Bernoulli beams with temperature-dependent material properties is investigated by considering uniform [...] Read more.
Functionally graded porous beams are increasingly used in lightweight engineering structures, where thermal effects and material inhomogeneity significantly influence vibration behavior. In this study, the thermoelastic free vibration of functionally graded porous Euler–Bernoulli beams with temperature-dependent material properties is investigated by considering uniform and symmetric porosity distributions, together with uniform, linear, and nonlinear temperature fields. The governing equations are derived based on classical Euler–Bernoulli beam theory and solved using the Differential Transformation Method, while the accuracy of the semi-analytical formulation is verified through a Hermite-based finite element model. The results show that increasing temperature reduces the bending stiffness due to thermal axial forces and leads to a rapid decrease in natural frequency as the critical buckling temperature is approached. Increasing porosity generally decreases the natural frequency, although a slight increase may occur in symmetric distributions because of the accompanying reduction in mass density. The present study provides a computational framework for the thermo-vibration analysis of functionally graded porous beams in lightweight structural applications. Full article
(This article belongs to the Section Acoustics and Vibrations)
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20 pages, 4038 KB  
Article
Impact of Construction Material Properties Variability on the Seismic Fragility Assessment of RC Structures in Bucharest
by Florin Pavel and Lucian Petru Florescu
Buildings 2026, 16(7), 1344; https://doi.org/10.3390/buildings16071344 - 27 Mar 2026
Viewed by 240
Abstract
This study investigates how historical variability in construction materials influences the seismic fragility of reinforced concrete (RC) buildings in Bucharest. Mechanical properties of reinforcing steels (OB37, TOR47, and PC52) and concretes used between 1950 and 2000 are statistically characterized using archival records and [...] Read more.
This study investigates how historical variability in construction materials influences the seismic fragility of reinforced concrete (RC) buildings in Bucharest. Mechanical properties of reinforcing steels (OB37, TOR47, and PC52) and concretes used between 1950 and 2000 are statistically characterized using archival records and experimental data. The analysis highlights significant discrepancies between prescribed and in situ concrete strengths, as well as substantial differences in ductility, overstrength, and strength variability among historical steel types. To evaluate structural implications, a representative 11-storey pre-1970 RC building is modeled using nonlinear static and incremental dynamic analysis. The results show markedly lower capacity and higher fragility in the transversal direction. Time-dependent deterioration is examined by incorporating carbonation-induced reinforcement corrosion using FIB-based formulations. Even moderate corrosion leads to measurable reductions in stiffness, ductility, and lateral capacity, producing higher fragility across all considered damage states. Seismic loss estimations further demonstrate an increase in expected annual losses for both principal directions when corrosion is considered. The findings underscore the need for era-specific material models and deterioration mechanisms to achieve accurate seismic vulnerability assessments of Bucharest’s aging RC building stock. Full article
(This article belongs to the Special Issue Seismic Performance and Durability of Engineering Structures)
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23 pages, 3050 KB  
Article
Micromechanical Prediction of Elastic Properties of Unidirectional Glass and Carbon Fiber-Reinforced Epoxy Composites Using the Halpin–Tsai Model
by Sahnoun Zengah, Rabeh Slimani, Abdelghani Baltach, Ali Taghezout, Ali Benhamena, Dursun Murat Sekban, Ecren Uzun Yaylacı and Murat Yaylacı
Polymers 2026, 18(7), 822; https://doi.org/10.3390/polym18070822 - 27 Mar 2026
Viewed by 418
Abstract
This study presents a calibrated analytical micromechanical framework for predicting the linear elastic behavior of unidirectional glass fiber/epoxy and carbon fiber/epoxy composites over a wide range of fiber volume fractions. The approach combines the classical rule of mixtures for the longitudinal Young’s modulus [...] Read more.
This study presents a calibrated analytical micromechanical framework for predicting the linear elastic behavior of unidirectional glass fiber/epoxy and carbon fiber/epoxy composites over a wide range of fiber volume fractions. The approach combines the classical rule of mixtures for the longitudinal Young’s modulus with the semi empirical Halpin–Tsai equations to estimate the transverse Young’s modulus and the in-plane shear modulus. The framework is specifically formulated to support durability-oriented composite design through rapid and physically consistent estimation of elastic properties governing load transfer and stress distribution. Material parameters, including fiber and matrix Young’s moduli (Ef, Em), shear moduli (Gf, Gm), Poisson’s ratios (νf, νm), and fiber volume fraction (Vf up to 0.80), are taken from established material property databases and implemented within a literature-informed modeling scheme. To preserve physical realism at high fiber contents, a shear correction factor is introduced for Vf > 0.50 to account for microstructural interaction and fiber clustering effects. The predicted effective elastic constants (E1, E2, G12, ν12) exhibit consistent and physically meaningful trends across the full fiber volume fraction range. The model predictions were evaluated against trends widely reported in the composite micromechanics literature, and the results showed overall agreement in the nonlinear reduction in stiffness gains at elevated fiber volume fractions. Comparative results indicate that carbon fiber/epoxy composites achieve up to approximately 30% higher stiffness than glass fiber/epoxy systems at equivalent fiber contents, reflecting the influence of stiffness contrast on composite response. The analysis further indicates that stiffness saturation begins approximately in the Vf = 0.60–0.70 range, where the incremental gains in E2 and G12 become noticeably smaller for both composite systems. This behavior provides design-relevant guidance by showing that, beyond this range, further increases in fiber content may offer limited stiffness improvement relative to the associated manufacturing complexity. Overall, the calibrated Halpin–Tsai methodology offers a practical and computationally efficient tool for preliminary evaluation and design-stage optimization of the elastic performance of high-performance composite structures. Full article
(This article belongs to the Section Polymer Composites and Nanocomposites)
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33 pages, 1418 KB  
Article
A Structural Decomposition-Based Optimization Approach for the Integrated Scheduling of Blending Processes in Raw Material Yards
by Wenyu Xiong, Feiyang Sun, Xiongzhi Guo, Jiangfei Yin, Chao Sun and Yan Xiong
Appl. Sci. 2026, 16(7), 3256; https://doi.org/10.3390/app16073256 - 27 Mar 2026
Viewed by 204
Abstract
The blending process in raw material yards is essential for maintaining precise material proportions in downstream production, directly influencing product quality and energy efficiency in industries such as steel and coal processing. However, stringent operational constraints, including silo capacity limits, discharge rates, equipment [...] Read more.
The blending process in raw material yards is essential for maintaining precise material proportions in downstream production, directly influencing product quality and energy efficiency in industries such as steel and coal processing. However, stringent operational constraints, including silo capacity limits, discharge rates, equipment movement delays, and a strict no-empty-silo requirement, result in a strongly coupled, high-dimensional combinatorial scheduling problem. In this paper, we develop a mixed-integer nonlinear programming (MINLP) model to capture the complex dynamics of silo weight and equipment operations. The primary scientific contribution of this work lies in the theoretical discovery of a structural decoupling property within the complex MINLP. We analytically prove that by fixing the replenishment sequence, the intractable global problem can be rigorously decomposed into two subproblems: a linear programming (LP) problem for silo-filling cart scheduling and a shortest-path problem solvable via dynamic programming (DP) for reclaimer scheduling. Leveraging this decomposition, a two-stage metaheuristic algorithm is proposed, combining greedy initialization with multi-round simulated annealing enhanced by local search. Experimental validation using real industrial data demonstrates that the proposed method consistently outperforms the greedy algorithm. Crucially, while the commercial solver Gurobi struggles to converge within a practical 1800 s time limit, our approach yields comparable solution quality in mere seconds. Furthermore, robustness analysis under a 20% demand surge confirms the algorithm’s adaptive capability, maintaining the silo weight stability through re-optimization. This research provides a robust, computationally efficient solution for the blending process in raw material yards. Full article
(This article belongs to the Section Applied Industrial Technologies)
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19 pages, 8732 KB  
Technical Note
SMA Simulator: An Efficient Tool for Simulating the Partial Nonlinear Loading Cycles of Shape Memory Alloy Wire Actuators
by Peter L. Bishay
Actuators 2026, 15(4), 183; https://doi.org/10.3390/act15040183 - 26 Mar 2026
Viewed by 342
Abstract
The behavior of shape memory alloy (SMA) materials is more complex than linear isotropic metals because of their nonlinear thermomechanical coupling. When an SMA material is mechanically stressed or joule-heated, phase transformation happens in the material, and accordingly some material properties dramatically change. [...] Read more.
The behavior of shape memory alloy (SMA) materials is more complex than linear isotropic metals because of their nonlinear thermomechanical coupling. When an SMA material is mechanically stressed or joule-heated, phase transformation happens in the material, and accordingly some material properties dramatically change. In any loading or unloading scenario, the initial state of the material should be known because it significantly affects its behavior. Stress and strain alone are not enough to describe such materials. Temperature and martensitic fraction are also required to simulate SMA materials accurately. This paper presents a MATLAB application, called “SMA Simulator,” that was developed to simulate the nonlinear behavior of SMA wires under mechanical or thermal loads. This tool is very effective in helping users understand the shape memory and pseudoelastic effects in such smart materials, as it allows for plotting the loading path in the 3D stress–strain–temperature space while monitoring the evolution of the martensitic fraction. Any load–unload scenario can be studied, including multiple consecutive partial loading cycles. Since the application is not based on any numerical method that would require extensive meshing, the computational time is minimal, allowing users to perform more simulations and acquire results instantaneously. Full article
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25 pages, 2455 KB  
Article
Physics-Informed Machine Learning for Carbonation Depth Prediction in Concrete
by Moutaman M. Abbas and Alina Bărbulescu
Materials 2026, 19(6), 1271; https://doi.org/10.3390/ma19061271 - 23 Mar 2026
Viewed by 376
Abstract
The durability of reinforced concrete structures is significantly affected by the carbonation process, which decreases the alkalinity of the pore solution and initiates corrosion of the steel reinforcement. However, the square roots of time equations, which are Fickian diffusion-based, are not able to [...] Read more.
The durability of reinforced concrete structures is significantly affected by the carbonation process, which decreases the alkalinity of the pore solution and initiates corrosion of the steel reinforcement. However, the square roots of time equations, which are Fickian diffusion-based, are not able to accurately capture the nonlinear interactions of material properties with environmental factors. To overcome this limitation, this research introduces a novel hybrid model based on the integration of a physics-informed neural network (PINN) with residual regression via CatBoost, a categorical boosting algorithm. Using an expanded dataset of 6000 samples, the first stage of the model, which is based on the physics-informed neural network, is able to learn the underlying physics of the diffusion process by imposing monotonicity constraints. The second stage of the model, which is based on the CatBoost algorithm, is able to learn the residuals of the nonlinear interactions of factors such as the curing time, water–cement ratio, and supplementary cementitious material reactivity, which are not captured by the underlying physics of the diffusion law. Data augmentation via physics-based resampling increased the dataset from 3000 to 6000 samples. Validation of the model using 1200 samples resulted in R2 = 0.871, MAE = 15.362, and RMSE = 24.37. SHAP confirmed that the model was physically consistent with the principles of concrete technology, reversing the counterintuitive linear correlations to accurately capture the protective effect of longer curing times. The suggested framework offers a practical method for enhancing durability evaluation and aiding the maintenance and service-life management of reinforced concrete structures. Full article
(This article belongs to the Special Issue Recent Progress in Sustainable Construction Materials)
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21 pages, 4493 KB  
Article
Direct Shear Rheological Tests on Clays and Model Analysis
by Yingguang Fang, Kang Gao, Zhenfeng Ou and Renguo Gu
Buildings 2026, 16(6), 1246; https://doi.org/10.3390/buildings16061246 - 21 Mar 2026
Viewed by 213
Abstract
This study aims to investigate the influence of clay mineral content on the rheological properties and long-term deformation stability of clays, and to establish a unified model capable of quantitatively describing the nonlinear rheological behavior of clays with different mineral compositions. Direct shear [...] Read more.
This study aims to investigate the influence of clay mineral content on the rheological properties and long-term deformation stability of clays, and to establish a unified model capable of quantitatively describing the nonlinear rheological behavior of clays with different mineral compositions. Direct shear rheological tests were conducted on specimens prepared with different mixing ratios of bentonite, kaolin, and quartz. Combined with micro-mechanism analysis, the controlling factors of clay rheological behavior were explored. The experimental results show that the creep stress threshold, elastic viscosity, and average plastic viscosity decrease significantly with increasing clay mineral content. The rheological deformation exhibits distinct nonlinear characteristics, and clay mineral content plays a controlling role in the rheological behavior. Based on experimental and mechanistic analysis, a unified rheological model was established, which reflects the material origin of rheology and captures nonlinear rheological characteristics. This model can predict the entire time-history mechanical behavior of clays with different mineral compositions across the three stages of instantaneous deformation, decay rheology, and steady-state rheology under different shear stress levels using a single set of parameters. Validation was performed through direct shear rheological tests under 50 working conditions for five types of clay specimens, demonstrating good consistency between the model calculations and experimental results. The unified rheological model reveals the material origin and physical essence of clay rheology, demonstrates high universality, and advances the understanding of the influence of mineral composition on rheology from the current phenomenological qualitative description to quantitative calculation for the first time, significantly enhancing its engineering application value. This provides a more reliable tool for predicting long-term deformation and assessing the stability of clay foundations. Full article
(This article belongs to the Section Building Structures)
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15 pages, 1844 KB  
Review
Transverse Mechanical Response of Carbon Nanotube Yarns: An Experimental Study Using Atomic Force Microscopy and Raman Spectroscopy
by Iriana Garcia Guerra, Deissy. J. Feria, Gustavo M. A. Alves, Jandro L. Abot, Inés Pereyra and Marcelo N. P. Carreño
C 2026, 12(1), 27; https://doi.org/10.3390/c12010027 - 20 Mar 2026
Viewed by 416
Abstract
Carbon nanotube yarns (CNTYs) have received more consideration recently due to their excellent specific mechanical, electrical and thermal properties, making them promising materials for different applications. Until now, the axial properties of the yarn have been thoroughly investigated; however, the transverse or radial [...] Read more.
Carbon nanotube yarns (CNTYs) have received more consideration recently due to their excellent specific mechanical, electrical and thermal properties, making them promising materials for different applications. Until now, the axial properties of the yarn have been thoroughly investigated; however, the transverse or radial properties, orthogonal to the fiber axis, remain relatively unknown due to the challenges associated with their measurement. In this study, the transverse or radial response of the CNTY including its elastic modulus was determined using Atomic Force Microscopy (AFM) and Raman Spectroscopy. Determining transverse properties in fibrous materials presents challenges owing to their geometry, inherent anisotropy, whereby mechanical characteristics exhibit directional disparities; i.e., the properties in the transverse direction may be several orders of magnitude smaller than those in the axial direction. To overcome these difficulties, AFM was utilized to perform nanoindentation experiments, where a tipless flexible cantilever probe was used to apply a controlled force to the CNTY surface. The resulting indentation depth was then analyzed to determine the transversal elastic modulus. Preliminary findings indicate that the transverse elastic modulus of the CNTYs ranges from 10–54 kPa for strain levels below 3%. Complementary Raman spectroscopy provided insight into the bulk-scale mechanical behavior of CNTYs. Incremental compressive loading between microscope slides induced nonlinear upshifts in the 2D Raman band (from ~2686.6 to 2691.4 cm−1), indicating nanoscale tube realignment, inter-tube densification, and compaction. From lateral diameter measurements under load, a stress–strain curve was constructed, revealing three distinct regimes: one with an initial elastic modulus of 3.12 MPa (0.3–11.2% strain), another one with an elastic modulus increasing to 8.46 MPa (11.2–14.4%), and finally one with an elastic modulus peaking at 16.86 MPa beyond 14.4% strain. Together, these methods delineate the hierarchical and anisotropic nature of CNTYs, validating the importance of multiscale mechanical characterization for their deployment in piezoresistive sensors and multifunctional composites. This study establishes a robust framework for quantifying the transverse mechanical response of CNTYs. Full article
(This article belongs to the Collection Novel Applications of Carbon Nanotube-Based Materials)
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18 pages, 2851 KB  
Article
Investigating the Triaxial Mechanical Behaviour of Silicone Rubber Material
by Jie Yang, Nan Chen, Jun Gao, Yang Wang, Shuchang Long, Xiaohu Yao, Zhibin Wu and Junfeng Zhao
Polymers 2026, 18(6), 755; https://doi.org/10.3390/polym18060755 - 20 Mar 2026
Viewed by 290
Abstract
Silicone rubber is extensively used in engineering applications due to its toughness and impact resistance; however, traditional characterisation methods fail to capture its nonlinear deformation characterisation and triaxial mechanical behaviour. To address this, we derived a constitutive model within the framework of continuum [...] Read more.
Silicone rubber is extensively used in engineering applications due to its toughness and impact resistance; however, traditional characterisation methods fail to capture its nonlinear deformation characterisation and triaxial mechanical behaviour. To address this, we derived a constitutive model within the framework of continuum mechanics that assumes a condition of near incompressibility and conducted uniaxial, planar, and equibiaxial tension tests to fit the model parameters. Through systematic analysis of triaxial mechanical responses under these three loading modes, we determined the material’s nonlinear large-deformation behaviour and sensitivity to the biaxiality ratio. Comparative analyses with classical hyperelastic models show that the proposed model achieves a good balance between the number of parameters and fitting accuracy. After the parameter-fitting process, we performed finite element simulations of the three loading modes. The simulation results show good agreement with experimental data in terms of deformation patterns and stress–strain curves. This study provides a novel theoretical tool for evaluating the mechanical properties and structural designs of soft materials. Full article
(This article belongs to the Section Polymer Processing and Engineering)
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