Extreme Mechanics Letters最新文献

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Front cover CO1
IF 4.3 3区 工程技术
Extreme Mechanics Letters Pub Date : 2025-01-01 DOI: 10.1016/S2352-4316(25)00001-X
{"title":"Front cover CO1","authors":"","doi":"10.1016/S2352-4316(25)00001-X","DOIUrl":"10.1016/S2352-4316(25)00001-X","url":null,"abstract":"","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"74 ","pages":"Article 102289"},"PeriodicalIF":4.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143143044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Simulating flow-induced reconfiguration by coupling corotational plate finite elements with a simplified pressure drag
IF 4.3 3区 工程技术
Extreme Mechanics Letters Pub Date : 2025-01-01 DOI: 10.1016/j.eml.2024.102271
Danick Lamoureux , Sophie Ramananarivo , David Melancon , Frédérick P. Gosselin
{"title":"Simulating flow-induced reconfiguration by coupling corotational plate finite elements with a simplified pressure drag","authors":"Danick Lamoureux ,&nbsp;Sophie Ramananarivo ,&nbsp;David Melancon ,&nbsp;Frédérick P. Gosselin","doi":"10.1016/j.eml.2024.102271","DOIUrl":"10.1016/j.eml.2024.102271","url":null,"abstract":"<div><div>Developing engineering systems that rely on flow-induced reconfiguration, the phenomenon where a structure deforms under flow to reduce its drag, requires design tools that can predict the behavior of these flexible structures. Current methods include using fully coupled computational fluid dynamics and finite element analysis solvers or highly specialized theories for specific geometries. Coupled numerical methods are computationally expensive to use and non-trivial to setup, while specialized theories are difficult to generalize and take a long time to develop. A compromise between speed, accuracy, and versatility is required to be implemented into the design cycle of flexible structures under flow. This paper offers a new numerical implementation of the pressure drag in the context of a corotational finite element formulation on MATLAB. The presented software is verified against different semi-analytical theories applied to slender plates and disks cut along their radii as well as validated against experiments on kirigami sheets and draping disks. <strong>Usage:</strong> The developed code and verification cases presented here are available on GitHub <span><span>https://github.com/lm2-poly/FIRM</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"74 ","pages":"Article 102271"},"PeriodicalIF":4.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143143132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Humidity-induced actuation of silk yarn
IF 4.3 3区 工程技术
Extreme Mechanics Letters Pub Date : 2025-01-01 DOI: 10.1016/j.eml.2024.102279
Yaping Chen , Lei Liu , Yuyang Xie , Jiongjiong Hu , Dabiao Liu
{"title":"Humidity-induced actuation of silk yarn","authors":"Yaping Chen ,&nbsp;Lei Liu ,&nbsp;Yuyang Xie ,&nbsp;Jiongjiong Hu ,&nbsp;Dabiao Liu","doi":"10.1016/j.eml.2024.102279","DOIUrl":"10.1016/j.eml.2024.102279","url":null,"abstract":"<div><div>Silkworm silk is a promising material for smart textiles due to its excellent mechanical properties, biocompatibility with human body, and remarkable hygroscopicity. Silk yarn can provide reversible and repeatable actuation responses during humidification-and-drying cycles. In this study, we investigate the torsional and tensile actuation performances of silk yarn stimulated by humidity from an experimental and theoretical perspective. We find that increasing the twist level and number of silk fibers significantly improves the actuation performance. Silk yarn undergoes an irreversible relaxation upon first being exposed to moisture. It exhibits a repeatable humidity-contraction stress response when wetted further. The actuation strain of silk yarn varies with humidity and increases monotonically with twist level. A theoretical model based on the water absorption equation and the standard reinforcing model is developed to describe the humidity-induced torsional and tensile actuation of silk yarn. The theoretical predictions agree well with the experiments. This work sheds light on the physical mechanisms of humidity-induced actuation in silk yarn and inspires the design of miniature soft actuators.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"74 ","pages":"Article 102279"},"PeriodicalIF":4.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143143133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Size-dependent strengthening in nanowires: The roles of adatom diffusion and surface curvature on surface dislocation nucleation
IF 4.3 3区 工程技术
Extreme Mechanics Letters Pub Date : 2024-12-30 DOI: 10.1016/j.eml.2024.102282
Lijie He , Guangming Cheng , Yong Zhu , Harold S. Park
{"title":"Size-dependent strengthening in nanowires: The roles of adatom diffusion and surface curvature on surface dislocation nucleation","authors":"Lijie He ,&nbsp;Guangming Cheng ,&nbsp;Yong Zhu ,&nbsp;Harold S. Park","doi":"10.1016/j.eml.2024.102282","DOIUrl":"10.1016/j.eml.2024.102282","url":null,"abstract":"<div><div>Understanding the factors governing incipient dislocation nucleation in nanoscale solids is crucial for predicting their mechanical strength and plasticity. While previous experimental studies of surface dislocation nucleation in metal nanowires have observed a strong nonlinear size effect, commonly referred to as “smaller is stronger”, the atomistic origins of this phenomenon remain unresolved. In this study, we investigate the hypothesis that surface curvature, in conjunction with surface adatom diffusion, can have a significant effect on size-dependent strengthening in metal nanowires. The hypothesis is supported by transmission electron microscopy images that reveal a definitive correlation between edge sharpness and nanowire diameter, with smaller diameters exhibiting more blunted edges. To do so, we develop a nucleation-based Kinetic Monte Carlo model that incorporates activation energy barriers for surface dislocation nucleation that are surface-curvature and adatom dependent. The model reveals that the activation energy reduction caused by adatoms is highly sensitive to the nanowire surface curvature, with blunted edges leading to higher activation energy for dislocation nucleation. Therefore, our model and results suggest that size-dependent surface curvature, in conjunction with the role of diffusing adatoms in assisting surface dislocation nucleation, can have a significant effect on size-dependent strengthening in metal nanowires.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"75 ","pages":"Article 102282"},"PeriodicalIF":4.3,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143175302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Electroadhesion-driven friction enhancement using electret films 利用驻极体薄膜的电粘附驱动的摩擦增强
IF 4.3 3区 工程技术
Extreme Mechanics Letters Pub Date : 2024-12-01 DOI: 10.1016/j.eml.2024.102270
Shaoqi Huang, Yifan Li, Shuwen Zhang, Hu Zhao, Siyang Song, Chongpu Zhai, Minglong Xu
{"title":"Electroadhesion-driven friction enhancement using electret films","authors":"Shaoqi Huang,&nbsp;Yifan Li,&nbsp;Shuwen Zhang,&nbsp;Hu Zhao,&nbsp;Siyang Song,&nbsp;Chongpu Zhai,&nbsp;Minglong Xu","doi":"10.1016/j.eml.2024.102270","DOIUrl":"10.1016/j.eml.2024.102270","url":null,"abstract":"<div><div>Friction control has attracted significant attention due to its potential to improve device efficiency and reduce wear. However, achieving rapid, reversible, and robust friction regulation remains a persistent challenge. In this study, we propose a novel strategy for contact control using electret films, which can effectively modulate electroadhesion to enable large-scale friction control. We develop a general model describing the interfacial electro-mechanical coupling mechanism, which is validated through systematic experiments. Both experimental and theoretical results demonstrate that the relationship between the pull-off force and the applied interfacial voltage follows a parabolic curve, with its maxima mainly depending on the charge density, thickness, and dielectric constant of the electret film. With the electret film of about 50 μm in thickness and an applied voltage of approximately 300 V, both the static and dynamic friction coefficients can be increased to more than twice their initial values. This study provides valuable insights into the optimization of mechanical systems in terms of performance enhancement, lifespan extension, energy losses, and thermal management.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"73 ","pages":"Article 102270"},"PeriodicalIF":4.3,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142747550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Automated de novo design of architectured materials: Leveraging eXplainable Artificial Intelligence (XAI) for inspiration from stochastic microstructure outliers 建筑材料的自动化从头设计:利用可解释的人工智能(XAI)从随机微观结构异常值中获得灵感
IF 4.3 3区 工程技术
Extreme Mechanics Letters Pub Date : 2024-12-01 DOI: 10.1016/j.eml.2024.102269
Zhengkun Feng , Weijun Lei , Leidong Xu , Shikui Chen , Hongyi Xu
{"title":"Automated de novo design of architectured materials: Leveraging eXplainable Artificial Intelligence (XAI) for inspiration from stochastic microstructure outliers","authors":"Zhengkun Feng ,&nbsp;Weijun Lei ,&nbsp;Leidong Xu ,&nbsp;Shikui Chen ,&nbsp;Hongyi Xu","doi":"10.1016/j.eml.2024.102269","DOIUrl":"10.1016/j.eml.2024.102269","url":null,"abstract":"<div><div>Engineered architectured Materials, such as metamaterials with periodic patterns, achieve superior properties compared with their stochastic counterparts, such as the random microstructures found in natural materials. The primary research question focuses on the feasibility of learning advantageous microstructural features from stochastic microstructure samples to facilitate the generative design of periodic microstructures, resulting in unprecedented properties. Instead of relying on brainstorming-based, <em>ad hoc</em> design inspiration approaches, we propose an eXplainable Artificial Intelligence (XAI)-based framework to automatically learn critical features from the exceptional outliers (with respect to properties) in stochastic microstructure samples, enabling the generation of novel periodic microstructure patterns with superior properties. This framework is demonstrated on three benchmark cases: designing 2D cellular metamaterials to maximize stiffness in all directions, to maximize the Poisson’s ratio in all directions, and to minimize the thermal expansion ratio. The effectiveness of the design framework is validated by comparing its novel microstructure designs with known stochastic and periodic microstructure designs in terms of the properties of interest.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"73 ","pages":"Article 102269"},"PeriodicalIF":4.3,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142747551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Design the bionic sucker with high adsorption performance based on Sinogastromyzon szechuanensis 以川菜为原料,设计高吸附性能的仿生吸盘
IF 4.3 3区 工程技术
Extreme Mechanics Letters Pub Date : 2024-12-01 DOI: 10.1016/j.eml.2024.102273
Qian Cong , Dexue Zhang , Jin Xu , Tingkun Chen , Jingfu Jin , Chaozong Liu
{"title":"Design the bionic sucker with high adsorption performance based on Sinogastromyzon szechuanensis","authors":"Qian Cong ,&nbsp;Dexue Zhang ,&nbsp;Jin Xu ,&nbsp;Tingkun Chen ,&nbsp;Jingfu Jin ,&nbsp;Chaozong Liu","doi":"10.1016/j.eml.2024.102273","DOIUrl":"10.1016/j.eml.2024.102273","url":null,"abstract":"<div><div>Based on the observed micromorphology of the <em>Sinogastromyzon szechuanensis</em>, a groove morphology was designed on the sucker working surface. The length, width, and number of the grooved morphology were selected as the design factors for the bionic morphology. The bionic and standard sucker was fabricated using the mold method, and the sucker adsorption performance was tested. Compared to the standard sucker adsorption force on the substrate (33.20 N), the bio-inspired sucker adsorption force could increase by a maximum of 71.22 %. The change law of the adsorption force was the same as the change law of negative pressure holding time. The bionic sucker could form multiple micro-sealing cavities from the groove morphology while forming a normal sealing cavity with the substrate. The bionic sucker adsorption force was greater than that of the standard sucker. As the length and width of the groove increased, the micro-sealing cavity formed by the groove shape made it difficult to form micro-suckers during the adsorption process, and the adsorption force was affected. With the increase in the number of grooves, the number of micro-suckers formed between the morphology and the substrate during the adsorption process could increase, and the adsorption force was increased.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"73 ","pages":"Article 102273"},"PeriodicalIF":4.3,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142747552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Acoustic chiral mode transfer for symmetry-broken states in anti-parity-time symmetric systems 反奇偶时对称系统中对称破缺态的声学手性模式转移
IF 4.3 3区 工程技术
Extreme Mechanics Letters Pub Date : 2024-11-22 DOI: 10.1016/j.eml.2024.102261
Youdong Duan , Lei Zhang , Yonghui Zhang , Linlin Geng , Qiuquan Guo , Jun Yang , Gengkai Hu , Xiaoming Zhou
{"title":"Acoustic chiral mode transfer for symmetry-broken states in anti-parity-time symmetric systems","authors":"Youdong Duan ,&nbsp;Lei Zhang ,&nbsp;Yonghui Zhang ,&nbsp;Linlin Geng ,&nbsp;Qiuquan Guo ,&nbsp;Jun Yang ,&nbsp;Gengkai Hu ,&nbsp;Xiaoming Zhou","doi":"10.1016/j.eml.2024.102261","DOIUrl":"10.1016/j.eml.2024.102261","url":null,"abstract":"<div><div>Dynamic encircling of an anti-parity-time (anti-PT) symmetric exceptional point (EP) leads to chiral transfer of symmetry-broken modes, which has been explored in various systems except acoustics. In this work, acoustic counterpart of this behavior is numerically demonstrated in coupled waveguide systems with anti-PT-symmetric EPs. The model consists of three coupled waveguides designed to mimic a three-state system that can be described by the coupled mode theory. By adiabatically eliminating the intermediate state with high loss, the anti-PT symmetry and associated EP can be formed in an effective system comprising the remaining two states. According to the parametric path enclosing the EP, acoustic propagation model is designed to support the space-driven acoustic mode evolution. Numerical simulations are conducted to demonstrate acoustic chiral transfer of symmetry-broken states.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"73 ","pages":"Article 102261"},"PeriodicalIF":4.3,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142722061","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Nonlinear two-scale beam simulations accelerated by thermodynamics-informed neural networks 热力学信息神经网络加速非线性双尺度梁模拟
IF 4.3 3区 工程技术
Extreme Mechanics Letters Pub Date : 2024-11-22 DOI: 10.1016/j.eml.2024.102260
Helen Le Clézio , Konstantinos Karapiperis , Dennis M. Kochmann
{"title":"Nonlinear two-scale beam simulations accelerated by thermodynamics-informed neural networks","authors":"Helen Le Clézio ,&nbsp;Konstantinos Karapiperis ,&nbsp;Dennis M. Kochmann","doi":"10.1016/j.eml.2024.102260","DOIUrl":"10.1016/j.eml.2024.102260","url":null,"abstract":"<div><div>We introduce an efficient computational framework for the simulation of complex beam networks and architected materials. At its core stands a thermodynamics-informed neural network, which serves as a surrogate material model for the cross-sectional response of hyperelastic, slender beams with varying cross-sectional sizes and geometries. The beam description relies on a formal asymptotic expansion from 3D elasticity, which decomposes the problem into an efficient macroscale simulation of the beam’s centerline and a finite elasticity problem on the cross-section (microscale) at each point along the beam. From the solution on the microscale, an effective energy is passed to the macroscale simulation, where it serves as the material model. We introduce a Sobolev-trained neural network as a surrogate model to approximate the effective energy of the microscale. We compare three different neural network architectures, viz. two well established Multi-Layer Perceptron based approaches — a simple feedforward neural network (FNN) and a partially input convex neural network (PICNN) — as well as a recently proposed Kolmogorov-Arnold (KAN) network, and we evaluate their suitability. The models are trained on varying cross-sectional geometries, particularly interpolating between square, circular, and triangular cross-sections, all of varying sizes and degrees of hollowness. Based on its smooth and accurate prediction of the energy landscape, which allows for automatic differentiation, the KAN model was chosen as the surrogate material model, whose effectiveness we demonstrate in a suite of examples, ranging from cantilever beams to 3D beam networks and architected materials. The surrogate model also shows excellent extrapolation capabilities to load cases outside the training dataset.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"73 ","pages":"Article 102260"},"PeriodicalIF":4.3,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142722060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Full range fragmentation simulation of nanoflake filler-matrix composite coatings on a polymer substrate 聚合物基底上纳米片填料-基质复合涂层的全方位破碎模拟
IF 4.3 3区 工程技术
Extreme Mechanics Letters Pub Date : 2024-11-21 DOI: 10.1016/j.eml.2024.102268
Cagan Diyaroglu , Rebecca Villanueva , Umar Raza , Selda Oterkus , Erkan Oterkus , Kyungjin Kim
{"title":"Full range fragmentation simulation of nanoflake filler-matrix composite coatings on a polymer substrate","authors":"Cagan Diyaroglu ,&nbsp;Rebecca Villanueva ,&nbsp;Umar Raza ,&nbsp;Selda Oterkus ,&nbsp;Erkan Oterkus ,&nbsp;Kyungjin Kim","doi":"10.1016/j.eml.2024.102268","DOIUrl":"10.1016/j.eml.2024.102268","url":null,"abstract":"<div><div>This paper presents a comprehensive experimental and computational study to explore the damage evolution mechanisms of polymer matrix nanocomposite films consisting of rigid ceramic fillers coated on a polymer substrate. The weight ratio of montmorillonite (MMT) fillers in the polyvinyl alcohol (PVA) matrix ranges from 30 % to 70 %, and these are applied onto a polyethylene terephthalate (PET) substrate. Through experiments, apart from damage behaviors, the water vapor transmission rates are also measured to gain insight into moisture diffusion characteristics with varying weight ratios of fillers. The optimal weight ratio of nanocomposite films consisting of a PVA matrix with MMT fillers can vary depending on the purpose of damage resistance and moisture barrier characteristics. A peridynamic theory is employed to simulate various damage scenarios of bi-layer nanocomposite films. The solution strategy presented incorporates the use of the cut-boundary and finite element methods to reduce substrate thickness and make initial predictions of crack onset strains, respectively, under quasi-static loading conditions. Several damage scenarios are considered for thin and thick PVA films on the PET substrate, as well as weak to strong interfaces between the PET-PVA and PVA-MMT layers. Additionally, different distributions of MMT fillers are also considered by varying the distances between them and inserting inclusions. The peridynamic damage analyses encompass crack initiation, propagation, and final failure stages across a wide range of strains, including various damage modes such as matrix cracking, cracking at the filler-matrix, or matrix-substrate interfaces, leading to the cohesive film cracking and delamination.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"73 ","pages":"Article 102268"},"PeriodicalIF":4.3,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142701414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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