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Search Results (755)

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Keywords = continuum mechanics

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24 pages, 1111 KiB  
Review
Music Listening as Exploratory Behavior: From Dispositional Reactions to Epistemic Interactions with the Sonic World
by Mark Reybrouck, Piotr Podlipniak and David Welch
Behav. Sci. 2024, 14(9), 825; https://doi.org/10.3390/bs14090825 (registering DOI) - 16 Sep 2024
Viewed by 278
Abstract
Listening to music can span a continuum from passive consumption to active exploration, relying on processes of coping with the sounds as well as higher-level processes of sense-making. Revolving around the major questions of “what” and “how” to explore, this paper takes a [...] Read more.
Listening to music can span a continuum from passive consumption to active exploration, relying on processes of coping with the sounds as well as higher-level processes of sense-making. Revolving around the major questions of “what” and “how” to explore, this paper takes a naturalistic stance toward music listening, providing tools to objectively describe the underlying mechanisms of musical sense-making by weakening the distinction between music and non-music. Starting from a non-exclusionary conception of “coping” with the sounds, it stresses the exploratory approach of treating music as a sound environment to be discovered by an attentive listener. Exploratory listening, in this view, is an open-minded and active process, not dependent on simply recalling pre-existing knowledge or information that reduces cognitive processing efforts but having a high cognitive load due to the need for highly focused attention and perceptual readiness. Music, explored in this way, is valued for its complexity, surprisingness, novelty, incongruity, puzzlingness, and patterns, relying on processes of selection, differentiation, discrimination, and identification. Full article
(This article belongs to the Special Issue Music Listening as Exploratory Behavior)
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<p>Overview of the elicitor–response schematic with modulating factors and transfer function. Reprinted from [<a href="#B11-behavsci-14-00825" class="html-bibr">11</a>]. (Copyright © 2022 Reybrouck and Eerola. Creative Commons Attribution License (CC BY)).</p>
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<p>Spectrographic depiction of birdsong (nightingale, about 22 s, <b>upper pane</b>) and a piece of music (Bartók, Sonata for two pianos and percussion, 3rd movement, about 27 s, <b>lower pane</b>). The diagrams indicate time (<span class="html-italic">x</span>-axis) and frequency (<span class="html-italic">y</span>-axis) with the darker regions indicating more energy.</p>
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32 pages, 18298 KiB  
Article
CFD Analyses of Density Gradients under Conditions of Supersonic Flow at Low Pressures
by Robert Bayer, Petr Bača, Jiří Maxa, Pavla Šabacká, Tomáš Binar and Petr Vyroubal
Sensors 2024, 24(18), 5968; https://doi.org/10.3390/s24185968 - 14 Sep 2024
Viewed by 259
Abstract
This paper deals with CFD analyses of the difference in the nature of the shock waves in supersonic flow under atmospheric pressure and pressure conditions at the boundary of continuum mechanics for electron microscopy. The first part describes the verification of the CFD [...] Read more.
This paper deals with CFD analyses of the difference in the nature of the shock waves in supersonic flow under atmospheric pressure and pressure conditions at the boundary of continuum mechanics for electron microscopy. The first part describes the verification of the CFD analyses in combination with the experimental chamber results and the initial analyses using optical methods at low pressures on the boundary of continuum mechanics that were performed. The second part describes the analyses on an underexpanded nozzle performed to analyze the characteristics of normal shock waves in a pressure range from atmospheric pressure to pressures at the boundary of continuum mechanics. The results obtained by CFD modeling are prepared as a basis for the design of the planned experimental sensing of density gradients using optical methods, and for validation, the expected pressure and temperature courses from selected locations suitable for the placement of temperature and pressure sensors are prepared from the CFD analyses. Full article
(This article belongs to the Section Physical Sensors)
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<p>Real experimental chamber (<b>a</b>), simplified 2D axisymmetric model of the experimental chamber (<b>b</b>), scheme of the ESEM (<b>c</b>), and scheme of the experimental chamber (<b>d</b>).</p>
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<p>Structured mesh for the CFD analysis (<b>a</b>), with the zoomed area showing the mesh refinement (<b>b</b>).</p>
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<p>Changes in the state variables across a normal shock wave.</p>
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<p>Used optical system.</p>
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<p>Two-dimensional axisymmetric model of the chambers for the CFD analysis, with labeled boundary conditions (<b>a</b>) and with the zoomed area showing its dimensions (mm) (<b>b</b>).</p>
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<p>Points of the pressure measurements on the nozzle wall in the experimental chamber.</p>
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<p>Mach number distribution.</p>
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<p>Static pressure distribution.</p>
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<p>Path along which selected state variables are plotted (blue line).</p>
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<p>Static pressure and Mach number layout on the path.</p>
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<p>Static temperature (<b>a</b>) and velocity (<b>b</b>) distribution on the path.</p>
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<p>Static temperature and density layout on the path.</p>
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<p>First velocity derivative imaging.</p>
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<p>Graphical density gradient distribution (<b>a</b>) and density gradient layout on the path (<b>b</b>).</p>
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<p>Locations for the <span class="html-italic">y+</span> verification.</p>
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<p>Points for the Reynolds number verification.</p>
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<p>Design of the shortened nozzle with its dimensions (mm) (<b>a</b>) with an emphasized nozzle outlet diameter (line) with the point for the values from the CFD simulations (<b>b</b>).</p>
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<p>Mach number layout of the shortened nozzle for each variant on the path (axis).</p>
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<p>Two-dimensional axisymmetric model of the underexpanded nozzle of the chambers for the CFD analysis with labeled boundary conditions (<b>a</b>) and with the zoomed area showing its dimensions (mm) (<b>b</b>).</p>
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<p>Mach number layout of each variant on the path (axis).</p>
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<p>Axis of the flow (blue line—path).</p>
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<p>Mach number layout of each variant on the path (axis) with the adjusted scale.</p>
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<p>Mach number layout of each variant on the path (axis) with another adjusted scale.</p>
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<p>Pressure layout of each variant on the path (axis).</p>
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<p>Pressure layout of each variant on the path (axis) with the adjusted scale.</p>
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<p>Pressure layout of each variant on the path (axis) with another adjusted scale.</p>
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<p>Pressure layout of each variant on the path (axis) with different adjusted scale.</p>
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<p>Density gradient layout of each variant on the path (axis).</p>
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<p>Examined nozzle surface (red line—nozzle wall).</p>
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<p>Pressure layout of each variant on the nozzle wall.</p>
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<p>Temperature layout of each variant on the nozzle wall.</p>
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<p>Points for the Reynolds number verification.</p>
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<p>Mach number distribution of each variant: 101,325 Pa (<b>a</b>), 50,000 Pa (<b>b</b>), 10,000 Pa (<b>c</b>), 5000 Pa (<b>d</b>), and 2000 Pa (<b>e</b>).</p>
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<p>Pressure distribution of each variant: 101,325 Pa (<b>a</b>), 50,000 Pa (<b>b</b>), 10,000 Pa (<b>c</b>), 5000 Pa (<b>d</b>), and 2000 Pa (<b>e</b>).</p>
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<p>Density gradient distribution of each variant: 101,325 Pa (<b>a</b>), 50,000 Pa (<b>b</b>), 10,000 Pa (<b>c</b>), 5000 Pa (<b>d</b>), and 2000 Pa (<b>e</b>).</p>
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26 pages, 8179 KiB  
Article
Unraveling the Effect of Strain Rate and Temperature on the Heterogeneous Mechanical Behavior of Polymer Nanocomposites via Atomistic Simulations and Continuum Models
by Ali A. Youssef, Hilal Reda and Vagelis Harmandaris
Polymers 2024, 16(17), 2530; https://doi.org/10.3390/polym16172530 - 6 Sep 2024
Viewed by 398
Abstract
Polymer nanocomposites are characterized by heterogeneous mechanical behavior and performance, which is mainly controlled by the interaction between the nanofiller and the polymer matrix. Optimizing their material performance in engineering applications requires understanding how both the temperature and strain rate of the applied [...] Read more.
Polymer nanocomposites are characterized by heterogeneous mechanical behavior and performance, which is mainly controlled by the interaction between the nanofiller and the polymer matrix. Optimizing their material performance in engineering applications requires understanding how both the temperature and strain rate of the applied deformation affect mechanical properties. This work investigates the effect of strain rate and temperature on the mechanical properties of poly(ethylene oxide)/silica (PEO/SiO2) nanocomposites, revealing their behavior in both the melt and glassy states, via atomistic molecular dynamics simulations and continuum models. In the glassy state, the results indicate that Young’s modulus increases by up to 99.7% as the strain rate rises from 1.0 × 10−7 fs−1 to 1.0 × 10−4 fs−1, while Poisson’s ratio decreases by up to 39.8% over the same range. These effects become even more pronounced in the melt state. Conversely, higher temperatures lead to an opposing trend. A local, per-atom analysis of stress and strain fields reveals broader variability in the local strain of the PEO/SiO2 nanocomposites as temperature increases and/or the deformation rate decreases. Both interphase and matrix regions lose rigidity at higher temperatures and lower strain rates, blurring their distinctiveness. The results of the atomistic simulations concerning the elastic modulus and Poisson’s ratio are in good agreement with the predictions of the Richeton–Ji model. Additionally, these findings can be leveraged to design advanced polymer composites with tailored mechanical properties and could optimize structural components by enhancing their performance under diverse engineering conditions. Full article
(This article belongs to the Special Issue Rheological Properties of Polymers and Polymer Composites)
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Graphical abstract

Graphical abstract
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<p>Snapshots of the PEO/SiO<sub>2</sub> model systems, using periodically wrapped coordinates, in (<b>a</b>) initial (equilibrium) and (<b>b</b>) deformed in the x direction (ε = 0.4) configurations at T = 270 K. Blue dots represent the nearly spherical SiO<sub>2</sub> nanoparticle, while red dots represent the surrounding PEO polymer in the unit cell system.</p>
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<p>Variations in mechanical properties with temperature and strain rate: (<b>a</b>) Young modulus, (<b>b</b>) Poisson ratio. Darker colors indicate a transition towards a glassy state (higher E &amp; lower ν values), while lighter colors represent a more fluid, melty state (lower E &amp; higher ν values).</p>
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<p>Linear mechanical properties of the PEO/SiO<sub>2</sub> nanocomposites model as a function of strain rate: (<b>a</b>) Young’s modulus, (<b>b</b>) Poisson’s ratio. The error bars are computed by analyzing ten uncorrelated configurations. The percentage error values between the MD simulation results and the RJ model are displayed above each data point on the plot.</p>
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<p>Linear mechanical properties of the PEO/SiO<sub>2</sub> nanocomposite model as a function of temperature: (<b>a</b>) Young’s modulus, (<b>b</b>) Poison’s ratio. The error bars are computed by analyzing ten uncorrelated configurations. The percentage error values between the MD simulation results and the RJ model are displayed above each data point on the plot.</p>
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<p>Schematic overview of designated zones within spheres around the nanoparticle in an in-plane box section.</p>
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<p>Elasticity modulus variations in (<b>a</b>) interphase and (<b>b</b>) matrix regions with temperature and strain rate dependency.</p>
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<p>PNC’s elasticity modulus as a function of strain rate for systems at temperatures (<b>a</b>) below <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mi>g</mi> </mrow> </msub> </mrow> </semantics></math> (220 K), (<b>b</b>) equal to <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mi>g</mi> </mrow> </msub> </mrow> </semantics></math> (270 K), and (<b>c</b>) above <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mi>g</mi> </mrow> </msub> </mrow> </semantics></math> (330 K).</p>
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<p>Elasticity modulus of PEO/SiO<sub>2</sub> nanocomposites as a function of temperature for systems at strain rates (<b>a</b>) 1.0 × 10<sup>−5</sup> fs<sup>−1</sup> and (<b>b</b>) 1.0 × 10<sup>−6</sup> fs<sup>−1</sup>.</p>
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<p>Analysis of the standard deviation with respect to the global strain and (inset) probability distribution of the local strain. The red, black, and blue curves represent the probability distribution in frames corresponding to global strains of 0.03, 0.06, and 0.09, respectively. The line styles for the red and blue inset plots match the legend of the black inset. (<b>a</b>–<b>c</b>) For bulk regions at 220 K, 270 K, and 330 K, respectively; and (<b>d</b>–<b>f</b>) for interphase regions at 220 K, 270 K, and 330 K, respectively.</p>
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<p>Variation in the mean-squared displacement (<b>a</b>) along x-direction and (<b>b</b>) for all components (sum of MSD along x, y, and z directions) in the interphase and matrix regions as a function of global applied strain under different strain rates, for systems at temperatures below (220 K), at (270 K), and above (330 K) the glass transition temperature (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mi>g</mi> </mrow> </msub> </mrow> </semantics></math>).</p>
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<p>Variation in the mean-squared displacement (<b>a</b>) along x-direction and (<b>b</b>) for all components (sum of MSD along x, y, and z directions) in the interphase and matrix regions as a function of global applied strain under different strain rates, for systems at temperatures below (220 K), at (270 K), and above (330 K) the glass transition temperature (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mi>g</mi> </mrow> </msub> </mrow> </semantics></math>).</p>
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<p>Temperature effect (150–400 K) on systems at constant strain rates: (<b>a</b>) <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>ε</mi> </mrow> <mo>˙</mo> </mover> </mrow> </semantics></math> = 1.0 × 10<sup>−5</sup> (<span class="html-italic">fs</span><sup>−1</sup>) and (<b>b</b>) <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>ε</mi> </mrow> <mo>˙</mo> </mover> </mrow> </semantics></math> = 1.0 × 10<sup>−6</sup> (<span class="html-italic">fs</span><sup>−1</sup>).</p>
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<p>Strain rate effect on systems at constant temperatures: (<b>a</b>) T220 K, (<b>b</b>) T270 K, and (<b>c</b>) T330 K.</p>
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13 pages, 2413 KiB  
Article
Modeling and Vibration Analysis of Carbon Nanotubes as Nanomechanical Resonators for Force Sensing
by Jun Natsuki, Xiao-Wen Lei, Shihong Wu and Toshiaki Natsuki
Micromachines 2024, 15(9), 1134; https://doi.org/10.3390/mi15091134 - 6 Sep 2024
Viewed by 403
Abstract
Carbon nanotubes (CNTs) have attracted considerable attention as nanomechanical resonators because of their exceptional mechanical properties and nanoscale dimensions. In this study, a novel CNT-based probe is proposed as an efficient nanoforce sensing nanomaterial that detects external pressure. The CNT probe was designed [...] Read more.
Carbon nanotubes (CNTs) have attracted considerable attention as nanomechanical resonators because of their exceptional mechanical properties and nanoscale dimensions. In this study, a novel CNT-based probe is proposed as an efficient nanoforce sensing nanomaterial that detects external pressure. The CNT probe was designed to be fixed by clamping tunable outer CNTs. By using the mobile-supported outer CNT, the position of the partially clamped outer CNT can be controllably shifted, effectively tuning its resonant frequency. This study comprehensively investigates the modeling and vibration analysis of gigahertz frequencies with loaded CNTs used in sensing applications. The vibration frequency of a partially clamped CNT probe under axial loading was modeled using continuum mechanics, considering various parameters such as the clamping location, length, and boundary conditions. In addition, the interaction between external forces and CNT resonators was investigated to evaluate their sensitivity for force sensing. Our results provide valuable insights into the design and optimization of CNT-based nanomechanical resonators for high-performance force sensing applications. Full article
(This article belongs to the Special Issue Two-Dimensional Materials for Electronic and Optoelectronic Devices)
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<p>Analytical model of cantilevered CNT-based probe clamped in movable outer nanotube.</p>
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<p>Dependence of vibrational frequency on external force in the CNT probe with clamping length (<span class="html-italic">s</span> = 20 nm) and different positions (<span class="html-italic">a</span>).</p>
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<p>Dependence of clamping location on vibrational frequency in the CNT probe under different external forces <span class="html-italic">F</span> (<span class="html-italic">s</span> = 20 nm).</p>
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<p>Influence of vdW interaction coefficient (<span class="html-italic">k<sub>w</sub></span>) on the vibrational frequency of CNT at clamping position of <span class="html-italic">a</span> = 15 nm, and clamping length of <span class="html-italic">s</span> = 20 nm.</p>
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<p>Relationship between the vibrational frequency and the position ratio for different nonlocal scale parameters (<span class="html-italic">s</span> = 20 nm, and an axial force of 8 nN).</p>
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<p>Relationship between vibrational frequency and axial compressive axial force for different nonlocal scale parameters (<span class="html-italic">a</span> = 15 nm, <span class="html-italic">s</span> = 20 nm).</p>
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<p>Dependence of the position ratio on the frequency shift under different external forces <span class="html-italic">F</span> (<span class="html-italic">s</span> = 20 nm).</p>
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17 pages, 4862 KiB  
Article
Modelling and Characterisation of Orthotropic Damage in Aluminium Alloy 2024
by Nenad Djordjevic, Ravindran Sundararajah, Rade Vignjevic, James Campbell and Kevin Hughes
Materials 2024, 17(17), 4281; https://doi.org/10.3390/ma17174281 - 29 Aug 2024
Viewed by 341
Abstract
The aim of the work presented in this paper was development of a thermodynamically consistent constitutive model for orthotopic metals and determination of its parameters based on standard characterisation methods used in the aerospace industry. The model was derived with additive decomposition of [...] Read more.
The aim of the work presented in this paper was development of a thermodynamically consistent constitutive model for orthotopic metals and determination of its parameters based on standard characterisation methods used in the aerospace industry. The model was derived with additive decomposition of the strain tensor and consisted of an elastic part, derived from Helmholtz free energy, Hill’s thermodynamic potential, which controls evolution of plastic deformation, and damage orthotopic potential, which controls evolution of damage in material. Damage effects were incorporated using the continuum damage mechanics approach, with the effective stress and energy equivalence principle. Material characterisation and derivation of model parameters was conducted with standard specimens with a uniform cross-section, although a number of tests with non-uniform cross-sections were also conducted here. The tests were designed to assess the extent of damage in material over a range of plastic deformation values, where displacement was measured locally using digital image correlation. The new model was implemented as a user material subroutine in Abaqus and verified and validated against the experimental results for aerospace-grade aluminium alloy 2024-T3. Verification was conducted in a series of single element tests, designed to separately validate elasticity, plasticity and damage-related parts of the model. Validation at this stage of the development was based on comparison of the numerical results with experimental data obtained in the quasistatic characterisation tests, which illustrated the ability of the modelling approach to predict experimentally observed behaviour. A validated user material subroutine allows for efficient simulation-led design improvements of aluminium components, such as stiffened panels and the other thin-wall structures used in the aerospace industry. Full article
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<p>Instron 8032 Servo hydraulic test machine with tensile test specimen and 3D Dantec digital image correlation system Q400.</p>
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<p>AA2024-T3 specimens used for quasistatic testing: (<b>a</b>) standard specimen with uniform size of the gauge cross-section, denoted UCS; (<b>b</b>) specimen with non-uniform size of the gauge cross-section, where plastic deformation was localised within a small zone in the middle of the gauge section, denoted VCS.</p>
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<p>(<b>a</b>) UCS specimen sample images of optical measurement using Dantec 3D DIC system Q400 images and (<b>b</b>) longitudinal strain surface distribution just before failure (range from 0 to 240).</p>
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<p>(<b>a</b>) UCS specimen sample images of optical measurement using Dantec 3D DIC system Q400 images and (<b>b</b>) longitudinal strain surface distribution just before failure (range from 0 to 240).</p>
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<p>True stress true strain curves obtained with two specimens: standard uniform cross-section (UCS) and specimen with varying cross-section (VSC).</p>
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<p>Instron 8032 Servo hydraulic machine cyclic test input (cross-head displacement versus time) used in Dantec Dynamics Q-400 DIC non-contact measurements.</p>
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<p>AA2024-T3 cyclic test results in rolling 0° direction with the unloading/reloading slopes that determine elastic modulus degradation due to damage; black lines represent the Young’s moduli of material at a certain level of plastic deformation.</p>
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<p>AA2024-T3 uniaxial cyclic test data from coupons for damage characterisation of AA-2024-T3 material on elastic modulus degradation ratio versus plastic strain.</p>
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<p>B vs. β fit from uniaxial experimental results of AA-2024-T3 material cyclic tests, R<sup>2</sup> = 1.</p>
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<p>True stress—true strain curves calculated from the uniaxial experimental data. R<sup>2</sup> = 0.983.</p>
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<p>Constitutive model implementation flow chart for the damage model.</p>
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<p>FEM models with considered mesh size, boundary conditions and damage contour output.</p>
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<p>Uniaxial tensile stress test: experimental results versus simulation results.</p>
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<p>Evolution of damage variables versus true strain: rolling direction, <math display="inline"><semantics> <mrow> <msub> <mi>D</mi> <mn>1</mn> </msub> </mrow> </semantics></math> (0 degree to rolling direction), transverse direction <math display="inline"><semantics> <mrow> <msub> <mi>D</mi> <mn>2</mn> </msub> </mrow> </semantics></math> (90 degree to rolling direction or transverse direction (TD)) and <math display="inline"><semantics> <mrow> <msub> <mi>D</mi> <mn>3</mn> </msub> </mrow> </semantics></math> (through-thickness direction TTD).</p>
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28 pages, 3030 KiB  
Perspective
Crime and Nourishment: A Narrative Review Examining Ultra-Processed Foods, Brain, and Behavior
by Susan L. Prescott, Alan C. Logan, Erica M. LaFata, Ashka Naik, David H. Nelson, Matthew B. Robinson and Leslie Soble
Dietetics 2024, 3(3), 318-345; https://doi.org/10.3390/dietetics3030025 - 28 Aug 2024
Viewed by 925
Abstract
Recently, there has been increased scientific and clinical interest in the potential harms associated with ultra-processed foods, including poor mental health, aggression, and antisocial behavior. Research spanning epidemiology, mechanistic pre-clinical work, addiction science, microbiome and exposome science, and human intervention trials has underscored [...] Read more.
Recently, there has been increased scientific and clinical interest in the potential harms associated with ultra-processed foods, including poor mental health, aggression, and antisocial behavior. Research spanning epidemiology, mechanistic pre-clinical work, addiction science, microbiome and exposome science, and human intervention trials has underscored that nutrition is of relevance along the criminal justice continuum. As such, the emerging dietetics research is salient to the thousands of international psychologists and allied mental health professionals that are engaged in justice work, including forensics, prevention, and intervention. In addition, relationships between nutrition and behavior relate to “food crime”, an emergent area unifying criminal justice researchers with psychology, public health, and other interdisciplinary sectors. Food crime scrutinizes the vast harms, including non-communicable diseases and adverse behavioral outcomes, as influenced by the distribution of addictive ultra-processed food products. Here, we examine the emergent research, including biophysiological mechanisms, and evidence indicating that dietary patterns/components intersect with psychosocial vulnerabilities linked with risks of antisocial behavior and justice involvement. Viewed through a prevention lens, the study of nutrition and aggressive behavior should be prioritized, especially if the outcomes emerge as externalities of the global consumption of ultra-processed food. In the context of criminal justice and behavior, there is a need for forensic examination of how industry influence and power structures can undermine matters of food justice. Full article
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<p>The Crime of Malnourishment: The emerging science of nutritional criminology and food crime emphasizes the need for multiple lines of interdisciplinary research across the criminal justice spectrum. With permission of the artist, Susan L. Prescott, MD, Ph.D.</p>
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<p>Biopsychosocial pathways, both positive and negative, at the intersection of nutrition and behavior.</p>
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15 pages, 10160 KiB  
Article
Structural and Electronic Properties of Novel Azothiophene Dyes: A Multilevel Study Incorporating Explicit Solvation Effects
by Laura Vautrin, Alexandrine Lambert, Faouzi Mahdhaoui, Riad El Abed, Taoufik Boubaker and Francesca Ingrosso
Molecules 2024, 29(17), 4053; https://doi.org/10.3390/molecules29174053 - 27 Aug 2024
Viewed by 377
Abstract
Among azobenzene derivatives, azothiophenes represent a relatively recent family of compounds that exhibit similar characteristics as dyes and photoreactive systems. Their technological applications are extensive thanks to the additional design flexibility conferred by the heteroaromatic ring. In this study, we present a comprehensive [...] Read more.
Among azobenzene derivatives, azothiophenes represent a relatively recent family of compounds that exhibit similar characteristics as dyes and photoreactive systems. Their technological applications are extensive thanks to the additional design flexibility conferred by the heteroaromatic ring. In this study, we present a comprehensive investigation of the structural and electronic properties of novel dyes derived from 3-thiophenamine, utilizing a multilevel approach. We thoroughly examined the potential energy surfaces of the E and Z isomers for three molecules, each bearing different substituents on the phenyl ring at the para position relative to the diazo group. This exploration was conducted through quantum chemistry calculations at various levels of theory, employing a continuum solvent model. Subsequently, we incorporated an explicit solvent (a dimethyl sulfoxide–water mixture) to simulate the most stable isomers using classical molecular dynamics, delivering a clear picture of the local solvation structure and intermolecular interactions. Finally, a hybrid quantum mechanics/molecular mechanics (QM/MM) approach was employed to accurately describe the evolution of the solutes’ properties within their environment, accounting for finite temperature effects. Full article
(This article belongs to the Special Issue Study on Synthesis and Photochemistry of Dyes)
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<p>(<b>a</b>) Structures of the E and Z isomers of azothiophenes, created using the JSME structure editor [<a href="#B14-molecules-29-04053" class="html-bibr">14</a>]. (<b>b</b>) Intramolecular interaction (represented using dashed lines) between the lone pair of the S atom on the heteroaromatic ring and the <math display="inline"><semantics> <mi>π</mi> </semantics></math> electron cloud of the phenyl ring, stabilizing the Z isomer.</p>
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<p>(<b>a</b>) Mulliken charges (in a.u.) and direction of the molecular dipole vector (not in scale) for the three E isomers. The dipole moment values are 5.6 D, 2.7 D, and 12.6 D for Azothio-a, Azothio-b, and Azothio-c, respectively. (<b>b</b>) Visualization of the frontier orbitals of the three molecules and computed HOMO-LUMO gaps. Results from B3LYP/6-311G(d,p) calculations.</p>
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<p>Absorption spectra of neutral species at the B3LYP/6-311G(d,p) level.</p>
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<p>Comparison for spectra of protonated species. In the top and middle panels, we compare the computed spectra for the E and E-twist minima at three different levels of quantum chemistry. In the bottom panel, we report the experimental spectra: Azothio-a, black line; Azothio-b, red line; Azothio-c, blue line. In the computed spectra, those obtained for the E-twist conformations are reported as dashed lines.</p>
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<p>Radial distribution functions describing specific solute–solvent interactions for Azothio-a, Azothio-b and Azothio-c (from top to bottom), computed along the classical MD trajectories. The interactions between the H atoms on the protonated amino site of the solutes and (i) the O atoms of the water molecules (ii) the O atoms of DMSO molecules are displayed in red and in black, respectively.</p>
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<p>Three-dimensional histograms collecting the number density of significant solvent atoms surrounding (<b>a</b>) Azothio-a, (<b>b</b>) Azothio-b, and (<b>c</b>) Azothio-c along the classical MD trajectories. The O and the H atoms of water molecules are displayed in red and light gray, respectively, whereas the O and the S atoms of DMSO molecules are shown in red and yellow. Concerning the solute (licorice representation), C atoms are displayed in light blue, H atoms in white, O atoms in red, N atoms in blue, S atoms in yellow.</p>
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<p>Time evolution of relevant geometric parameters in Azothio-a (<b>left</b>, black dots), Azothio-b (<b>center</b>, black dots), and Azothio-c (<b>right</b>) along the QM/MM dynamics. From top to bottom: C-N-N-C dihedral angle, S-C-N-N dihedral angle, distances between the N atom and each of the H atoms of the amino group (black, red and blue dots).</p>
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<p>Water and DMSO molecules surrounding the amino group in (<b>a</b>) Azothio-a, (<b>b</b>) Azothio-b, and (<b>c</b>) Azothio-c, along the QM/MM dynamics. The directions of the hydrogen bonds are displayed as dashed lines, as a guide for the eye. The atoms colors are the same as defined in <a href="#molecules-29-04053-f006" class="html-fig">Figure 6</a>.</p>
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<p>Proposed mechanistic pathway for the azo-coupling reactions of 3-aminothiophene with 4-R-benzenediazonium cations (R = OCH<sub>3</sub>, H, and CN) in a 50:50 water/DMSO (<span class="html-italic">v</span>/<span class="html-italic">v</span>) mixture at 298 K.</p>
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<p>Names for the three compounds studied in this work (the E isomer is depicted in the three cases). H atoms are displayed in white, C atoms in gray, N atoms in blue, O atoms in red, S atoms in yellow.</p>
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<p>PES minima for the E and the Z isomers of Azothio-a.</p>
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19 pages, 2385 KiB  
Article
Characterization and Modeling of Out-of-Plane Behavior of Fiber-Based Materials: Numerical Illustration of Wrinkle in Deep Drawing
by Cedric W. Sanjon, Yuchen Leng, Yi Yan, Peter Groche, Marek Hauptmann, Nicole Ludat and Jens-Peter Majschak
Materials 2024, 17(17), 4177; https://doi.org/10.3390/ma17174177 - 23 Aug 2024
Viewed by 365
Abstract
The characterization and modeling of the out-of-plane behavior of fiber-based materials is essential for understanding their mechanical properties and improving their performance in various applications, especially in the forming process. Despite this, research on paper and paperboard has mainly focused on its in-plane [...] Read more.
The characterization and modeling of the out-of-plane behavior of fiber-based materials is essential for understanding their mechanical properties and improving their performance in various applications, especially in the forming process. Despite this, research on paper and paperboard has mainly focused on its in-plane behavior rather than its out-of-plane behavior. However, for accurate material characterization and modeling, it is critical to consider the out-of-plane behavior. In particular, delamination occurs during forming processes such as creasing, folding, and deep drawing. In this study, three material models for paperboard are presented: a single all-material continuum model and two composite models using different cohesion methods. The two composite models decouple in-plane and out-of-plane behavior and consist of continuum models describing the behavior of individual layers and cohesive interface models connecting the layers. Material characterization experiments are performed to derive the model parameters and verify the models. The models are validated using three-point bending and bulge tests and show good agreement. A case study is also conducted on the application of the three models in the simulation of a deep drawing process with respect to wrinkle formation. By comparing the simulation results of wrinkle formation in the deep drawing process, the composite models, especially the cohesive interface composite model, show greater accuracy in replicating the experimental results, indicating that a single continuum model can also be used to represent wrinkles. Full article
(This article belongs to the Section Materials Simulation and Design)
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<p>Illustration of delaminated paperboard structure.</p>
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<p>(<b>a</b>) Geometric parameters of in-plane shear sample. (<b>b</b>) Shear stress (in MPa) cloud charts in the simulation. (<b>c</b>) Shear stress distribution using GOM Aramis (Geometry A).</p>
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<p>(<b>a</b>) Schematic illustration of the out-of-plane tensile test. (<b>b</b>) Simulation model of the experiment.</p>
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<p>(<b>a</b>) Schematic illustration of the out-of-plane shear test. (<b>b</b>) Simulation model of the experiment.</p>
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<p>Composite material modeling with consideration of delamination behavior: (<b>a</b>) model with cohesive interaction, (<b>b</b>) model with interface part with different properties.</p>
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<p>(<b>a</b>) Validation of continuum model and composite model using in-plane tensile tests in 3 directions. (<b>b</b>) Validation of continuum model using in-plane shear test.</p>
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<p>Interface model: damage initiation criterion and relevant parameters.</p>
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<p>(<b>a</b>) Validation of cohesive model using out-of-plane tensile tests. (<b>b</b>) Validation of cohesive model using out-of-plane shear test.</p>
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<p>(<b>a</b>) Comparison of three material models for out-of-plane compression test; (<b>b</b>) Penetration of cohesive elements into interface model.</p>
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<p>(<b>a</b>) Experimental setup of the three-point bending test. (<b>b</b>) Experimental setup and samples of the bulge test. (<b>c</b>) Geometric model of deep drawing simulation.</p>
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<p>Comparison of friction coefficients of samples with two, one, and no wrinkles.</p>
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<p>(<b>a</b>) Comparison of the experimental and numerical results of the bending test. (<b>b</b>) Microscopic Observation. (<b>c</b>) Delamination in the simulation.</p>
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<p>(<b>a</b>) Comparison of the experimental and numerical results using 3 different material models of the bulge test. (<b>b</b>) Slippage in simulation.</p>
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<p>Comparison of experimental and simulation results of three material models (top view, direction of red arrow: MD).</p>
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<p>Comparison of wrinkle formation between experimental and simulation results of three material models (side view).</p>
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<p>Comparison of the influence of mesh size on the wrinkle simulation.</p>
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<p>Comparison of three samples of deep drawing process under the same process parameter.</p>
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12 pages, 2681 KiB  
Article
Analogue of High-Q Transparency Band and Sensitivity in All-Dielectric Metasurfaces Supporting Bound States in the Continuum
by Ling Shuai, Suxia Xie, Haoxuan Nan and Xin Guan
Photonics 2024, 11(8), 775; https://doi.org/10.3390/photonics11080775 - 20 Aug 2024
Viewed by 469
Abstract
Bound states in the continuum (BICs), which are characterized by their high-quality factor, have become a focal point in modern optical research. This study investigates BICs within a periodic array of dielectric resonators, specifically composed of a silicon rectangular bar coupled with four [...] Read more.
Bound states in the continuum (BICs), which are characterized by their high-quality factor, have become a focal point in modern optical research. This study investigates BICs within a periodic array of dielectric resonators, specifically composed of a silicon rectangular bar coupled with four silicon rectangular blocks. Through the analysis of mode coupling, we demonstrate that the interaction between the blocks significantly modulates the eigenmodes of the bar, causing a redshift in all modes and enabling the formation of electromagnetically induced transparency based on BICs (EIT-BIC). Unlike typical EIT mechanisms, this EIT-BIC arises from the coupling of “bright” and “dark” modes both from the rectangular bar, offering novel insights for nanophotonic and photonic device design. Further, our systematic exploration of BIC formation mechanisms and their sensing properties by breaking structural symmetries and changing environmental refractive indices has shed light on the underlying physics. This research not only consolidates a robust theoretical framework for understanding BIC behavior but also paves the way for high-quality factor resonator and sensor development, as well as the precise control of photonic states. The findings significantly deepen our understanding of these phenomena and hold substantial promise for future photonic applications. Full article
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<p>(<b>a</b>) Overall schematic of the metasurface. The geometry consists of an all-dielectric silicon resonator and a silicon dioxide substrate. (<b>b</b>) Schematic of the unit cell consisting of two coupled resonators. The geometrical parameters of the structure are W<sub>11</sub> = W<sub>12</sub> = W<sub>13</sub> = W<sub>14</sub> = 25 μm, W<sub>2</sub> = 25 μm, L<sub>11</sub> = 13.75 μm, L<sub>2</sub> = 92 μm, H<sub>1</sub> = 12.1 μm, and H<sub>2</sub> = 0.6 μm, with P<sub>X</sub> = 92 μm and P<sub>y</sub> = 96 μm. (<b>c</b>) Calculated radiative Q-factor of the symmetric metasurface, a = P<sub>X</sub>, and (<b>d</b>) calculated band structure.</p>
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<p>(<b>a</b>) Spectral response of the single rectangular bar in one lattice of the metasurface. (<b>b</b>) Spectral response of the four rectangular blocks in one lattice of the metasurface, as B<sub>1</sub>, B<sub>2</sub>, B<sub>3</sub>, and B<sub>4</sub>. (<b>c</b>) Spectral response of the metasurface with both bar and blocks. (<b>d</b>) Spectral response of the metasurface as a function of incident angle.</p>
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<p>(<b>a</b>–<b>c</b>) Near electric field distributions on the X–Y cross-section at half thickness of Si metasurface for different incident angles around BIC-I. Corresponding frequencies are at 2.16 THz, 2.13 THz, and 2.13 THz, respectively. (<b>d</b>–<b>f</b>) Near electric field distributions on the X–Y cross-section at half thickness of Si metasurface for different incident angles around BIC-II. Corresponding frequencies are at 2.16 THz, 2.42 THz, and 2.44 THz, respectively.</p>
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<p>(<b>a</b>) Transmittance spectra with the change in the width of the four rectangular blocks at the incidence angle θ = 2.8°. The selected widths are W<sub>11</sub> = W<sub>12</sub> = W<sub>13</sub> = W<sub>14</sub> = 8.33 μm, 16.67 μm, 25 μm, and 33.33 μm, respectively. (<b>b</b>) Transmittance spectra with a simultaneous decrease in the width of rectangular B<sub>1</sub> and a corresponding increase in the width of rectangular B<sub>2</sub> at the incident angle θ = 0° with W<sub>13</sub> = W<sub>14</sub> = 12.5 μm. (<b>c</b>) Transmittance spectra of simultaneously decreasing the width of the rectangular B<sub>3</sub> and correspondingly increasing the width of the rectangular B<sub>2</sub> for the incident angle θ = 0° with W<sub>11</sub> = W<sub>14</sub> = 12.5 μm.</p>
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<p>Transmittance spectra of the rectangular B<sub>1</sub> and rectangular B<sub>2</sub> for an incidence angle of θ = 3°, with a change in the distance Δy moved down along the rectangular bar and Δy ranging from 0 to 70 μm.</p>
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<p>(<b>a</b>) Spectral response of quasi-BIC-I and quasi-BIC-II with the change in ambient refractive index at the incident angle of θ = 2.8°. The refractive indices are 1.0, 1.2, 1.4, 1.6, 1.8, and 2.0, respectively. (<b>b</b>) Center frequency of quasi-BIC-I at different ambient refractive indices. (<b>c</b>) Center frequencies of quasi-BIC-II under different ambient refractive indices. (<b>d</b>) FOM for quasi-BIC-I under different ambient refractive indices. (<b>e</b>) FOM for quasi-BIC-II under different ambient refractive indices.</p>
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9 pages, 1556 KiB  
Proceeding Paper
Application of the Finite Element Method (FEM) to Analyze the Mechanical Behavior of Piezoelectric Materials When an Electric Field Is Applied to a Piezoelectric Structure (Inverse Piezoelectricity)
by Mehdi Boudouh, Brahim El Khalil Hachi, Mohamed Haboussi and Sadam Houcine Habib
Eng. Proc. 2024, 67(1), 13; https://doi.org/10.3390/engproc2024067013 - 19 Aug 2024
Viewed by 225
Abstract
Modeling the inverse impact of piezoelectricity on the mechanical response of smart (piezoelectric) materials through the finite element method (FEM) requires a comprehensive framework that encompasses a multitude of components and intricacies. The utilization of the FEM by researchers is aimed at scrutinizing [...] Read more.
Modeling the inverse impact of piezoelectricity on the mechanical response of smart (piezoelectric) materials through the finite element method (FEM) requires a comprehensive framework that encompasses a multitude of components and intricacies. The utilization of the FEM by researchers is aimed at scrutinizing and comprehending the complex interplay between the mechanical response and piezoelectric characteristics of smart materials. The process of modeling entails the application of numerical methods that facilitate the examination of the reverse effects of piezoelectricity on mechanical behavior with a high degree of precision and accuracy. Through the FEM, a robust and efficient approach is provided to replicate the intricate behavior and response of smart materials under diverse loading conditions, taking into account the intricate interactions between the mechanical and electrical domains. By adopting this modeling strategy, researchers can acquire valuable insights into the fundamental mechanisms and phenomena that govern the inverse influence of piezoelectricity, thereby laying the groundwork for the advancement of cutting-edge smart materials with enhanced performance and functionality. Consequently, the modeling of the inverse effects of piezoelectricity on the mechanical behavior of smart materials using the finite element method emerges as a pivotal and indispensable facet of material science research, playing a significant role in propelling progress across various domains such as robotics, energy harvesting, and structural health monitoring. The primary aim of this research paper is to simulate the impact of inverse piezoelectricity on the mechanical behavior of piezoelectric materials; we have employed the principles of continuum mechanics to address both mechanical and electrical aspects in order to compute the mechanical field when an electric field is administered to the piezoelectric configuration. Full article
(This article belongs to the Proceedings of The 3rd International Electronic Conference on Processes)
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<p>Illustration of the direct (<b>a</b>) and inverse (<b>b</b>) piezoelectric effects.</p>
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<p>Fundamental vibration modes of a piezoelectric ceramic.</p>
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<p>Dimensions of the beam used in the simulation by COMSOL Multiphysics<sup>®</sup>5.6.</p>
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<p>Displacement magnitude.</p>
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<p>von Mises stress.</p>
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<p>(<b>a</b>) The electrical potential; (<b>b</b>) the curve of displacement magnitude as a function of the length of the arc.</p>
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12 pages, 6023 KiB  
Article
Second Harmonic Generation in Apodized Chirped Periodically Poled Lithium Niobate Loaded Waveguides Based on Bound States in Continuum
by Junjie He, Mianjie Lin and Fei Ma
Photonics 2024, 11(8), 769; https://doi.org/10.3390/photonics11080769 - 18 Aug 2024
Viewed by 581
Abstract
With the rapid development of optical communication and quantum information, the demand for efficient and broadband nonlinear frequency conversion has increased. At present, most single-frequency conversion processes in lithium niobate on insulator (LNOI) waveguides suffer from lateral leakage without proper design, leading to [...] Read more.
With the rapid development of optical communication and quantum information, the demand for efficient and broadband nonlinear frequency conversion has increased. At present, most single-frequency conversion processes in lithium niobate on insulator (LNOI) waveguides suffer from lateral leakage without proper design, leading to an additional increase in propagation loss. Achieving broadband frequency conversion also encounters this problem in that there are no relevant works that have solved this yet. In this paper, we theoretically propose an efficient and flat broadband second harmonic generation (SHG) in silicon nitride loaded apodized chirped periodically poled LNOI waveguides. By using a bound states in the continuum (BICs) mechanism to reduce the propagation loss and utilizing the characteristic that the BICs are insensitive to wavelength, an ultra-low-loss wave band of 80 nm is realized. Then, by employing an apodized chirped design, a flat broadband SHG is achieved. The normalized conversion efficiency (NCE) is approximately 222%W−1cm−2, and the bandwidth is about 100 nm. Moreover, the presented waveguides are simple and can be fabricated without direct etching of lithium niobate, exhibiting excellent fabrication tolerance. Our work may open a new avenue for exploring low-loss and flat broadband nonlinear frequency conversion on various on-chip integrated photonic platforms. Full article
(This article belongs to the Section Optoelectronics and Optical Materials)
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<p>(<b>a</b>) Three-dimensional structure diagram of silicon nitride loaded apodized chirped periodically poled LNOI waveguide, consisting of a silicon nitride waveguide, X-cut lithium niobate thin film and silicon dioxide substrate. (<b>b</b>) Schematic diagram depicting the <span class="html-italic">z-x</span> cross section of waveguide structure, where <span class="html-italic">w</span> and <span class="html-italic">t</span> denote the width and thickness of the silicon nitride waveguide respectively, and <span class="html-italic">h</span> represents the thickness of the lithium niobate thin film.</p>
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<p>The modal field distribution of TE bound mode for (<b>a</b>) FF wave at 1600 nm and (<b>b</b>) SH wave at 800 nm.</p>
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<p>(<b>a</b>) Effective refractive index distribution of SH wave at 800 nm in region I and II. The red line represents the refractive index distribution of TM mode, the blue line represents the refractive index distribution of TE mode, the green part represents the TM continuous modes, and the black line represents the TE bound mode in the TM continuous modes. (<b>b</b>) The photonic potential distribution of SH wave at 800 nm. The potential well of TE mode is higher than that of TM mode.</p>
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<p>(<b>a</b>) Dissipated channels of bound mode to continuous mode. (<b>b</b>) The propagation loss of FF and SH waves in TE bound mode varies with silicon nitride waveguide width <span class="html-italic">w</span>. At width <span class="html-italic">w</span> = 1.62 μm, the propagation loss reaches minimum, indicating the BICs.</p>
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<p>(<b>a</b>) The effective refractive index of FF and SH waves varies with wavelength. (<b>b</b>) The TE bound mode propagation loss of FF and SH waves varies with wavelength; the red line and blue line represent the propagation loss of FF and SH waves, respectively. The propagation loss of SH wave is less than 0.05 dB/cm within a bandwidth of 80 nm from 1554 nm to 1634 nm.</p>
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<p>(<b>a</b>) The poling period required for quasi phase matching when the FF wavelength changes. (<b>b</b>) Schematic diagram of apodized step-chirped periodically poled structure. Arrows represent the poling direction of lithium niobate thin film.</p>
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<p>(<b>a</b>) The red line and the blue line represent respectively the G<sup>2</sup> curves corresponding to chirped periodic poling and uniformly single-period poling with the same waveguide parameters, where the dotted and solid red line represent respectively the step chirp and apodized chirp. (<b>b</b>) The NCE of broadband SHG considering the propagation loss. The blue line represents BICs with waveguide width of <span class="html-italic">w</span> = 1.62 μm, and the red line represents non-BICs with waveguide width of <span class="html-italic">w</span> = 1.30 μm.</p>
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<p>Fabrication tolerance of (<b>a</b>) etched sidewall angle and (<b>b</b>) width of silicon nitride loaded waveguides.</p>
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40 pages, 10077 KiB  
Article
The Character of Couples and Couple Stresses in Continuum Mechanics
by Ali R. Hadjesfandiari
Symmetry 2024, 16(8), 1046; https://doi.org/10.3390/sym16081046 - 14 Aug 2024
Viewed by 595
Abstract
In this paper, the concepts of moments and couples in mechanics are examined from a fundamental perspective. Representing a couple by its moment vector is very useful in rigid body mechanics, where the states of internal stresses and deformation are not studied. This [...] Read more.
In this paper, the concepts of moments and couples in mechanics are examined from a fundamental perspective. Representing a couple by its moment vector is very useful in rigid body mechanics, where the states of internal stresses and deformation are not studied. This is because only the moment of couples appears in the governing equation of moment equilibrium. On the other hand, when considering the state of internal stresses and deformation in continuum mechanics, not only the moment of couples but also the line of action of their constituent parallel opposite forces must be specified. In defining a well-posed problem for a continuum, including the governing equations of moment equilibrium or motion, boundary conditions, and constitutive relations, only the moment of couples (e.g., body couples, couple tractions, couple stresses) appear without specifying the line of action of the constituent parallel forces. Nevertheless, the physical state of stress and deformation in the continuum must be unique and determinate. Therefore, this physical requirement imposes some restrictions on the form of body couples, couple tractions, and couple stresses. Here, the uniqueness of interactions in the continuum is used to establish that the continuum does not support a distribution of body couples or a distribution of surface twisting couple tractions with normal moments. Furthermore, the mechanism of action of the couple traction as a double layer of shear force tractions is established, along with the skew-symmetric character of the couple stress moment tensor. Full article
(This article belongs to the Special Issue Symmetry in Statistical Mechanics and Complex Dynamical Systems)
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<p>Moment of force <math display="inline"><semantics> <mstyle mathvariant="bold" mathsize="normal"> <mi>F</mi> </mstyle> </semantics></math> about point <span class="html-italic">O</span>.</p>
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<p>The couple <math display="inline"><semantics> <mstyle mathvariant="bold" mathsize="normal"> <mi>F</mi> </mstyle> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>−</mo> <mstyle mathvariant="bold" mathsize="normal"> <mi>F</mi> </mstyle> </mrow> </semantics></math> and its moment about point <span class="html-italic">O</span>.</p>
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<p>Equipollent couples on the body <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mi>F</mi> <mi>h</mi> <mo>=</mo> <msup> <mi>F</mi> <mo>′</mo> </msup> <msup> <mi>h</mi> <mo>′</mo> </msup> </mrow> </semantics></math>.</p>
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<p>The couple <math display="inline"><semantics> <mstyle mathvariant="bold" mathsize="normal"> <mi>F</mi> </mstyle> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>−</mo> <mstyle mathvariant="bold" mathsize="normal"> <mi>F</mi> </mstyle> </mrow> </semantics></math> and its moment when approaching to a concentrated couple.</p>
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<p>The concentrated couple <math display="inline"><semantics> <mstyle mathvariant="bold" mathsize="normal"> <mi>F</mi> </mstyle> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>−</mo> <mstyle mathvariant="bold" mathsize="normal"> <mi>F</mi> </mstyle> </mrow> </semantics></math> and its moment <math display="inline"><semantics> <mstyle mathvariant="bold" mathsize="normal"> <mover accent="true"> <mi>M</mi> <mo stretchy="false">→</mo> </mover> </mstyle> </semantics></math> at point <span class="html-italic">A</span>.</p>
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<p>Equipollent concentrated couples at point <span class="html-italic">A</span>.</p>
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<p>A system of two concentrated couples with moments <math display="inline"><semantics> <mrow> <msub> <mstyle mathvariant="bold" mathsize="normal"> <mover accent="true"> <mi>M</mi> <mo stretchy="false">→</mo> </mover> </mstyle> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mstyle mathvariant="bold" mathsize="normal"> <mover accent="true"> <mi>M</mi> <mo stretchy="false">→</mo> </mover> </mstyle> <mn>2</mn> </msub> </mrow> </semantics></math> and the equipollent resultant couple with moment <math display="inline"><semantics> <mrow> <msup> <mstyle mathvariant="bold" mathsize="normal"> <mover accent="true"> <mi>M</mi> <mo stretchy="false">→</mo> </mover> </mstyle> <mi>R</mi> </msup> <mo>=</mo> <msub> <mstyle mathvariant="bold" mathsize="normal"> <mover accent="true"> <mi>M</mi> <mo stretchy="false">→</mo> </mover> </mstyle> <mn>1</mn> </msub> <mo>+</mo> <msub> <mstyle mathvariant="bold" mathsize="normal"> <mover accent="true"> <mi>M</mi> <mo stretchy="false">→</mo> </mover> </mstyle> <mn>2</mn> </msub> </mrow> </semantics></math> at point <span class="html-italic">A</span>.</p>
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<p>A system of one resultant force <math display="inline"><semantics> <mrow> <msup> <mstyle mathvariant="bold" mathsize="normal"> <mi>F</mi> </mstyle> <mi>R</mi> </msup> </mrow> </semantics></math> and one resultant couple with moment <math display="inline"><semantics> <mrow> <msubsup> <mstyle mathvariant="bold" mathsize="normal"> <mover accent="true"> <mi>M</mi> <mo stretchy="false">→</mo> </mover> </mstyle> <mi>O</mi> <mi>R</mi> </msubsup> </mrow> </semantics></math> at point <span class="html-italic">O</span>, equipollent to a system of forces.</p>
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<p>A system of one resultant force <math display="inline"><semantics> <mrow> <msup> <mstyle mathvariant="bold" mathsize="normal"> <mi>F</mi> </mstyle> <mi>R</mi> </msup> </mrow> </semantics></math> and one resultant couple with moment <math display="inline"><semantics> <mrow> <msubsup> <mstyle mathvariant="bold" mathsize="normal"> <mover accent="true"> <mi>M</mi> <mo stretchy="false">→</mo> </mover> </mstyle> <mi>O</mi> <mi>R</mi> </msubsup> </mrow> </semantics></math> at point <span class="html-italic">O</span>, equivalent to a system of external forces and effective forces.</p>
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<p>Transmissibility of force <math display="inline"><semantics> <mstyle mathvariant="bold" mathsize="normal"> <mi>F</mi> </mstyle> </semantics></math> on a rigid body.</p>
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<p>Equipollent couples on a rigid body are equivalent.</p>
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<p>Freedom of a couple with moment <math display="inline"><semantics> <mstyle mathvariant="bold" mathsize="normal"> <mover accent="true"> <mi>M</mi> <mo stretchy="false">→</mo> </mover> </mstyle> </semantics></math> on a rigid body.</p>
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<p>Equipollent concentrated couples at point <span class="html-italic">A</span> are not equivalent in continuum mechanics.</p>
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<p>Equipollent couples (<b>a</b>,<b>b</b>) on the end cross-sections are represented by their moment <math display="inline"><semantics> <mrow> <msub> <mstyle mathvariant="bold" mathsize="normal"> <mover accent="true"> <mi>M</mi> <mo stretchy="false">→</mo> </mover> </mstyle> <mi>B</mi> </msub> </mrow> </semantics></math> in (<b>c</b>).</p>
Full article ">Figure 15
<p>Moment <math display="inline"><semantics> <mrow> <msub> <mstyle mathvariant="bold" mathsize="normal"> <mover accent="true"> <mi>M</mi> <mo stretchy="false">→</mo> </mover> </mstyle> <mi>B</mi> </msub> </mrow> </semantics></math> on the end cross-sections are replaced with an equipollent triangular normal force stress distribution predicted from beam theory.</p>
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<p>The body configuration.</p>
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<p>Force <math display="inline"><semantics> <mrow> <mi>d</mi> <mstyle mathvariant="bold" mathsize="normal"> <mi>F</mi> </mstyle> <mo>=</mo> <mstyle mathvariant="bold" mathsize="normal"> <mi>f</mi> </mstyle> <mi>d</mi> <mi>V</mi> </mrow> </semantics></math> and couple with moment <math display="inline"><semantics> <mrow> <mi>d</mi> <mstyle mathvariant="bold" mathsize="normal"> <mover accent="true"> <mi>M</mi> <mo stretchy="false">→</mo> </mover> </mstyle> <mo>=</mo> <mstyle mathvariant="bold" mathsize="normal"> <mover accent="true"> <mi>c</mi> <mo stretchy="false">→</mo> </mover> </mstyle> <mi>d</mi> <mi>V</mi> </mrow> </semantics></math> in the volume element <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>V</mi> </mrow> </semantics></math>.</p>
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<p>Force <math display="inline"><semantics> <mrow> <mi>d</mi> <mstyle mathvariant="bold" mathsize="normal"> <mi>F</mi> </mstyle> <mo>=</mo> <msup> <mstyle mathvariant="bold" mathsize="normal"> <mi>t</mi> </mstyle> <mrow> <mfenced> <mi>n</mi> </mfenced> </mrow> </msup> <mi>d</mi> <mi>S</mi> </mrow> </semantics></math> and couple with moment <math display="inline"><semantics> <mrow> <mi>d</mi> <mover accent="true"> <mi mathvariant="bold">M</mi> <mo stretchy="false">→</mo> </mover> <mo>=</mo> <msup> <mover accent="true"> <mi mathvariant="bold">m</mi> <mo stretchy="false">→</mo> </mover> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </msup> <mi>d</mi> <mi>S</mi> </mrow> </semantics></math> on the surface element <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>S</mi> </mrow> </semantics></math>.</p>
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<p>Force traction <math display="inline"><semantics> <mrow> <msup> <mi mathvariant="bold">t</mi> <mrow> <mfenced> <mi>n</mi> </mfenced> </mrow> </msup> </mrow> </semantics></math> and couple traction moment <math display="inline"><semantics> <mrow> <msup> <mstyle mathvariant="bold" mathsize="normal"> <mover accent="true"> <mi>m</mi> <mo stretchy="false">→</mo> </mover> </mstyle> <mrow> <mfenced> <mi>n</mi> </mfenced> </mrow> </msup> </mrow> </semantics></math> on the surface element <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>S</mi> </mrow> </semantics></math>.</p>
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<p>Normal and tangential components of surface force traction <math display="inline"><semantics> <mrow> <msup> <mi mathvariant="bold">t</mi> <mrow> <mfenced> <mi>n</mi> </mfenced> </mrow> </msup> </mrow> </semantics></math>.</p>
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<p>Normal and tangential components of surface couple traction moment <math display="inline"><semantics> <mrow> <msup> <mover accent="true"> <mi mathvariant="bold">m</mi> <mo stretchy="false">→</mo> </mover> <mrow> <mfenced> <mi>n</mi> </mfenced> </mrow> </msup> </mrow> </semantics></math>.</p>
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<p>Force and couple traction vectors on planes perpendicular to coordinate axes.</p>
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<p>Components of force stress and indeterminate stress moment tensors.</p>
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<p>Couple with moment <math display="inline"><semantics> <mrow> <mi>d</mi> <mstyle mathvariant="bold" mathsize="normal"> <mover accent="true"> <mi>M</mi> <mo stretchy="false">→</mo> </mover> </mstyle> <mo>=</mo> <mstyle mathvariant="bold" mathsize="normal"> <mover accent="true"> <mi>c</mi> <mo stretchy="false">→</mo> </mover> </mstyle> <mi>d</mi> <mi>V</mi> </mrow> </semantics></math> in the volume <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>V</mi> </mrow> </semantics></math>.</p>
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<p>Different equipollent couple force systems (<b>a</b>,<b>b</b>) with moment <math display="inline"><semantics> <mrow> <mi>d</mi> <mstyle mathvariant="bold" mathsize="normal"> <mover accent="true"> <mi>M</mi> <mo stretchy="false">→</mo> </mover> </mstyle> <mo>=</mo> <mstyle mathvariant="bold" mathsize="normal"> <mover accent="true"> <mi>c</mi> <mo stretchy="false">→</mo> </mover> </mstyle> <mi>d</mi> <mi>V</mi> </mrow> </semantics></math> in the volume element <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>V</mi> </mrow> </semantics></math>.</p>
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<p>Normal and tangential components of moment <math display="inline"><semantics> <mrow> <mi>d</mi> <mover accent="true"> <mi mathvariant="bold">M</mi> <mo stretchy="false">→</mo> </mover> <mo>=</mo> <msup> <mover accent="true"> <mi mathvariant="bold">m</mi> <mo stretchy="false">→</mo> </mover> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </msup> <mi>d</mi> <mi>S</mi> </mrow> </semantics></math> of the surface couple.</p>
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<p>A twisting couple with normal moment <math display="inline"><semantics> <mrow> <mi>d</mi> <msup> <mover accent="true"> <mi mathvariant="bold">M</mi> <mo stretchy="false">→</mo> </mover> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </msup> <mo>=</mo> <msup> <mover accent="true"> <mi mathvariant="bold">m</mi> <mo stretchy="false">→</mo> </mover> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </msup> <mi>d</mi> <mi>S</mi> </mrow> </semantics></math> on the surface element <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>S</mi> </mrow> </semantics></math>.</p>
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<p>Equipollent surface twisting couples (<b>a</b>,<b>b</b>) with moment <math display="inline"><semantics> <mrow> <mi>d</mi> <msup> <mover accent="true"> <mi mathvariant="bold">M</mi> <mo stretchy="false">→</mo> </mover> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </msup> <mo>=</mo> <msup> <mover accent="true"> <mi mathvariant="bold">m</mi> <mo stretchy="false">→</mo> </mover> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </msup> <mi>d</mi> <mi>S</mi> </mrow> </semantics></math>.</p>
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<p>A bending couple with tangential moment <math display="inline"><semantics> <mrow> <mi>d</mi> <msup> <mover accent="true"> <mi mathvariant="bold">M</mi> <mo stretchy="false">→</mo> </mover> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msup> <mo>=</mo> <msup> <mover accent="true"> <mi mathvariant="bold">m</mi> <mo stretchy="false">→</mo> </mover> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msup> <mi>d</mi> <mi>S</mi> </mrow> </semantics></math> on the surface element <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>S</mi> </mrow> </semantics></math>.</p>
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<p>Equipollent bending couples (<b>a</b>,<b>b</b>) with moment <math display="inline"><semantics> <mrow> <mi>d</mi> <msup> <mover accent="true"> <mi mathvariant="bold">M</mi> <mo stretchy="false">→</mo> </mover> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msup> <mo>=</mo> <msup> <mover accent="true"> <mi mathvariant="bold">m</mi> <mo stretchy="false">→</mo> </mover> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msup> <mi>d</mi> <mi>S</mi> </mrow> </semantics></math>, represented by forces non-parallel to surface element <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>S</mi> </mrow> </semantics></math> in the normal plane.</p>
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<p>Couple forces parallel to surface element <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>S</mi> </mrow> </semantics></math> in the normal plane with the tangential moment <math display="inline"><semantics> <mrow> <mi>d</mi> <msup> <mover accent="true"> <mi mathvariant="bold">M</mi> <mo stretchy="false">→</mo> </mover> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msup> <mo>=</mo> <msup> <mover accent="true"> <mi mathvariant="bold">m</mi> <mo stretchy="false">→</mo> </mover> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msup> <mi>d</mi> <mi>S</mi> </mrow> </semantics></math>.</p>
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<p>Force traction <math display="inline"><semantics> <mrow> <msup> <mi mathvariant="bold">t</mi> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mrow> </semantics></math> and the consistent couple traction <math display="inline"><semantics> <mrow> <msup> <mover accent="true"> <mi mathvariant="bold">m</mi> <mo stretchy="false">→</mo> </mover> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </msup> <mo>=</mo> <msup> <mover accent="true"> <mi mathvariant="bold">m</mi> <mo stretchy="false">→</mo> </mover> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mrow> </semantics></math> system.</p>
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<p>Components of force and couple stress tensors in consistent couple stress theory.</p>
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<p>Components of couple stress tensor <math display="inline"><semantics> <mstyle mathvariant="bold" mathsize="normal"> <mi>μ</mi> </mstyle> </semantics></math> and couple stress vector <math display="inline"><semantics> <mstyle mathvariant="bold" mathsize="normal"> <mover accent="true"> <mi>μ</mi> <mo stretchy="false">→</mo> </mover> </mstyle> </semantics></math>.</p>
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<p>The couple stress component <math display="inline"><semantics> <mrow> <msub> <mi>μ</mi> <mn>3</mn> </msub> </mrow> </semantics></math> in the direction of its corresponding double-layer shear force stresses.</p>
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<p>The couple stress component <math display="inline"><semantics> <mrow> <msub> <mi>μ</mi> <mn>3</mn> </msub> </mrow> </semantics></math> parallel to its corresponding double-layer shear force stresses in the <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <msub> <mi>x</mi> <mn>3</mn> </msub> </mrow> </semantics></math> plane.</p>
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<p>The couple stress vector in the direction of its double-layer shear force tractions.</p>
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<p>The couple stress vector in the direction of its double-layer shear force stresses creating pure bending along the <math display="inline"><semantics> <mrow> <msub> <msup> <mi>x</mi> <mo>′</mo> </msup> <mn>3</mn> </msub> </mrow> </semantics></math> axis.</p>
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8 pages, 459 KiB  
Opinion
Quiescence-Origin Senescence: A New Paradigm in Cellular Aging
by Guang Yao
Biomedicines 2024, 12(8), 1837; https://doi.org/10.3390/biomedicines12081837 - 13 Aug 2024
Viewed by 1709
Abstract
Cellular senescence, traditionally viewed as a consequence of proliferating and growing cells overwhelmed by extensive stresses and damage, has long been recognized as a critical cellular aging mechanism. Recent research, however, has revealed a novel pathway termed “quiescence-origin senescence”, where cells directly transition [...] Read more.
Cellular senescence, traditionally viewed as a consequence of proliferating and growing cells overwhelmed by extensive stresses and damage, has long been recognized as a critical cellular aging mechanism. Recent research, however, has revealed a novel pathway termed “quiescence-origin senescence”, where cells directly transition into senescence from the quiescent state, bypassing cell proliferation and growth. This opinion paper presents a framework conceptualizing a continuum between quiescence and senescence with quiescence deepening as a precursor to senescence entry. We explore the triggers and controllers of this process and discuss its biological implications. Given that the majority of cells in the human body are dormant rather than proliferative, understanding quiescence-origin senescence has significant implications for tissue homeostasis, aging, cancer, and various disease processes. The new paradigm in exploring this previously overlooked senescent cell population may reshape our intervention strategies for age-related diseases and tissue regeneration. Full article
(This article belongs to the Special Issue Cellular Senescence: Recent Advances and Discoveries)
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<p>Quiescence-origin senescence. Conventional senescence originates from proliferating and growing cells via mTOR-mediated geroconversion, when cell growth continues aberrantly after the cell cycle is blocked in response to severe stress and damage. In comparison, quiescence-origin senescence originates from quiescent cells via quiescence deepening, accompanied by a progressively increasing Rb–E2F switch threshold in response to decreased lysosomal autophagy and increased ROS accumulation and protein aggregation. Senescent cells are irreversibly arrested under physiological conditions. Deep quiescent cells are reversible but require stronger growth stimulation and take a longer time to re-enter the cell cycle than shallow quiescent cells. The boundary between very deep quiescence and quiescence-origin senescence (the red dashed line) is blurred.</p>
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22 pages, 44198 KiB  
Article
Real-Time Simulation of Tube Hydroforming by Integrating Finite-Element Method and Machine Learning
by Liang Cheng, Haijing Guo, Lingyan Sun, Chao Yang, Feng Sun and Jinshan Li
J. Manuf. Mater. Process. 2024, 8(4), 175; https://doi.org/10.3390/jmmp8040175 - 12 Aug 2024
Viewed by 583
Abstract
The real-time, full-field simulation of the tube hydroforming process is crucial for deformation monitoring and the timely prediction of defects. However, this is rather difficult for finite-element simulation due to its time-consuming nature. To overcome this drawback, in this paper, a surrogate model [...] Read more.
The real-time, full-field simulation of the tube hydroforming process is crucial for deformation monitoring and the timely prediction of defects. However, this is rather difficult for finite-element simulation due to its time-consuming nature. To overcome this drawback, in this paper, a surrogate model framework was proposed by integrating the finite-element method (FEM) and machine learning (ML), in which the basic methodology involved interrupting the computational workflow of the FEM and reassembling it with ML. Specifically, the displacement field, as the primary unknown quantity to be solved using the FEM, was mapped onto the displacement boundary conditions of the tube component with ML. To this end, the titanium tube material as well as the hydroforming process was investigated, and a fairly accurate FEM model was developed based on the CPB06 yield criterion coupled with a simplified Kim–Tuan hardening model. Numerous FEM simulations were performed by varying the loading conditions to generate the training database for ML. Then, a random forest algorithm was applied and trained to develop the surrogate model, in which the grid search method was employed to obtain the optimal combination of the hyperparameters. Sequentially, the principal strain, the effective strain/stress, as well as the wall thickness was derived according to continuum mechanics theories. Although further improvements were required in certain aspects, the developed FEM-ML surrogate model delivered extraordinary accuracy and instantaneity in reproducing multi-physical fields, especially the displacement field and wall-thickness distribution, manifesting its feasibility in the real-time, full-field simulation and monitoring of deformation states. Full article
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<p>(<b>a</b>) Schematic description of the tubular blank and the dimension. ND, RD, and TD denote normal direction, rolling direction, and tangent direction, respectively. (<b>b</b>) Inverse-pole-figure map of the tube material. (<b>c</b>) Histogram of grain size distribution. (<b>d</b>) Pole figures to show the texture components of the material.</p>
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<p>(<b>a</b>) Stress–strain curves obtained from four repeated tensile tests along RD. The tensile curve quoted from [<a href="#B45-jmmp-08-00175" class="html-bibr">45</a>] is also superimposed for comparison. (<b>b</b>) DIC images showing the evolution of the axial strain distribution during tension. (<b>c</b>) Lankford coefficient curves derived from the DIC results.</p>
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<p>(<b>a</b>) Schematic representations of the tube hydroforming processes. (<b>b</b>) Typical loading curves for tube hydroforming.</p>
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<p>Simplified finite-element model of the hydroforming process.</p>
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<p>True stress–true strain curve (symbol) obtained by uniaxial tension in RD and the fitting/extrapolation results (solid line) by the simplified K-T model.</p>
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<p>(<b>a</b>) Comparison between the simulated results (symbol) and the experimental results (solid line). (<b>b</b>) Evolution of the axial-to-width strain ratio of the tensile specimen using FEM simulation (bold lines) and tensile tests (thin lines).</p>
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<p>Comparison of the (<b>a</b>) total branch heights and (<b>b</b>) wall thicknesses of the tube ends between the prediction and the measured results.</p>
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<p>(<b>a</b>) A shell element ABCD with a rectangular shape prior to deformation. (<b>b</b>) The shape of the element after arbitrary deformation. <span class="html-italic">a</span><sub>0</sub> and <span class="html-italic">b</span><sub>0</sub> denote the edge lengths prior to deformation while <span class="html-italic">a</span> and <span class="html-italic">b</span> are those after deformation.</p>
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<p>(<b>a</b>) The pressurization curves of the two hydroforming simulation runs. (<b>b</b>) Predicted displacement curves of the boundaries for the two virtual tests.</p>
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<p>Comparison of the displacement field between (<b>a</b>–<b>c</b>) sample 35-6.7 and (<b>e</b>,<b>f</b>) sample 65-2.1 under the same boundary condition shown in <a href="#jmmp-08-00175-f009" class="html-fig">Figure 9</a>. (<b>a</b>,<b>d</b>), (<b>b</b>,<b>e</b>), and (<b>c</b>,<b>f</b>) are displacement distributions in the x, y, and z direction.</p>
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<p>Structure and workflow of the proposed surrogate model.</p>
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<p>The parameter grid showing various pressurization curves used for simulation. The insert graphs depict forming defects at different forming conditions.</p>
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<p>Pressurization curve used for the extra-simulation test.</p>
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<p>Comparison of multi-physical field between those predicted by surrogate model (dot) and the FEM model (solid) at different forming times. The loading condition is depicted in <a href="#jmmp-08-00175-f013" class="html-fig">Figure 13</a>.</p>
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<p>Quantitative comparison of the predicted field variables between ML model and offline FEM model for all nodes/elements at various forming times: (<b>a</b>) displacement of nodes; (<b>b</b>) effective strain of elements; (<b>c</b>) effective stress of elements; (<b>d</b>) wall thickness. The mean error is also tabulated in the figure, where <span class="html-italic">y</span><sub>ML</sub> and <span class="html-italic">y</span><sub>FE</sub> are the predicted results by ML model and FEM model, respectively.</p>
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23 pages, 37635 KiB  
Article
Design, Analysis and Experiment of a Modular Deployable Continuum Robot
by Aihu Jia, Xinyu Liu, Yuntao Guan, Yongxi Liu, Qianze Helian, Chenshuo Liu, Zheming Zhuang and Rongjie Kang
Machines 2024, 12(8), 544; https://doi.org/10.3390/machines12080544 - 10 Aug 2024
Viewed by 845
Abstract
Continuum robots, possessing great flexibility, can accomplish tasks in complex work scenes, regarded as an important direction in robotics. However, the current continuum robots are not satisfying enough in terms of fabrication and maintenance, and their workspace is limited by structure and other [...] Read more.
Continuum robots, possessing great flexibility, can accomplish tasks in complex work scenes, regarded as an important direction in robotics. However, the current continuum robots are not satisfying enough in terms of fabrication and maintenance, and their workspace is limited by structure and other aspects. In this paper, to address the above problems, a modular deployable robot, which adopts an origami structure instead of a flexible hinge, is proposed. A fabrication method is innovated, the Spherical Linkage Parallel Mechanism (SLPM) unit is optimized, and the installation and fabrication process of the robot is simplified through modularization. The forward kinematics and inverse kinematics of the robot and its workspace are analyzed by using the screw theory. The prototype of the robot is constructed, and its folding performance, bending performance, and motion accuracy are tested, and the error analysis and compensation optimization are carried out. After the optimization, the position error of the robot is reduced by about 65%, and the standard deviation is greatly lowered, which effectively improves the motion accuracy and stability of the robot. Full article
(This article belongs to the Section Robotics, Mechatronics and Intelligent Machines)
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<p>Modular deployable continuum robot.</p>
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<p>The deployable structure.</p>
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<p>All parts of SLPM unit and installation process. (<b>a</b>) All parts; (<b>b</b>) Deployable structure installation; (<b>c</b>) Deployable structure demonstration; (<b>d</b>) Deployable structure and connecting plate assembly; (<b>e</b>) SLPM unit in 2D pattern; (<b>f</b>) Complete SLPM unit.</p>
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<p>Robot module and drive wire arrangement.</p>
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<p>Robot prototype. (<b>a</b>) Control box; (<b>b</b>) Integral robot model (robotic arm).</p>
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<p>Equivalent mechanism of SLPM unit.</p>
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<p>Forward kinematic model of SLPM unit.</p>
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<p>The maximum bending angle of the SLPM unit.</p>
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<p>Workspace of a single module. (<b>a</b>) Three-position workspace; (<b>b</b>) Range of workspace in the x-z plane; (<b>c</b>) Range of workspace in the y-z plane; (<b>d</b>) Range of workspace in the x-y plane.</p>
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<p>Workspace of the robot. (<b>a</b>) Three-position workspace; (<b>b</b>) Range of workspace in the x-z plane; (<b>c</b>) Range of workspace in the y-z plane; (<b>d</b>) Range of workspace in the x-y plane.</p>
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<p>Inverse kinematic model of single module.</p>
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<p>Inverse kinematic model of the robot.</p>
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<p>Meshing and its quality analysis. (<b>a</b>) Meshing; (<b>b</b>) Quality analysis.</p>
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<p>Displacement–force curve when subjected to transverse force.</p>
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<p>Angle–moment curve when subjected to twisting force.</p>
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<p>The SLPM unit before and after the compression.</p>
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<p>Stiffness characteristic curve.</p>
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<p>Control system framework.</p>
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<p>Control box.</p>
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<p>SLPM unit state. (<b>a</b>) Fully compressed; (<b>b</b>) Fully extended.</p>
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<p>Folding experiment.</p>
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<p>Bending performance test in upright state. (<b>a</b>) Bend 90°; (<b>b</b>) Bend 120°; (<b>c</b>) Bend 150°; (<b>d</b>) Bend 180°.</p>
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<p>Bending performance tests. (<b>a</b>) In inverted state; (<b>b</b>) Obstacle avoiding.</p>
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<p>Reflective marker arrangements. (A, B, C are the three reflective markers.)</p>
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<p>Motion accuracy under the linear trajectory.</p>
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<p>Feedback compensation flow.</p>
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<p>Comparison of motion accuracy before and after compensation for linear trajectory.</p>
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<p>Comparison of motion accuracy before and after compensation. (<b>a</b>) Square trajectory; (<b>b</b>) Circular trajectory.</p>
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