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Search Results (943)

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23 pages, 8064 KiB  
Article
Uncertainty-Based Design: Finite Element and Explainable Machine Learning Modeling of Carbon–Carbon Composites for Ultra-High Temperature Solar Receivers
by Vahid Daghigh, Hamid Daghigh and Michael W. Keller
J. Compos. Sci. 2025, 9(3), 100; https://doi.org/10.3390/jcs9030100 - 23 Feb 2025
Abstract
Design under uncertainty has significantly grown in research developments during the past decade. Additionally, machine learning (ML) and explainable ML (XML) have offered various opportunities to provide reliable predictable models. The current article investigates the use of finite element modeling (FEM), ML and [...] Read more.
Design under uncertainty has significantly grown in research developments during the past decade. Additionally, machine learning (ML) and explainable ML (XML) have offered various opportunities to provide reliable predictable models. The current article investigates the use of finite element modeling (FEM), ML and XML predictions, and uncertain-based design of carbon-carbon (C-C) composites for use in ultra-high temperatures. A C-C composite concentrating solar power (CSP) as a microvascular receiver is considered as a case study. These C-C composites are fiber composites with directly integrated carbonized microchannels to form a lightweight, high-absorptivity material that includes an embedded microvascular network of channels. The topology of these microchannels is engineered to optimize heat transfer to a supercritical carbon dioxide (sCO2) heat transfer fluid. The mechanical characterization of C-C composites is highly challenging. Thus, designing every component made of C-C composites for ultra-high temperature applications needs an uncertainty-based analysis. As a part of a comprehensive project on the development of a novel carbonized microvascular C-C composite, this paper explores C-C composite sensitivity analysis, FEM, ML prediction, and XML analysis. The resulting composite can then be carbonized and coated with an oxidation-resistant coating to form a thermally efficient and mechanically robust C-C composite. An ANSYS 3-D-FE model was used to analyze the CSP’s stress/strain. To consider the variability in the mechanical and thermal properties of C-C composites, various mechanical properties are considered as the ANSYS FEM’s input. A synthetic dataset from 730 ANSYS runs was produced to feed into the ML and XML algorithms for uncertainty analysis and prediction. The ML and XML algorithms could accurately predict the CSP stresses/strains. Full article
(This article belongs to the Section Carbon Composites)
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<p>Schematic view of the C-C composite concentrating solar power collector and mechanical boundary conditions (the microchannel format was inspired by [<a href="#B4-jcs-09-00100" class="html-bibr">4</a>,<a href="#B20-jcs-09-00100" class="html-bibr">20</a>,<a href="#B21-jcs-09-00100" class="html-bibr">21</a>,<a href="#B22-jcs-09-00100" class="html-bibr">22</a>]). (Note: U represents displacement, and R represents rotation).</p>
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<p>KNN regression analysis. The red circle represents the neighborhood area of interest.</p>
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<p>Overview of training and testing set divisions using k-fold cross-validation, depicting data division into k segments (k = 5).</p>
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<p>Temperature distribution over the C-C composite; a quartered model where the top and bottom surfaces are set to be 851 °C and 586 °C, respectively.</p>
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<p>Equivalent stress distribution over the C-C composite; (<b>a</b>) half of the quarter model, (<b>b</b>) magnified image of the area with the maximum stress.</p>
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<p>Equivalent alternating stress distribution over the C-C composite; (<b>a</b>,<b>b</b>) the quarter model, and half of the quarter model with the magnified area containing maximum stress.</p>
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<p>Equivalent elastic strain over the C-C composite; (<b>a</b>) the quarter model, (<b>b</b>) half of the quarter model with the magnified area containing maximum stress.</p>
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<p>Biaxiality indication for stress distribution over the C-C composite; (<b>a</b>) the quarter model, and (<b>b</b>) half of the quarter model.</p>
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<p>Biaxiality indication for stress distribution over the C-C composite; (<b>a</b>) the quarter model, and (<b>b</b>) half of the quarter model.</p>
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<p>Correlation coefficients considering six inputs and two outputs.</p>
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<p>Actual equivalent strain data generated by finite element versus predicted data by machine learning; the left column contains the UD_KNN, and the right column contains the ID_KNN (strain is represented in mm/mm, indicating its dimensionless nature).</p>
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<p>Actual equivalent strain data generated by finite element versus predicted data by machine learning; the left column contains the UD_KNN, and the right column contains the ID_KNN (strain is represented in mm/mm, indicating its dimensionless nature).</p>
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<p>Actual equivalent stress data generated by finite element versus predicted data by machine learning; the left column contains the UD_KNN, and the right column contains the ID_KNN (the stress unit is MPa).</p>
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<p>Actual equivalent stress data generated by finite element versus predicted data by machine learning; the left column contains the UD_KNN, and the right column contains the ID_KNN (the stress unit is MPa).</p>
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<p>SHAP summary plot, showing the feature importance for predicting maximum stress. The mean absolute SHAP values quantify the impact of each feature on the model’s output (equivalent maximum stress).</p>
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<p>Distribution of SHAP values showing the magnitude and directional influence of mechanical properties on equivalent maximum stress predictions, with feature values indicated by color gradient (blue: negative to red: positive).</p>
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<p>Mean absolute SHAP values illustrate the relative importance of mechanical properties in predicting equivalent maximum strain. The bar lengths represent the average magnitude of influence for each parameter, with all properties showing absolute contributions to the model’s equivalent maximum strain predictions.</p>
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<p>SHAP value distributions show the magnitude, direction, and feature–value relationships of mechanical properties’ effects on equivalent maximum strain predictions.</p>
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26 pages, 7283 KiB  
Review
Validated and Optimized Strategies for Preserving Historical Heritage Towards Natural and Anthropic Risks: Insights from the DETECT-AGING Project
by Gian Piero Lignola, Nicola Buratti, Serena Cattari, Fulvio Parisi, Filippo Ubertini, Sara Alfano, Laura Ierimonti, Andrea Meoni, Daniele Sivori and Giorgio Virgulto
Buildings 2025, 15(5), 693; https://doi.org/10.3390/buildings15050693 - 22 Feb 2025
Abstract
This paper summarizes simple and practically attractive new methodologies based on validated and optimized strategies for preserving historical heritage towards natural or anthropic risks in order to assist public administrations and stakeholders involved at various levels in the protection of cultural heritage. This [...] Read more.
This paper summarizes simple and practically attractive new methodologies based on validated and optimized strategies for preserving historical heritage towards natural or anthropic risks in order to assist public administrations and stakeholders involved at various levels in the protection of cultural heritage. This represents the outcome of the PRIN 2017 project DETECT-AGING—degradation effects on structural safety of cultural heritage constructions through simulations and health monitoring. Results were built on recent advances in structural performance modelling of historical masonry structures, interpretation of effects of degradation, advanced numerical simulations, and structural health monitoring, with the final aim to go beyond the state of the art in regard to assessing and establishing: (i) degradation effects from the level of materials to the scale of components; (ii) methodologies able to transfer information on mechanical behaviour from a micro-scale to a macro-scale; (iii) the use of ambient vibration measurements to address epistemic modelling uncertainties in historical masonry buildings; (iv) structural health monitoring (SHM) to detect the occurrence of damage and locate/quantify damage; (v) the capability of equivalent frame models (EFMs) to support the SHM of masonry structures in place of more refined 3D finite element models (FEMs); (vi) variations in the structural response that can be monitored by sensor networks as a function of simulated degradation. Full article
(This article belongs to the Section Building Structures)
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<p>Examples of masonry constituents’ degradation considered in this research.</p>
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<p>Flowchart of the DETECT-AGING project.</p>
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<p>Linear regression models for the prediction of (<b>a</b>) force–displacement curves accounting for (<b>b</b>) mean cracked stiffness given initial elastic stiffness, (<b>c</b>) mean initial stiffness loss given the compressive strength of tuff stone, (<b>d</b>) mean initial stiffness loss given the compressive strength of a mortar, (<b>e</b>) mean elastic limit shear force loss given the initial stiffness loss, and (<b>f</b>) mean peak shear force loss given the initial stiffness loss.</p>
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<p>FEM cracking pattern corresponding to (<b>a</b>) flexural failure and (<b>b</b>) shear failure.</p>
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<p>One-story frame model developing two rigid modes governed by the translational components <span class="html-italic">U</span> and <span class="html-italic">V</span> along the <span class="html-italic">x</span> and <span class="html-italic">y</span> directions at frequencies <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>f</mi> </mrow> <mrow> <mi>U</mi> </mrow> <mrow> <mi>*</mi> </mrow> </msubsup> <mo> </mo> <mi mathvariant="normal">and</mi> <mo> </mo> <msubsup> <mrow> <mi>f</mi> </mrow> <mrow> <mi>V</mi> </mrow> <mrow> <mi>*</mi> </mrow> </msubsup> </mrow> </semantics></math>, a rigid mode governed by the rotational component <span class="html-italic">θ</span> at frequency <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>f</mi> </mrow> <mrow> <mi>θ</mi> </mrow> <mrow> <mi>*</mi> </mrow> </msubsup> </mrow> </semantics></math>, and one deformable mode governed by the shear strain <span class="html-italic">Γ</span> at frequency <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>f</mi> </mrow> <mrow> <mi>Γ</mi> <mo>.</mo> </mrow> <mrow> <mi>*</mi> </mrow> </msubsup> </mrow> </semantics></math>.</p>
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<p>Validation of the practice-oriented analytical formulation to model the flange effect in EFMs of masonry buildings, achieved from the comparison between high-fidelity nonlinear FE analyses and experimental dynamic data from monitored buildings. (<b>a</b>) FE analysis on a simple I-shaped 3D assembly, (<b>b</b>) percent error in estimating axial loads after the application of vertical loads (<span class="html-italic">d<sub>top</sub> </span>= 0 mm) and horizontal loads (up to <span class="html-italic">d<sub>top</sub> </span>= 6.75 mm) as a function of average vertical stress for different values of <span class="html-italic">ω</span>. (<b>c</b>) Validation at the building scale comparing the EFM of the Fabriano building calibrated with different values of <span class="html-italic">ω</span> with the experimental dynamic identification in terms of percentage error on natural frequencies and MAC values. Adapted from [<a href="#B58-buildings-15-00693" class="html-bibr">58</a>].</p>
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<p>Solution of the direct problem (modal analysis) for a three-story structure. (<b>a</b>) Distributed-parameter FEM and a lumped-parameter EFM modelling approaches. (<b>b</b>) Comparison between the REM and ROM models in terms of relative difference in natural frequency Δ<span class="html-italic">f</span>/<span class="html-italic">f</span> and the mode shape correlation index MAC as a function of the floor-to-inter-story mass ratio <span class="html-italic">η</span> and lateral slenderness parameter <span class="html-italic">δ</span>, (<b>c</b>) with a focus on the dependence on the mass ratio <span class="html-italic">η</span>. Adapted from [<a href="#B59-buildings-15-00693" class="html-bibr">59</a>].</p>
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<p>Monitoring masonry walls using an integrated smart brick network: (<b>a</b>) cracking pattern detected on the wall at the end of the test; (<b>b</b>) strains measured by smart bricks and LVDTs against the applied load; (<b>c</b>) strain state of the tested wall at one-third of the peak shear stress from numerical simulations; (<b>d</b>) strain state of the tested wall at the peak shear stress from numerical simulations.</p>
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<p>Monitoring masonry buildings using an integrated smart brick network: (<b>a</b>) picture of the full-scale masonry building prototype; (<b>b</b>) the laying of a smart brick during the construction phase; (<b>c</b>) a smart brick embedded within the masonry and connected to the DAQ system for strain measurements.</p>
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<p>Comparison between the calibrated EFM and FEM of the Consoli Palace in Gubbio, Italy. (<b>a</b>) The low number of elements and degrees of freedom of the synthetic EFM drastically reduces computational times for modal (MA) and nonlinear static (NLSA) analyses when compared to FEM. (<b>b</b>) The updated models achieve similar results in reproducing the experimental natural frequencies and mode shapes (MAC indices). Adapted from [<a href="#B67-buildings-15-00693" class="html-bibr">67</a>].</p>
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<p>Vibration-based monitoring of two full-scale masonry wall systems: (<b>a</b>) frequency decay observed in the specimen tested under increasing out-of-plane displacements and (<b>b</b>) frequency decay observed in the specimen tested under increasing differential foundation settlements.</p>
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<p>A schematic representation of a data fusion-based methodology.</p>
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19 pages, 6567 KiB  
Article
Investigation of the Noise Emitted from Elevated Urban Rail Transit Paved with Various Resilient Tracks
by Quanmin Liu, Kui Gao, Yifei Miao, Lizhong Song and Si Yue
Materials 2025, 18(5), 968; https://doi.org/10.3390/ma18050968 - 21 Feb 2025
Abstract
Based on the dynamic receptance method, a vehicle–track–bridge interaction model was developed to calculate the wheel–rail interaction forces and the forces transmitted to the bridge in an elevated urban rail transit system. A prediction model integrating the finite element method–boundary element method (FEM-BEM) [...] Read more.
Based on the dynamic receptance method, a vehicle–track–bridge interaction model was developed to calculate the wheel–rail interaction forces and the forces transmitted to the bridge in an elevated urban rail transit system. A prediction model integrating the finite element method–boundary element method (FEM-BEM) and the statistical energy analysis (SEA) method was established to obtain the noise from the main girder, track slab, and wheel–rail system for elevated urban rail transit. The calculated results agree well with the measured data. Thereafter, the noise radiation characteristics of a single source and the total noise of elevated urban rail transit systems with resilient fasteners, trapezoidal sleepers, and steel spring floating slabs were investigated. The results demonstrate that the noise prediction model for elevated urban rail transit that was developed in this study is effective. The diversity of track forms altered the noise radiation field of elevated urban rail transit systems significantly. Compared to monolithic track beds, where the fastener stiffness is assumed to be 60 × 106 N/m (MTB_60), steel spring floating slab tracks (FSTs), trapezoidal sleeper tracks (TSTs), and resilient fasteners with a stiffness of 40 × 106 N/m (MTB_40) and 20 × 106 N/m (MTB_20) can reduce bridge-borne noise by 24.6 dB, 8.8 dB, 2.1 dB, and 4.2 dB, respectively. These vibration-mitigating tracks can decrease the radiated noise from the track slab by −0.7 dB, −0.6 dB, 2.5 dB, and 2.6 dB, but increase wheel–rail noise by 0.4 dB, 0.8 dB, 1.3 dB, and 2.4 dB, respectively. The noise emanating from the main girder and the track slab was dominant in the linear weighting of the total noise of the elevated section with MTBs. For the TST and FST, the radiated noise from the track slab contributed most to the total noise. Full article
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<p>Noise prediction model for elevated urban rail transit systems.</p>
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<p>Three typical resilient track structures.</p>
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<p>Cross-sectional diagram of the box-girder (unit: mm).</p>
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<p>Layout of the noise and vibration measuring points (unit: m).</p>
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<p>Photos of the test: (<b>a</b>) train and elevated bridges; (<b>b</b>) sound sensors; (<b>c</b>) vibration sensor.</p>
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<p>Measured and numerical results of the bottom plate for the bridge: (<b>a</b>) acceleration level; (<b>b</b>) sound pressure level.</p>
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<p>Measured and numerical results: (<b>a</b>) track slab vibration; (<b>b</b>) sound pressure level at N1.</p>
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<p>Measured and numerical noise around the elevated urban rail transit system: (<b>a</b>) N6; (<b>b</b>) N9.</p>
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<p>The force for different tracks: (<b>a</b>) wheel–rail force; (<b>b</b>) supporting spring force.</p>
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<p>Sound pressure levels for different tracks: (<b>a</b>) bridge structure-borne noise; (<b>b</b>) track slab noise; (<b>c</b>) wheel–rail noise.</p>
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<p>Sound pressure levels for different tracks: (<b>a</b>) bridge structure-borne noise; (<b>b</b>) track slab noise; (<b>c</b>) wheel–rail noise.</p>
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<p>Contour map of the total noise at the mid-span section of the box-girder bridge with MTB_60.</p>
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<p>Contour map of the insertion loss at the mid-span section of the box-girder for various tracks: (<b>a</b>) MTB_20; (<b>b</b>) MTB _40; (<b>c</b>) TST; (<b>d</b>) FST.</p>
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<p>Contour map of the insertion loss at the mid-span section of the box-girder for various tracks: (<b>a</b>) MTB_20; (<b>b</b>) MTB _40; (<b>c</b>) TST; (<b>d</b>) FST.</p>
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9 pages, 3854 KiB  
Proceeding Paper
The Mechanical Characterization of a Gyroid-Based Metamaterial by Compression Testing
by Andrea Ciula, Gianluca Rubino and Pierluigi Fanelli
Eng. Proc. 2025, 85(1), 17; https://doi.org/10.3390/engproc2025085017 - 18 Feb 2025
Abstract
Gyroid-based mechanical metamaterials have garnered increasing attention for their unique mechanical properties, particularly in applications involving complex stress environments. This study focuses on the mechanical characterization of the gyroid cell, a member of the Triply Periodic Minimal Surfaces (TPMS) family, through both experimental [...] Read more.
Gyroid-based mechanical metamaterials have garnered increasing attention for their unique mechanical properties, particularly in applications involving complex stress environments. This study focuses on the mechanical characterization of the gyroid cell, a member of the Triply Periodic Minimal Surfaces (TPMS) family, through both experimental and numerical analyses. Three different gyroid morphologies were generated by varying a single parameter in the parametric equation of the gyroid surface. Specimens were fabricated by 3D printing based on Liquid Crystal Display (LCD) technology, and compression tests were conducted to measure the equivalent Young’s modulus. Numerical models developed using Finite Element Method (FEM) analysis were validated through the experimental findings. The results indicate a good correlation between the experimental and numerical data, particularly in the linear elastic region, confirming the suitability of FEM simulations in predicting the mechanical response of these cellular structures. The study serves as a foundational step towards a broader multi-physical characterization of TPMS-based metamaterials and paves the way for the future development of tailored metamaterials for specific applications, including sacrificial limiters in plasma-facing components of Tokamaks. Full article
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<p>Isometric view (<b>top</b>) and top view along z axis (<b>bottom</b>) of isometric gyroid cell (<b>left</b>) and two manipulated cell morphologies (<b>center</b> and <b>right</b>).</p>
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<p>Isotropic gyroid cell (cyan) and offset surfaces obtained with a non-zero constant term d (blue and yellow).</p>
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<p>Top, side, and isometric views and 3D-printed samples of the three examined cell morphologies with different values of parameter <span class="html-italic">a</span>.</p>
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<p>Force–displacement curves for all the compression tests. The dotted line is associated with a specimen printed in a different batch than all the others. The thick line indicates a specimen that has been previously lapped. In this figure, the settling zone (<b>a</b>) and the linear zone (<b>b</b>) are clearly distinguishable. The ranges in which the peak load values for cells of the same morphology fall are rather wide compared to their absolute value (<b>c</b>).</p>
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<p>Force–displacement curves of tested specimens with <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> obtained from experimental tests compared with numerical result from a model with the same morphology. The slope of the linear zone and the peak load are shown for each experimental curve.</p>
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<p>Force–displacement curves of tested specimens with <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> obtained from experimental tests compared with the numerical result from a model with the same morphology. The slope of the linear zone and the peak load are shown for each experimental curve.</p>
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<p>Force–displacement curves of tested specimens with <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> obtained from experimental tests compared with the numerical result from a model with the same morphology. The slope of the linear zone and the peak load are shown for each experimental curve.</p>
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<p>Trends derived from experimental analysis and confirmed by the FEM model of equivalent Young’s modulus <math display="inline"><semantics> <msub> <mi>E</mi> <mrow> <mi>e</mi> <mi>q</mi> </mrow> </msub> </semantics></math>, maximum load <math display="inline"><semantics> <msub> <mi>L</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </semantics></math>, and maximum displacement <math display="inline"><semantics> <msub> <mi>d</mi> <mrow> <mi>L</mi> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </semantics></math> as gyroid cell parameter <span class="html-italic">a</span> changes.</p>
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<p>Typical Von Mises equivalent stress distribution on the three gyroid cells investigated.</p>
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26 pages, 10090 KiB  
Article
Wear Resistance of Additively Manufactured Footwear Soles
by Shuo Xu, Shuvodeep De, Meysam Khaleghian and Anahita Emami
Lubricants 2025, 13(2), 89; https://doi.org/10.3390/lubricants13020089 - 17 Feb 2025
Abstract
This study systematically evaluated the wear resistance and mechanical performance of 3D-printed thermoplastic rubber (TPR) and flexible stereolithography (SLA) resin materials for footwear outsoles. Abrasion tests were conducted on 26 samples (2 materials × 13 geometries) to analyze the weight loss, variations in [...] Read more.
This study systematically evaluated the wear resistance and mechanical performance of 3D-printed thermoplastic rubber (TPR) and flexible stereolithography (SLA) resin materials for footwear outsoles. Abrasion tests were conducted on 26 samples (2 materials × 13 geometries) to analyze the weight loss, variations in the friction coefficient, temperature change, and deformation behavior. Finite element method (FEM) simulations incorporating the Ogden hyperelastic model were employed to investigate the stress distribution and wear patterns. The results revealed that TPR exhibits superior abrasion resistance and stable wear curves, making it suitable for high-load applications. On average, the TPR samples showed 27.3% lower weight loss compared to the SLA resin samples. The SLA resin samples exhibited a 65% higher mean coefficient of friction (COF) compared to the TPR samples. Furthermore, the SLA resin samples demonstrated a 94% higher temperature change during the sliding tests, reflecting greater friction-induced heating. The FEM simulations further validated TPR’s performance in high-stress regions and SLA resin’s deformation characteristics. This study’s findings not only highlight the performance differences between these two 3D-printed materials but also provide theoretical guidance for material selection based on wear behavior, contributing to the optimization of outsole design and its practical applications. Full article
(This article belongs to the Special Issue Wear and Friction in Hybrid and Additive Manufacturing Processes)
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<p>Pre-printing sample models for the Atomstack Cambrian 3D printer (1–13) and SLA printer (14–26) and the printed samples before abrasion testing.</p>
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<p>Sliding friction and wear test setup.</p>
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<p>The abrasion test friction force for the SLA resin sample 19 and TPR sample 6.</p>
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<p>The abrasion test weight loss of the testing samples: (<b>a</b>) TPR, and (<b>b</b>) SLA resin sample comparison.</p>
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<p>Contrast between the weight loss of sample 4 (TPR) and sample 17 (Resin) over the distances of testing.</p>
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<p>The mean COFs of concrete conditions for samples 1 through 26 for the first test.</p>
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<p>Key factors influencing wear.</p>
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<p>The wear damage results after an abrasion test: (<b>a</b>,<b>b</b>) depict the TPR samples, and (<b>c</b>–<b>e</b>) depict the resin samples.</p>
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<p>(<b>a</b>) The temperature change of samples 1 through 26. (<b>b</b>) Comparison of the temperature change between TRR and SLA.</p>
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<p>The wear and degradation results of different material surfaces after the abrasion test.</p>
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<p>FEM results compared with the experimental deformation for sample 17.</p>
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<p>FEM results compared with the experimental deformation for samples 1 vs. 14, 2 vs. 15, and 6 vs. 19.</p>
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<p>FEM results compared with the experimental deformation for samples 1 and 14.</p>
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<p>FEM results compared with the experimental deformation for shape-shifting sample 10.</p>
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<p>Samples printed with resin material.</p>
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<p>Model and boundary condition.</p>
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<p>(<b>a</b>) Coarse mesh with an average element edge length of 1 mm. (<b>b</b>) Refined mesh with an average element edge length of 0.8 mm. (<b>c</b>) von Mises stress plot for the coarse mesh. (<b>d</b>) von Mises stress plot for the coarse mesh.</p>
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20 pages, 4119 KiB  
Article
Multi-Harmonic Nonlinear Ultrasonic Fusion with Deep Learning for Subtle Parameter Identification of Micro-Crack Groups
by Qi Lin, Xiaoyang Bi, Xiangyan Ding, Bo Yang, Bingxi Liu, Xiao Yang, Jie Xue, Mingxi Deng and Ning Hu
Sensors 2025, 25(4), 1152; https://doi.org/10.3390/s25041152 - 13 Feb 2025
Abstract
Fatigue crack defects in metallic materials significantly reduce the remaining useful life (RUL) of parts. However, much of the existing research has focused on identifying single-millimeter-scale cracks using individual nonlinear ultrasonic responses. The identification of subtle parameters from complex ultrasonic responses of micro-crack [...] Read more.
Fatigue crack defects in metallic materials significantly reduce the remaining useful life (RUL) of parts. However, much of the existing research has focused on identifying single-millimeter-scale cracks using individual nonlinear ultrasonic responses. The identification of subtle parameters from complex ultrasonic responses of micro-crack groups remains a significant challenge in the field of nondestructive testing. We propose a novel multi-harmonic nonlinear response fusion identification method integrated with a deep learning (DL) model to identify the subtle parameters of micro-crack groups. First, we trained a one-dimensional convolutional neural network (1D CNN) with various time-domain signals obtained from finite element method (FEM) models and analyzed the sensitivity of different harmonic nonlinear responses to various subtle parameters of micro-crack groups. Then, high harmonics were fused to perform a decoupled identification of multiple subtle parameters. We enhanced the Dempster–Shafer (DS) evidence theory used in decision fusion by accounting for different sensitivities, achieving an identification accuracy of 93.73%. Building on this, we assigned sensor weights based on our proposed new conflict measurement method and further conducted decision fusion on the decision results from multiple ultrasonic sensors. Our proposed method achieves an identification accuracy of 95.68%. Full article
(This article belongs to the Section Physical Sensors)
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<p>The bilinear constitutive relation between stress and strain.</p>
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<p>The FEM model.</p>
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<p>(<b>a</b>) The truncated <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>U</mi> </mrow> <mrow> <mi>b</mi> </mrow> </msub> <mi mathvariant="normal">’</mi> </mrow> </semantics></math>. (<b>b</b>) The frequency domain. (<b>c</b>) The second harmonic. (<b>d</b>) The third harmonic.</p>
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<p>The overall subtle parameters space of the micro-crack groups.</p>
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<p>The identification framework for a single subtle parameter.</p>
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<p>The mean identification accuracies of quantity parameters under the different size conditions of (<b>a</b>) 0.22–0.40 mm, (<b>b</b>) 0.42–0.60 mm, (<b>c</b>) 0.62–0.80 mm, and (<b>d</b>) 0.82–1.00 mm.</p>
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<p>The mean identification accuracies of size parameters under the different quantity conditions of (<b>a</b>) 10–100, (<b>b</b>) 110–200, and (<b>c</b>) 210–300.</p>
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<p>The mean decoupled identification accuracies for quantity and size parameters.</p>
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<p>The decoupled identification framework at three levels for multiple subtle parameters: (<b>a</b>) Data-level fusionⅠ (data concatenating); (<b>b</b>) data-level fusionⅡ (multi-channel inputting); (<b>c</b>) feature-level fusion; (<b>d</b>) decision-level fusion.</p>
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<p>The decoupled identification framework of multi-sensor decision-level fusion for multiple subtle parameters.</p>
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<p>(<b>a</b>) The mean decoupled identification accuracies of quantity and size parameters. (<b>b</b>) The confusion matrix.</p>
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25 pages, 8099 KiB  
Article
Assessment of Externally Prestressed Beams with FRP Rebars Considering Bond–Slip Effects
by Zhangxiang Li, Bo Chen, Xueliang Wang and Tiejiong Lou
Materials 2025, 18(4), 787; https://doi.org/10.3390/ma18040787 - 11 Feb 2025
Abstract
This paper presents detailed numerical modeling of externally prestressed concrete (EPC) beams with fiber-reinforced polymer (FRP) rebars. Particular attention is paid to the bond–slip interactions between FRP rebars and concrete. A refined 3D finite element model (FEM) incorporating a script describing the bond–slip [...] Read more.
This paper presents detailed numerical modeling of externally prestressed concrete (EPC) beams with fiber-reinforced polymer (FRP) rebars. Particular attention is paid to the bond–slip interactions between FRP rebars and concrete. A refined 3D finite element model (FEM) incorporating a script describing the bond–slip of FRP rebars and concrete is developed in ABAQUS. The model effectiveness, rooted in the interface behavior between FRP rebars and concrete, is comprehensively assessed using experimental data. A comprehensive investigation has been conducted using FEM on the mechanical behavior of carbon fiber-reinforced polymer (CFRP) tendon–EPC beams with FRP rebars. Due to the bond–slip effect, FRP rebars in EPC beams exhibit a distinct phenomenon of stress degradation. This suggests that the traditional method based on plane cross-sectional assumptions is no longer suitable for the engineering design of EPC beams with FRP rebars. Moreover, the study assesses several models including typical design codes for their accuracy in predicting the elevation of ultimate stress in external tendons. It is demonstrated that some of the design codes are overly conservative when estimating the tendon stress in EPC beams with FRP rebars. Full article
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Figure 1
<p>Stress–strain responses for the materials employed. (<b>a</b>) concrete under compression; (<b>b</b>) concrete under tension; (<b>c</b>) prestressing tendons; (<b>d</b>) bonded rebars.</p>
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<p>Bond stress–slip graphs of FRP rebars and concrete. (<b>a</b>) ribbed FRP; (<b>b</b>) plain FRP [<a href="#B31-materials-18-00787" class="html-bibr">31</a>,<a href="#B32-materials-18-00787" class="html-bibr">32</a>,<a href="#B36-materials-18-00787" class="html-bibr">36</a>,<a href="#B37-materials-18-00787" class="html-bibr">37</a>].</p>
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<p>Assignment in mesh attribute and connector of specimens.</p>
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<p>Comparison with test data for bond–slip model validation. (<b>a</b>) C1; (<b>b</b>) C2 [<a href="#B38-materials-18-00787" class="html-bibr">38</a>].</p>
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<p>Simple EPC beams. (<b>a</b>) dimensions and rebar details; (<b>b</b>) external tendon configuration; (<b>c</b>) FEM mesh of T-2.</p>
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<p>Damage nephograms of T-2.</p>
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<p>Validation against tests. (<b>a</b>) load vs. midspan deflection; (<b>b</b>) load vs. tendon stress [<a href="#B40-materials-18-00787" class="html-bibr">40</a>].</p>
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<p>Externally prestressed T-beams for numerical assessment.</p>
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<p>FEM mesh of EPC beams.</p>
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<p>Nephograms of structure and bond rebars for typical beams.</p>
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<p>Effect of rebar type. (<b>a</b>) midspan deflection vs. load; (<b>b</b>) load vs. tendon stress increase; (<b>c</b>) tensile rebar strain vs. load.</p>
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<p>Effect of rebar type. (<b>a</b>) deflection vs. tendon stress increment; (<b>b</b>) moment vs. curvature; (<b>c</b>) moment vs. neutral axis depth.</p>
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<p>Effect of GFRP rebar elastic modulus. (<b>a</b>) midspan deflection vs. load; (<b>b</b>) load vs. tendon stress increase; (<b>c</b>) tensile rebar strain vs. load.</p>
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<p>Effect of concrete grade. (<b>a</b>) midspan deflection vs. load; (<b>b</b>) load vs. tendon stress increase; (<b>c</b>) tensile rebar strain vs. load.</p>
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<p>Effect of concrete grade. (<b>a</b>) deflection vs. tendon stress increment; (<b>b</b>) moment vs. curvature; (<b>c</b>) moment vs. neutral axis depth.</p>
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<p>Effect of reinforcement ratio on the load-deflection behavior. (<b>a</b>) EPC beams with CFRP rebars; (<b>b</b>) EPC beams with GFRP rebars.</p>
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<p>Ultimate behavior with varying reinforcement ratio. (<b>a</b>) ultimate deflection; (<b>b</b>) ultimate load; (<b>c</b>) ultimate tendon stress.</p>
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<p>Ultimate behavior with varying reinforcement ratio. (<b>a</b>) ultimate curvature; (<b>b</b>) ultimate neutral axis depth; (<b>c</b>) ultimate tensile rebar strain.</p>
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<p>Numerical and code predictions on Δ<span class="html-italic">σ<sub>p</sub></span>. (<b>a</b>) variation in Δ<span class="html-italic">σ<sub>p</sub></span> based on <span class="html-italic">ω</span><sub>0</sub>; (<b>b</b>) variation in Δ<span class="html-italic">σ<sub>p</sub></span> based on <span class="html-italic">c<sub>u</sub></span>/<span class="html-italic">d<sub>p</sub></span> [<a href="#B23-materials-18-00787" class="html-bibr">23</a>,<a href="#B43-materials-18-00787" class="html-bibr">43</a>,<a href="#B44-materials-18-00787" class="html-bibr">44</a>,<a href="#B45-materials-18-00787" class="html-bibr">45</a>,<a href="#B46-materials-18-00787" class="html-bibr">46</a>].</p>
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<p>Comparison of Δ<span class="html-italic">σ<sub>p</sub></span> by simplified models with numerical predictions [<a href="#B23-materials-18-00787" class="html-bibr">23</a>,<a href="#B43-materials-18-00787" class="html-bibr">43</a>,<a href="#B44-materials-18-00787" class="html-bibr">44</a>,<a href="#B45-materials-18-00787" class="html-bibr">45</a>,<a href="#B46-materials-18-00787" class="html-bibr">46</a>].</p>
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30 pages, 17496 KiB  
Article
Frequency-Domain Finite Element Modeling of Seismic Wave Propagation Under Different Boundary Conditions
by Ying Zhang, Haiyang Liu, Shikun Dai and Herui Zhang
Mathematics 2025, 13(4), 578; https://doi.org/10.3390/math13040578 - 10 Feb 2025
Abstract
Seismic wave propagation in complex terrains, especially in the presence of air layers, plays a crucial role in accurate subsurface imaging. However, the influence of different boundary conditions on seismic wave propagation characteristics has not been fully explored. This study employs the finite [...] Read more.
Seismic wave propagation in complex terrains, especially in the presence of air layers, plays a crucial role in accurate subsurface imaging. However, the influence of different boundary conditions on seismic wave propagation characteristics has not been fully explored. This study employs the finite element method (FEM) to simulate and analyze seismic wavefields under different boundary conditions, including perfectly matched layer (PML), Neumann free boundary conditions, and air layer conditions. First, the finite element solution for the 2D frequency-domain acoustic wave equation is introduced, and the correctness of the algorithm is validated using a homogeneous model. Then, both horizontal and undulating terrain interfaces are designed to investigate the kinematic and dynamic characteristics of the wavefields under different boundary conditions. The results show that PML boundaries effectively absorb seismic waves, prevent reflections, and ensure stable wave propagation, making them an ideal choice for simulating open boundaries. In contrast, Neumann boundaries generate significant reflected waves, particularly in undulating terrains, complicating the wavefield characteristics. Introducing an air layer alters the dynamics of the wavefield, leading to energy leakage and multi-path effects, which are more consistent with real-world seismic-geophysical models. Finally, the computational results using the Overthrust model under different boundary conditions further demonstrate that different boundary conditions significantly affect wavefield morphology. It is essential to select appropriate boundary conditions based on the specific simulation requirements, and boundary conditions with an air layer are most consistent with real seismic geological models. This study provides new insights into the role of boundary conditions in seismic numerical simulations and offers theoretical guidance for improving the accuracy of wavefield simulations in realistic geological scenarios. Full article
(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction, 2nd Edition)
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<p>Schematic diagram of model adaptive meshing.</p>
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<p>Schematic diagram of the homogeneous model. The red star represents a point source.</p>
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<p>Frequency-domain wavefield of the homogeneous model. ((<b>a</b>–<b>c</b>) are the real parts of the wavefield of 20 Hz, 40 Hz, and 60 Hz, and (<b>d</b>–<b>f</b>) are the imaginary parts of the wavefield of 20 Hz, 40 Hz, and 60 Hz).</p>
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<p>Time-domain wavefield snapshot of homogeneous model. (<b>a</b>–<b>f</b>) represent the wavefield snapshots at 0.05 s, 0.1 s, 0.15 s, 0.2 s, 0.3 s, and 0.4 s, respectively.</p>
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<p>Seismic trace record at z = 0 m.</p>
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<p>Models under different boundary conditions when the seismic source is located on the ground. The red star represents a point source. ((<b>a</b>) is the PML absorption boundary condition used on the ground, (<b>b</b>) is the free boundary condition used on the ground, and (<b>c</b>) is the addition of an air layer and the PML absorption boundary used above the air layer).</p>
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<p>When the seismic source is located on the ground, the real parts of the wavefield with frequencies of 20 Hz, 40 Hz, and 60 Hz under different boundary conditions. ((<b>a</b>–<b>c</b>) are the real parts of the wavefield with different frequencies under PML absorption boundary conditions, (<b>d</b>–<b>f</b>) are the real parts of the wavefield with different frequencies under Neumann boundary conditions, and (<b>g</b>–<b>i</b>) are the real parts of the wavefield with different frequencies considering the air layer).</p>
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<p>When the seismic source is located on the ground, the imaginary parts of the wavefield with frequencies of 20 Hz, 40 Hz, and 60 Hz under different boundary conditions. ((<b>a</b>–<b>c</b>) are the imaginary parts of the wavefield with different frequencies under PML absorption boundary conditions, (<b>d</b>–<b>f</b>) are the imaginary parts of the wavefield with different frequencies under Neumann boundary conditions, and (<b>g</b>–<b>i</b>) are the imaginary parts of the wavefield with different frequencies considering the air layer).</p>
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<p>Comparison of wavefield details captured under different boundary conditions at 20 Hz. The red arrow compares the wavefield energy near the source; the yellow arrow compares the wavefield shape near the surface. ((<b>a</b>–<b>c</b>) are the real parts of the 20 Hz wavefield under PML, Neumann, and air layer boundary conditions, respectively; (<b>d</b>–<b>f</b>) are the imaginary parts of the 20 Hz wavefield under PML, Neumann, and air layer boundary conditions, respectively).</p>
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<p>When the seismic source is located on the ground, the real and imaginary parts of the 20 Hz wavefield under different boundary conditions. ((<b>a</b>) is the comparison of the real part of the 20 Hz wavefield, and (<b>b</b>) is the comparison of the imaginary part of the 20 Hz wavefield).</p>
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<p>When the seismic source is located on the ground, the real and imaginary parts of the 40 Hz wavefield under different boundary conditions. ((<b>a</b>) is the comparison of the real part of the 40 Hz wavefield, and (<b>b</b>) is the comparison of the imaginary part of the 40 Hz wavefield).</p>
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<p>When the seismic source is located on the ground, the real and imaginary parts of the 60 Hz wavefield under different boundary conditions. ((<b>a</b>) is the comparison of the real part of the 60 Hz wavefield, and (<b>b</b>) is the comparison of the imaginary part of the 60 Hz wavefield).</p>
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<p>Comparison of wavefield snapshots under different boundary conditions when the seismic source is located on the ground. ((<b>a</b>–<b>c</b>) are snapshots of the wavefield at 0.05 s, 0.1 s, and 0.15 s under PML boundary conditions; (<b>d</b>–<b>f</b>) are snapshots of the wavefield at 0.05 s, 0.1 s, and 0.15 s under Neumann boundary conditions; and (<b>g</b>–<b>i</b>) are snapshots of the wavefield at 0.05 s, 0.1 s, and 0.15 s considering the air layer).</p>
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<p>Comparison of wavefield snapshots under different boundary conditions after removing the air layer. ((<b>a</b>–<b>c</b>) are snapshots of the wavefield at 0.05 s, 0.1 s, and 0.15 s under PML boundary conditions; (<b>d</b>–<b>f</b>) are snapshots of the wavefield at 0.05 s, 0.1 s, and 0.15 s under Neumann boundary conditions; and (<b>g</b>–<b>i</b>) are snapshots of the wavefield at 0.05 s, 0.1 s, and 0.15 s considering the air layer).</p>
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<p>Comparison curves of wavefield at different depths at 0.05 s under different boundary conditions when the seismic source is located on the ground.</p>
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<p>Comparison curves of wavefield at different depths at 0.1 s under different boundary conditions when the seismic source is located on the ground.</p>
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<p>Comparison curves of wavefield at different depths at 0.15 s under different boundary conditions when the seismic source is located on the ground.</p>
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<p>Seismic trace records under different boundary conditions when the source is on the ground. (<b>a</b>) PML. (<b>b</b>) Neumann. (<b>c</b>) With air layer.</p>
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<p>Model under different boundary conditions when the seismic source is located underground. The red star represents a point source. ((<b>a</b>) is the ground using PML absorption boundary conditions, (<b>b</b>) is the ground using free boundary conditions, and (<b>c</b>) is the addition of an air layer and the use of PML absorption boundaries above the air layer).</p>
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<p>When the seismic source is located underground, the real parts of the wavefield with frequencies of 20 Hz, 40 Hz, and 60 Hz under different boundary conditions. ((<b>a</b>–<b>c</b>) are the real parts of the wavefield with different frequencies under PML absorption boundary conditions, (<b>d</b>–<b>f</b>) are the real parts of the wavefield with different frequencies under Neumann boundary conditions, and (<b>g</b>–<b>i</b>) are the real parts of the wavefield with different frequencies considering the air layer).</p>
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<p>When the seismic source is located underground, the imaginary parts of the wavefield with frequencies of 20 Hz, 40 Hz, and 60 Hz under different boundary conditions. ((<b>a</b>–<b>c</b>) are the imaginary parts of the wavefield with different frequencies under PML absorption boundary conditions, (<b>d</b>–<b>f</b>) are the imaginary parts of the wavefield with different frequencies under Neumann boundary conditions, and (<b>g</b>–<b>i</b>) are the imaginary parts of the wavefield with different frequencies considering the air layer).</p>
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<p>When the seismic source is located underground, the real and imaginary parts of the 20 Hz wavefield under different boundary conditions. ((<b>A</b>) is the comparison of the real part of the 20 Hz wavefield, and (<b>B</b>) is the comparison of the imaginary part of the 20 Hz wavefield. In (<b>A</b>), (<b>a</b>−<b>f</b>) represent the real part of the wavefield at depths of 0 m, 100 m, 200 m, 300 m, 400 m, and 500 m, respectively. In (<b>B</b>), (<b>a</b>−<b>f</b>) represent the imaginary part of the wavefield at depths of 0 m, 100 m, 200 m, 300 m, 400 m, and 500 m, respectively).</p>
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<p>When the seismic source is located underground, the real and imaginary parts of the 40 Hz wavefield under different boundary conditions. ((<b>A</b>) is the comparison of the real part of the 40 Hz wavefield, and (<b>B</b>) is the comparison of the imaginary part of the 40 Hz wavefield. In (<b>A</b>), (<b>a</b>−<b>f</b>) represent the real part of the wavefield at depths of 0 m, 100 m, 200 m, 300 m, 400 m, and 500 m, respectively. In (<b>B</b>), (<b>a</b>−<b>f</b>) represent the imaginary part of the wavefield at depths of 0 m, 100 m, 200 m, 300 m, 400 m, and 500 m, respectively).</p>
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<p>When the seismic source is located underground, the real and imaginary parts of the 60 Hz wavefield under different boundary conditions. ((<b>A</b>) is the comparison of the real part of the 60 Hz wavefield, and (<b>B</b>) is the comparison of the imaginary part of the 60 Hz wavefield. In (<b>A</b>), (<b>a</b>−<b>f</b>) represent the real part of the wavefield at depths of 0 m, 100 m, 200 m, 300 m, 400 m, and 500 m, respectively. In (<b>B</b>), (<b>a</b>−<b>f</b>) represent the imaginary part of the wavefield at depths of 0 m, 100 m, 200 m, 300 m, 400 m, and 500 m, respectively).</p>
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<p>Comparison of wavefield snapshots under different boundary conditions when the seismic source is located underground. ((<b>a</b>–<b>c</b>) are snapshots of the wavefield at 0.05 s, 0.1 s, and 0.2 s under PML boundary conditions, respectively; (<b>d</b>–<b>f</b>) are snapshots of the wavefield at 0.05 s, 0.1 s, and 0.2 s under Neumann boundary conditions, respectively; and (<b>g</b>–<b>i</b>) are snapshots of the wavefield at 0.05 s, 0.1 s, and 0.2 s, respectively, when considering the air layer).</p>
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<p>Comparison curves of wavefield at different depths under different boundary conditions when the seismic source is located underground. ((<b>a</b>) is the waveform comparison curve at 0.05 s, (<b>b</b>) is the waveform comparison curve at 0.1 s, and (<b>c</b>) is the waveform comparison curve at 0.2 s).</p>
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<p>Seismic trace records under different boundary conditions when the epicenter is located underground.</p>
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<p>Model under different boundary conditions in undulating terrain conditions. The red star represents a point source. (The seismic source located on the ground). (<b>a</b>) The ground adopts PML absorption boundary conditions. (<b>b</b>) The ground adopts free boundary conditions. (<b>c</b>) Adds an air layer and uses PML absorption boundary above the air layer.</p>
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<p>Under undulating terrain conditions, the real parts of the wavefield with frequencies of 20 Hz, 40 Hz, and 60 Hz under different boundary conditions. ((<b>a</b>–<b>c</b>) are the real parts of the wavefield with different frequencies under PML absorption boundary conditions, (<b>d</b>–<b>f</b>) are the real parts of the wavefield with different frequencies under Neumann boundary conditions, and (<b>g</b>–<b>i</b>) are the real parts of the wavefield with different frequencies considering the air layer).</p>
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<p>Under undulating terrain conditions, the imaginary parts of the wavefield with frequencies of 20 Hz, 40 Hz, and 60 Hz under different boundary conditions. ((<b>a</b>–<b>c</b>) are the imaginary parts of the wavefield with different frequencies under PML absorption boundary conditions, (<b>d</b>–<b>f</b>) are the imaginary parts of the wavefield with different frequencies under Neumann boundary conditions, and (<b>g</b>–<b>i</b>) are the imaginary parts of the wavefield with different frequencies considering the air layer).</p>
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<p>Comparison of the details of the real and imaginary parts of the wave field captured at 20 Hz under different boundary conditions in undulating terrain conditions. The red arrow compares the wavefield energy near the ground. ((<b>a</b>–<b>c</b>) are the real parts of the 20 Hz wavefield under PML, Neumann, and air layer boundary conditions, respectively; (<b>d</b>–<b>f</b>) are the imaginary parts of the 20 Hz wavefield under PML, Neumann, and air layer boundary conditions, respectively).</p>
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<p>Under undulating terrain conditions, the real and imaginary parts of the 20 Hz wavefield under different boundary conditions. ((<b>A</b>) is the comparison of the real part of the 20 Hz wavefield, and (<b>B</b>) is the comparison of the imaginary part of the 20 Hz wavefield. In (<b>A</b>), (<b>a</b>−<b>f</b>) represent the real part of the wavefield at depths of 0 m, 100 m, 200 m, 300 m, 400 m, and 500 m, respectively. In (<b>B</b>), (<b>a</b>−<b>f</b>) represent the imaginary part of the wavefield at depths of 0 m, 100 m, 200 m, 300 m, 400 m, and 500 m, respectively).</p>
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<p>Under undulating terrain conditions, the real and imaginary parts of the 40 Hz wavefield under different boundary conditions. ((<b>A</b>) is the comparison of the real part of the 40 Hz wavefield, and (<b>B</b>) is the comparison of the imaginary part of the 40 Hz wavefield. In (<b>A</b>), (<b>a</b>−<b>f</b>) represent the real part of the wavefield at depths of 0 m, 100 m, 200 m, 300 m, 400 m, and 500 m, respectively. In (<b>B</b>), (<b>a</b>−<b>f</b>) represent the imaginary part of the wavefield at depths of 0 m, 100 m, 200 m, 300 m, 400 m, and 500 m, respectively).</p>
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<p>Under undulating terrain conditions, the real and imaginary parts of the 60 Hz wavefield under different boundary conditions. ((<b>A</b>) is the comparison of the real part of the 60 Hz wavefield, and (<b>B</b>) is the comparison of the imaginary part of the 60 Hz wavefield. In (<b>A</b>), (<b>a</b>−<b>f</b>) represent the real part of the wavefield at depths of 0 m, 100 m, 200 m, 300 m, 400 m, and 500 m, respectively. In (<b>B</b>), (<b>a</b>−<b>f</b>) represent the imaginary part of the wavefield at depths of 0 m, 100 m, 200 m, 300 m, 400 m, and 500 m, respectively).</p>
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<p>Comparison of snapshot images of different boundary wavefields under undulating terrain conditions. ((<b>a</b>–<b>c</b>) are snapshots of the wavefield at 0.05 s, 0.1 s, and 0.15 s under PML boundary conditions; (<b>d</b>–<b>f</b>) are snapshots of the wavefield at 0.05 s, 0.1 s, and 0.15 s under Neumann boundary conditions; and (<b>g</b>–<b>i</b>) are snapshots of the wavefield at 0.05 s, 0.1 s, and 0.15 s when considering the air layer).</p>
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<p>Overthrust onshore model.</p>
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<p>Real part of 30 Hz seismic wavefield under different boundary conditions. ((<b>a</b>–<b>c</b>) are the real parts of the 30 Hz wavefield under PML, Neumann, and air layer boundary conditions, respectively; (<b>d</b>–<b>f</b>) represent the vertical variation curves of the wavefield at x = 1000 m, 2500 m, and 4000 m, respectively).</p>
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<p>Comparison of wavefield snapshots under different boundary conditions. ((<b>a</b>–<b>c</b>) are snapshots of the wavefield at 0.1 s, 0.2 s, and 0.3 s under PML boundary conditions; (<b>d</b>–<b>f</b>) are snapshots of the wavefield at 0.1 s, 0.2 s, and 0.3 s under Neumann boundary conditions; and (<b>g</b>–<b>i</b>) are snapshots of the wavefield at 0.1 s, 0.2 s, and 0.3 s when considering the air layer).</p>
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<p>Comparison of seismic traces under different boundary conditions (z = 0 m). (<b>a</b>) PML. (<b>b</b>) Neumann. (<b>c</b>) With air layer.</p>
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20 pages, 4194 KiB  
Article
Algorithm for Acoustic Wavefield in Space-Wavenumber Domain of Vertically Heterogeneous Media Using NUFFT
by Ying Zhang and Shikun Dai
Mathematics 2025, 13(4), 571; https://doi.org/10.3390/math13040571 - 9 Feb 2025
Abstract
Balancing efficiency and accuracy is often challenging in the numerical solution of three-dimensional (3D) point source acoustic wave equations for layered media. To overcome this, an efficient solution method in the spatial-wavenumber domain is proposed, utilizing the Non-Uniform Fast Fourier Transform (NUFFT) to [...] Read more.
Balancing efficiency and accuracy is often challenging in the numerical solution of three-dimensional (3D) point source acoustic wave equations for layered media. To overcome this, an efficient solution method in the spatial-wavenumber domain is proposed, utilizing the Non-Uniform Fast Fourier Transform (NUFFT) to achieve arbitrary non-uniform sampling. By performing a two-dimensional (2D) Fourier transform on the 3D acoustic wave equation in the horizontal direction, the 3D equation is transformed into a one-dimensional (1D) space-wavenumber-domain ordinary differential equation, effectively simplifying significant 3D problems into one-dimensional problems and significantly reducing the demand for memory. The one-dimensional finite-element method is applied to solve the boundary value problem, resulting in a pentadiagonal system of equations. The Thomas algorithm then efficiently solves the system, yielding the layered wavefield distribution in the space-wavenumber domain. Finally, the wavefield distribution in the spatial domain is reconstructed through a 2D inverse Fourier transform. The correctness of the algorithm was verified by comparing it with the finite-element method. The analysis of the half-space model shows that this method can accurately calculate the wavefield distribution in the air layer considering the air layer while exhibiting high efficiency and computational stability in ultra-large-scale models. The three-layer medium model test further verified the adaptability and accuracy of the algorithm in calculating the distribution of acoustic waves in layered media. Through a sensitivity analysis, it is shown that the denser the mesh node partitioning, the higher the medium velocity, and the lower the point source frequency, the higher the accuracy of the algorithm. An algorithm efficiency analysis shows that this method has extremely low memory usage and high computational efficiency and can quickly solve large-scale models even on personal computers. Compared with traditional FEM, the algorithm has much higher advantages in terms of memory usage and efficiency. This method provides a new approach to the numerical solution of partial differential equations. It lays an essential foundation for background field calculation in the scattering seismic numerical simulation and full-waveform inversion of acoustic waves, with strong theoretical significance and practical application value. Full article
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<p>Schematic diagram of layered media.</p>
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<p>The analytical solution of the wavenumber domain for a point source in full space on the z = 0 m plane. (<b>a</b>–<b>c</b>) represent the real parts of the wavefield spectra at frequencies of 5 Hz, 15 Hz, and 30 Hz, respectively, while (<b>d</b>–<b>f</b>) represent the imaginary parts of the wavefield spectra at frequencies of 5 Hz, 15 Hz, and 30 Hz, respectively.</p>
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<p>Algorithm flowchart.</p>
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<p>The numerical solution, analytical solution, and absolute error of the point source in the full space of the z = 0 m plane. (<b>a</b>–<b>c</b>) are the numerical solution, analytical solution, and absolute error of the real part of the point source acoustic wavefield, respectively; (<b>d</b>–<b>f</b>) are the numerical solution, analytical solution, and absolute error of the imaginary part of the point source acoustic wavefield, respectively.</p>
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<p>Half-space model diagram. The red star represents a point source.</p>
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<p>Calculation results of the real and imaginary parts of the wavefield in the half-space of the y = 50 m section; (<b>a</b>) 5 Hz (real part), (<b>b</b>) 10 Hz (real part), (<b>c</b>) 20 Hz (real part), (<b>d</b>) 5 Hz (imaginary part), (<b>e</b>) 10 Hz (imaginary part), (<b>f</b>) 20 Hz (imaginary part).</p>
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<p>A 3D display of the real and imaginary parts of the half-space wavefield; (<b>a</b>) 5 Hz (real part), (<b>b</b>) 5 Hz (imaginary part), (<b>c</b>) 10 Hz (real part), (<b>d</b>) 10 Hz (imaginary part), (<b>e</b>) 20 Hz (real part), (<b>f</b>) 20 Hz (imaginary part).</p>
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<p>Three-layer medium model diagram. The red star represents a point source.</p>
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<p>Calculation results of the real and imaginary parts of the wavefield in the half-space of the y = 50 m profile; (<b>a</b>) 5 Hz (real part), (<b>b</b>) 15 Hz (real part), (<b>c</b>) 30 Hz (real part), (<b>d</b>) 5 Hz (imaginary part), (<b>e</b>) 15 Hz (imaginary part), (<b>f</b>) 30 Hz (imaginary part).</p>
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<p>A 3D display of the real and imaginary parts of the half-space wavefield; (<b>a</b>) 5 Hz (real part), (<b>b</b>) 5 Hz (imaginary part), (<b>c</b>) 15 Hz (real part), (<b>d</b>) 15 Hz (imaginary part), (<b>e</b>) 30 Hz (real part), (<b>f</b>) 30 Hz (imaginary part).</p>
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24 pages, 19611 KiB  
Article
Field Investigation and Numerical Modeling for the Seismic Assessment of the Castle of Lanjarón, Spain
by Hayden Luger, Rafael Ramirez, Paloma Pineda and Paulo B. Lourenço
Appl. Sci. 2025, 15(3), 1518; https://doi.org/10.3390/app15031518 - 2 Feb 2025
Abstract
The Castle of Lanjarón is a 16th century stronghold located in Andalucía, Spain. After losing its military function, the castle was abandoned, leading to significant decay. Designated a national heritage site in 1985, recent efforts have sought to preserve its historical and cultural [...] Read more.
The Castle of Lanjarón is a 16th century stronghold located in Andalucía, Spain. After losing its military function, the castle was abandoned, leading to significant decay. Designated a national heritage site in 1985, recent efforts have sought to preserve its historical and cultural value. This study outlines an inspection and diagnosis campaign carried out on the castle. Non-destructive tests (NDTs) were employed to characterize the properties of the masonry, using both mechanical and wave-based methods. Dynamic identification was performed to determine dynamic and modal properties of the structure, which were used to develop and calibrate a three-dimensional (3D) finite element model (FEM) of the west wall, based on homogenized masonry material. Limit analysis and non-linear static (pushover) analysis under various boundary conditions were conducted to determine the maximum relative load factor in the out-of-plane direction. The results were compared to the expected peak ground acceleration (PGA) of the area, showing that the maximum load capacity of the wall exceeds local seismic demands with a safety factor of 1.39. The study highlights the efficacy of pairing a homogenized macro-modeling approach with wave-based and dynamic identification methods, particularly for resource efficiency. Finally, recommendations for future conservation efforts have been provided. Full article
(This article belongs to the Special Issue Structural Seismic Design and Evaluation)
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<p>Visual overview of the Castle of Lanjarón: (<b>a</b>) aerial view of the castle looking west [<a href="#B13-applsci-15-01518" class="html-bibr">13</a>]; (<b>b</b>) view of the castle from the south showing the barbican and keep; (<b>c</b>) view of the inner enclosure from the entrance under the keep; (<b>d</b>) view showing the long west wall.</p>
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<p>Current conservation state of the Castle of Lanjarón: (<b>a</b>) state of metallic elements in the castle; (<b>b</b>) alveolized limestone ashlar; (<b>c</b>) blocked drainage tube; (<b>d</b>) significant plant growth on structural elements hides a masonry arch.</p>
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<p>Current conservation state of the Castle of Lanjarón: (<b>a</b>) state of metallic elements in the castle; (<b>b</b>) alveolized limestone ashlar; (<b>c</b>) blocked drainage tube; (<b>d</b>) significant plant growth on structural elements hides a masonry arch.</p>
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<p>(<b>a</b>) Schmidt hammer; (<b>b</b>) Schmidt pendulum hammer; (<b>c</b>) penetrometer; (<b>d</b>) scratch test instrument.</p>
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<p>(<b>a</b>) Indirect sonic test location (extent shown by black rectangle); (<b>b</b>) test grid with locations for vertical indirect sonic tests; (<b>c</b>) test grid with locations for horizontal indirect sonic tests. Hammer impact points are highlighted in yellow, accelerometer points are red, and points with null readings are white.</p>
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<p>(<b>a</b>) Direct sonic test location outside the keep (extent shown by black rectangle); (<b>b</b>) test grid with locations for direct sonic tests.</p>
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<p>Plan view of site with test locations, highlighting the west wall.</p>
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<p>Results from sonic testing: (<b>a</b>) unfiltered elastic moduli by test type; (<b>b</b>) filtered elastic moduli by test type; (<b>c</b>) unfiltered elastic moduli by test distance; (<b>d</b>) filtered elastic moduli by test distance.</p>
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<p>Results from sonic testing: (<b>a</b>) reconstructed dataset after test type filtering; (<b>b</b>) reconstructed dataset after distance filtering.</p>
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<p>FE model of west wall with nodes for MAC calculations.</p>
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<p>Overview of results from dynamic identification: (<b>a</b>) spectral density for west wall setups with estimators; (<b>b</b>) first three mode shapes for the fundamental frequencies of a fixed string.</p>
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<p>Mode shapes for west wall: (<b>a</b>) initial three experimentally determined mode shapes; (<b>b</b>) initial three numerically determined mode shapes.</p>
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<p>(<b>a</b>) MAC comparison between numerical and experimental mode shapes for model considering the addition of a void in the north tower; (<b>b</b>) model representation of the void in the north tower.</p>
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<p>Capacity curve comparing fully fixed and fully free end conditions for pushover analysis of the west wall.</p>
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<p>Results from the pushover analysis of the west wall with free end condition: (<b>a</b>) minimum principal stress (view from the outside of the wall); (<b>b</b>) maximum principal strain (view from the in-side of the wall).</p>
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<p>Results from the pushover analysis of the west wall with fully fixed end condition: (<b>a</b>) minimum principal stress (view from the outside of the wall); (<b>b</b>) maximum principal strain (view from the inside of the wall).</p>
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19 pages, 12564 KiB  
Article
Compressive Properties of Composite Sandwich Structure with Fractal Tree-Inspired Lattice Core
by Jian Han, Xin Ma, Rui Yang and Shiyong Sun
Materials 2025, 18(3), 606; https://doi.org/10.3390/ma18030606 - 29 Jan 2025
Abstract
A novel sandwich structure of a fractal tree-like lattice (SSFL) is proposed. The geometry characteristics were constructed based on the fractal tree-like patterns found in many biological structures, such as giant water lilies and dragon blood trees. The compressive performance of the proposed [...] Read more.
A novel sandwich structure of a fractal tree-like lattice (SSFL) is proposed. The geometry characteristics were constructed based on the fractal tree-like patterns found in many biological structures, such as giant water lilies and dragon blood trees. The compressive performance of the proposed structures with different fractal orders was experimentally and numerically investigated. The experimental samples were made by 3D printing technology. Axial compression tests were conducted to study the compressive performance and failure mode of the SSFLs. The results indicated that the new structure was good at multiple bearing and energy absorption. The finite element method (FEM) was performed to investigate the influence of geometry parameters on the compression behaviors of the SSFLs. The findings of this study provide an effective guide for using the fractal method to design lattice structures with a high bearing capacity. Full article
(This article belongs to the Special Issue Advances in Porous Lightweight Materials and Lattice Structures)
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<p>Evolution of the binary tree. Reprinted with permission from Ref. [<a href="#B39-materials-18-00606" class="html-bibr">39</a>]. 2021, Elsevier Ltd.</p>
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<p>Geometric design of the fractal lattice core.</p>
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<p>Geometric design of the fractal lattice core.</p>
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<p>Test specimens.</p>
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<p>Quasi-static compression finite element model of SSFL (SSFL-1 as an example).</p>
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<p>The critical dimensions of nylon dog-bone.</p>
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<p>Stress–strain response of SSFLs as measured experimentally and predicted by finite element model.</p>
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<p>Deformation mechanism of SSFLs at various strain levels as measured experimentally and predicted by finite element model: (<b>a</b>) SSPL, (<b>b</b>) SSFL-1, and (<b>c</b>) SSFL-2. The Abaqus contour plot is used to visualize the simulation results of the structures. It uses different colors to show the distribution of specific stresses within the model. In this illustration, red indicates that the stresses in the structure have reached the limits of the material, blue indicates zero stress, and green indicates an intermediate stress state.</p>
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<p>Deformation mechanism of SSFLs at various strain levels as measured experimentally and predicted by finite element model: (<b>a</b>) SSPL, (<b>b</b>) SSFL-1, and (<b>c</b>) SSFL-2. The Abaqus contour plot is used to visualize the simulation results of the structures. It uses different colors to show the distribution of specific stresses within the model. In this illustration, red indicates that the stresses in the structure have reached the limits of the material, blue indicates zero stress, and green indicates an intermediate stress state.</p>
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<p>The deformation modes of SSPLs in different cross-sections.</p>
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<p>The deformation modes of the SSFL-1s in different cross-sections.</p>
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<p>The deformation modes of the SSFL-2s in different cross-sections.</p>
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<p>The deformation modes of the SSFL-2s in different cross-sections.</p>
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<p>The stress–strain curves of the SSPLs and SSFLs in different cross-sections: (<b>a</b>) comparison for group A (a = 1, t = 1); (<b>b</b>) comparison for group B (a = 2, t = 1); (<b>c</b>) comparison for group C (a = 1, t = 2); (<b>d</b>) comparison for group D (a = 2, t = 2).</p>
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<p>The stress–strain curves of the SSPLs and SSFLs in different cross-sections: (<b>a</b>) comparison for group A (a = 1, t = 1); (<b>b</b>) comparison for group B (a = 2, t = 1); (<b>c</b>) comparison for group C (a = 1, t = 2); (<b>d</b>) comparison for group D (a = 2, t = 2).</p>
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<p>Comparison of specific energy absorption and unit volume energy absorption of SSPLs and SSFLs in different cross-sections.</p>
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<p>The deformation and stress–strain curves of the SSFLs: (a = 2, t = 1) in different H<sub>A</sub>/H. (<b>a</b>) SSFL-1 in H<sub>A</sub>/H = 10/15; (<b>b</b>) SSFL-2 in H<sub>A</sub>/H = 10/15; (<b>c</b>) SSFL-1 in H<sub>A</sub>/H = 10/17; (<b>d</b>) SSFL-2 in H<sub>A</sub>/H = 10/17; (<b>e</b>) SSFL-1 in H<sub>A</sub>/H = 10/21; (<b>f</b>) SSFL-2 in H<sub>A</sub>/H = 10/21.</p>
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<p>Comparison of specific energy absorption and unit volume energy absorption of SSFLs (a = 2, t = 1) in different H<sub>A</sub>/H.</p>
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<p>The deformation and stress–strain curves of the SSFLs (a = 2, t = 2) in different H<sub>A</sub>/H: (<b>a</b>) SSFL-1 in H<sub>A</sub>/H = 10/16; (<b>b</b>) SSFL-2 in H<sub>A</sub>/H = 10/16; (<b>c</b>) SSFL-1 in H<sub>A</sub>/H = 10/22; (<b>d</b>) SSFL-2 in H<sub>A</sub>/H = 10/22.</p>
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<p>Comparison of specific energy absorption and unit volume energy absorption of SSFLs (a = 2, t = 2) in different H<sub>A</sub>/H.</p>
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31 pages, 11675 KiB  
Review
Recording of Historic Buildings and Monuments for FEA: Current Practices and Future Directions
by Francesca Turchetti, Branka Cuca, Daniela Oreni and Athos Agapiou
Heritage 2025, 8(2), 55; https://doi.org/10.3390/heritage8020055 - 28 Jan 2025
Abstract
Cultural heritage (CH) sites and monuments share significant historical and cultural value, but at the same time, these are highly vulnerable to deterioration due to age, construction methods, and materials used. Therefore, stability studies for CH structures through numerical analyses allow researchers and [...] Read more.
Cultural heritage (CH) sites and monuments share significant historical and cultural value, but at the same time, these are highly vulnerable to deterioration due to age, construction methods, and materials used. Therefore, stability studies for CH structures through numerical analyses allow researchers and stakeholders to safeguard them against time and exposure to hazards. To obtain reliable results for stability studies, detailed and accurate geometric documentation is needed prior to any modeling or simulation. In this context, geomatics technologies like LiDAR and photogrammetry can offer great support in documenting their structural integrity, providing efficient, non-invasive data collection methods that generate 3D point clouds. Nevertheless, despite the benefits, geomatic methods remain underutilized in structural engineering due to limitations in converting 3D point clouds directly for use in finite element modeling (FEM) analysis. The paper aims to review current approaches for the generation of FE models for structural analysis employing data obtained from 3D digital surveys. Each approach is described in detail, providing examples from literature and highlighting its advantages and disadvantages. Studies show that analysis accuracy depends strongly on point cloud level of detail, underlining the importance of precise geomatic surveys. Emerging workflows and semi-automated methods enable point clouds to be integrated with BIM (building information modeling) and FEM, thereby enhancing the contribution that laser scanning techniques and 3D modeling provide for the analysis of the stability of structures belonging to cultural heritage. Full article
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<p>Overlay visualization by VOSviewer© of the number of citations for each keyword (represented by the size of the dots) with respect to the year of publication.</p>
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<p>Distribution of publications over the years.</p>
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<p>Geographic distribution of the first author’s affiliation, referred to the publications from 2007 to 2024, on the topic “FEM generation from point cloud for CH”.</p>
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<p>Classification of the methods for the development of FE models.</p>
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<p>Percentage distribution of methods for the development of finite element models, related to publications from 2007 to 2024.</p>
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<p>Example of the conversion of a point cloud (<b>a</b>) into FE model (<b>b</b>). This example shows one of the columns of Tombs 7 in Tombs of the Kings in Paphos, Cyprus.</p>
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<p>Localization of Tomb 7, Tombs of the Kings, Paphos, Cyprus.</p>
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<p>Example of a possible workflow for manual modeling.</p>
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<p>Example of a possible workflow for the scan-to-BIM-to-FEM approach.</p>
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<p>Flowchart of the voxel-based method.</p>
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<p>Workflow of the method “Convert mesh to NURBS”. A zoomed-in view of the mesh texture is evidenced in the red box.</p>
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<p>Flowchart of the method “Convert mesh to Solid model”.</p>
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12 pages, 5835 KiB  
Article
Biomechanical Optimization of the Human Bite Using Numerical Analysis Based on the Finite Element Method
by Maribel González-Martín, Paula Hermida-Cabrera, Aida Gutiérrez-Corrales, Eusebio Torres-Carranza, Gonzalo Ruiz-de-León, Berta García-Mira, Álvaro-José Martínez-González, Daniel Torres-Lagares, María-Ángeles Serrera-Figallo, José-Luis Gutiérrez-Pérez and María Baus-Domínguez
Biomimetics 2025, 10(2), 80; https://doi.org/10.3390/biomimetics10020080 - 28 Jan 2025
Abstract
Biomechanical bite analysis is essential for understanding occlusal forces and their distribution, especially in the design and validation of dental prostheses. Although the finite element method (FEM) has been widely used to evaluate these forces, the existing models often lack accuracy due to [...] Read more.
Biomechanical bite analysis is essential for understanding occlusal forces and their distribution, especially in the design and validation of dental prostheses. Although the finite element method (FEM) has been widely used to evaluate these forces, the existing models often lack accuracy due to simplified geometries and limited material properties. Methods: A detailed finite element model was developed using Abaqus Standard 2023 software (Dassault Systemes, Vélizy-Villacoublay, France), incorporating scanned 3D geometries of mandibular and maxillary bones. The model included cortical and cancellous bones (Young’s modulus: 5.5 GPa and 13.7 GPa, respectively) and was adjusted to simulate bite forces of 220.7 N based on experimental data. Occlusal forces were evaluated using flexible connectors that replicate molar-to-molar interactions, and the stress state was analyzed in the maxillary and mandibular bones. Results: The FEM model consisted of 1.68 million elements, with mesh sizes of 1–1.5 mm in critical areas. Bite forces on the molars were consistent with clinical trials: first molar (59.3 N), second molar (34.4 N), and third molar (16.7 N). The results showed that the maximum principal stresses in the maxillary bones did not exceed ±5 MPa, validating the robustness of the model for biomechanical predictions. Conclusion: The developed model provides an accurate and validated framework for analyzing the distribution of occlusal forces in intact dentures. This approach allows the evaluation of complex prosthetic configurations and their biomechanical impact, optimizing future designs to reduce clinical complications and improve long-term outcomes. The integration of high-resolution FEM models with clinical data establishes a solid foundation for the development of predictive tools in restorative dentistry. Full article
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<p>Distribution of bite pressures from the article by Turkistani et al [<a href="#B1-biomimetics-10-00080" class="html-bibr">1</a>]. The colour scale (not included in the reference) is defined from blue to red, where red indicates the highest pressure.</p>
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<p>FEM model of bite analysis with intact dentition. (<b>a</b>) General lateral view; (<b>b</b>) detail of lateral view; (<b>c</b>) Tie-type kinematic constraints; (<b>d</b>) temporomandibular joint. Different colours have been defined for clarity, and only represent different parts of the model skull. The only exception is image c, where the purple colour represents the articulation between the bones using Tie-type kinematic constraints. In addition, image d has been updated to better show the point of the temporomandibular joint.</p>
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<p>FEM model of bite analysis with intact dentition. (<b>a</b>) General lateral view; (<b>b</b>) detail of lateral view; (<b>c</b>) Tie-type kinematic constraints; (<b>d</b>) temporomandibular joint. Different colours have been defined for clarity, and only represent different parts of the model skull. The only exception is image c, where the purple colour represents the articulation between the bones using Tie-type kinematic constraints. In addition, image d has been updated to better show the point of the temporomandibular joint.</p>
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<p>Model of the interaction between teeth. Green is for solid FEM elements. Red for the spring element that model the interaction and yellow for the distributing coupling that distributes the interaction force to the tooth surface.</p>
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<p>Forces exerted by maxillary muscles and tendons.</p>
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<p>Occlusion forces in 220.7 N bite.</p>
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<p>Stress state: (<b>a</b>) maximum principal stresses [N/mm<sup>2</sup>]; (<b>b</b>) minimum principal stresses [N/mm<sup>2</sup>].</p>
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15 pages, 8194 KiB  
Article
Electromagnetically Driven Robot for Multipurpose Applications
by Abdulrahman Alrumayh, Khaled Alhassoon, Fahd Alsaleem, Mahmoud Shaban and Fahad Nasser Alsunaydih
Appl. Sci. 2025, 15(2), 973; https://doi.org/10.3390/app15020973 - 20 Jan 2025
Viewed by 317
Abstract
This paper presents a novel design of a continuum robot driven by electromagnets and springs, offering enhanced precision in multi-degree-of-freedom bending for diverse applications. Traditional continuum robots, while effective in navigating constrained environments, often face limitations in actuation methods, such as wire-based systems [...] Read more.
This paper presents a novel design of a continuum robot driven by electromagnets and springs, offering enhanced precision in multi-degree-of-freedom bending for diverse applications. Traditional continuum robots, while effective in navigating constrained environments, often face limitations in actuation methods, such as wire-based systems or pre-curved tubes. Our design overcomes these challenges by utilizing electromagnetically driven actuation, which allows each segment of the robot to bend independently at any angle, providing unprecedented flexibility and control. The technical challenges discussed emphasize the goals of this work, with the main aim being to develop a motion control system that uses electromagnets and springs to improve the accuracy and consistency of the robot’s movements. By balancing magnetic and spring forces, our system ensures predictable and stable motion in 3D space. The integration of this mechanism into multi-segmented robots opens up new possibilities in fields such as medical devices, search and rescue operations, and industrial inspection. Finite element method (FEM) simulations validate the efficiency of the proposed approach, demonstrating the precise control of the robot’s motion trajectory and enhancing its operational reliability in complex scenarios. Full article
(This article belongs to the Section Robotics and Automation)
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<p>(<b>a</b>) Block diagram of the proposed robot system, (<b>b</b>) actuator driving circuit, and (<b>c</b>) robots frame and segments.</p>
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<p>Single segment of the robotic design.</p>
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<p>The proposed disassemble parts.</p>
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<p>Force direction.</p>
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<p>Simulation of the magnetic field between electromagnet and PM.</p>
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<p>Magnetic field patterns on a permanent magnet.</p>
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<p>(<b>a</b>) The triangle edges to create the angle. (<b>b</b>) Illustrations of robot movement in different directions and angles.</p>
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<p>Variation in angle during robot movement.</p>
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<p>(<b>a</b>) Variation in current during robot movement based on angle. (<b>b</b>) Generated magnetic field based on angle and current.</p>
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<p>The magnetic force between the electromagnet and the permanent magnet.</p>
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<p>Travelling distance of one segment of the robot in the <span class="html-italic">x</span>-<span class="html-italic">y</span> direction.</p>
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25 pages, 5935 KiB  
Article
Mechanical Behavior of PEEK and PMMA Graphene and Ti6Al4V Implant-Supported Frameworks: In Silico Study
by Mariano Herrero-Climent, Fernando Sanchez-Lasheras, Jordi Martinez-Lopez, Javier Gil and Aritza Brizuela-Velasco
Materials 2025, 18(2), 441; https://doi.org/10.3390/ma18020441 - 18 Jan 2025
Viewed by 530
Abstract
A comparative analysis has been carried out between three different dental materials suitable for the prostheses manufacturing. The analysis performed is based on the finite elements method (FEM) and was made to evaluate their performance under three different loading conditions. Three different materials [...] Read more.
A comparative analysis has been carried out between three different dental materials suitable for the prostheses manufacturing. The analysis performed is based on the finite elements method (FEM) and was made to evaluate their performance under three different loading conditions. Three different materials were modeled with 3D CAD geometry, all of them suitable to be simulated by means of a linear elastic model. The materials employed were graphene polymethyl methacrylate (G-PMMA) with 0.25% of graphene, polyether ether ketone (PEEK), and Ti6Al4V. Three loading conditions have been defined: distal, medial, and central. In all cases under study, the load was applied progressively, 5 N by 5 N until a previously fixed threshold of 25 N was reached, which always ensures that work is carried out in the elastic zone. The behavior of G-PMMA and PEEK in the tests performed is similar. Regarding maximum deformations in the model, it has been found that deformations are higher in the G-PMMA models when compared to those made of PEEK. The highest values of maximum stress according to the von Mises criteria are achieved in models made of Ti6Al4V, followed by G-PMMA and PEEK. G-PMMA is more prone to plastic deformations compared to Ti6Al4V. However, due to its relatively higher stiffness compared to other common polymers, G-PMMA is able to withstand moderate stress levels before significant deformation occurs, placing it in the intermediate position between Ti6Al4V and PEEK in terms of stress capacity. It should be noted that there is also a difference in the results obtained depending on the applied load, whether distal, medial, or central, proving that, in all simulations, it is the distal test that offers the worst results in terms of presenting a higher value for both displacement and tension. The results obtained allow us to identify the advantages and limitations of each material in terms of structural strength, mechanical behavior, and adaptability to loading conditions that simulate realistic scenarios. Full article
(This article belongs to the Special Issue Advanced Dental Materials: From Design to Application, Second Volume)
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<p>Finite elements model: (<b>a</b>) Meshed 3D view of the model employed for the present research; (<b>b</b>) detail of the mesh.</p>
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<p>Load application points in the models under study (D: distal, M: medial, and C: central). Positions A, B, C, D and E are where dental implants are placed.</p>
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<p>Prosthetic structure obtained for the mechanical tests.</p>
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<p>Flexural mechanical test (<b>a</b>) G-PMMA, (<b>b</b>) PEEK, (<b>c</b>) Ti6Al4V.</p>
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<p>Mid-plane deformation map of the distally loaded G-PMMA model (units: mm).</p>
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<p>Deformation map of the Ti6Al4V bushing most affected by the application of the distal load in the G-PMMA model (units: mm).</p>
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<p>Stress map of the G-PMMA model with distal loading (units: MPa).</p>
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<p>Stress map of the most loaded bushing of Ti6Al4V in the G-PMMA model with distal load.</p>
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<p>Mid-plane deformation map of the distally loaded PEEK model (units: mm).</p>
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<p>Deformation map of the Ti6Al4V bushing most affected by the application of the distal load in the PEEK model (units: mm).</p>
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<p>Stress map of the PEEK model with distal loading (units: MPa).</p>
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<p>Stress map of the most loaded bushing of Ti6Al4V in the PEEK model with distal load.</p>
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<p>Mid-plane deformation map of the distally loaded Ti6Al4V model (units: mm).</p>
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<p>Deformation map of the Ti6Al4V bushing most affected by the application of the distal load in the Ti6Al4V model (units: mm).</p>
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<p>Stress map of the Ti6Al4V model with distal loading (units: MPa).</p>
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<p>Stress map of the most loaded bushing of Ti6Al4V in the Ti6Al4V model with distal load.</p>
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<p>Maximum deformation of all the models (in mm.) by materials and force position.</p>
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<p>Maximum stress values according to the von Mises criteria of all the models (MPa.) by materials and force position.</p>
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<p>Maximum deformation values (in mm.) achieved in the most loaded bushes of each model by materials and force position.</p>
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<p>Maximum stress by von Mises criteria (in MPa) achieved in the most loaded bushes of each model by materials and force position.</p>
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<p>Deformation in millimeters obtained under a load of 150 N in flexural tests.</p>
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