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Enhancing postural stability in musculoskeletal quadrupedal locomotion through tension feedback for CPG-based controller. 通过基于 CPG 控制器的张力反馈,增强肌肉骨骼四足运动的姿势稳定性。
IF 3.1 3区 计算机科学 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2024-11-07 DOI: 10.1088/1748-3190/ad839e
Hiroaki Tanaka, Ojiro Matsumoto, Takumi Kawasetsu, Koh Hosoda

A central pattern generator (CPG)-based controller enhances the adaptability of quadrupedal locomotion, for example, by controlling the trunk posture. The conventional CPG-based controllers with attitude control often utilized the posture angle as feedback information. However, if the robot's body is as soft as a musculoskeletal structure, it can detect the over-tilting of the trunk based on proprioceptive information of the muscles. In general, proprioceptive information such as muscle tension changes more rapidly than posture angle information. Therefore, a feedback loop based on proprioceptive information has great potential to respond to sudden disturbances that occur during locomotion over uneven terrain. In this research, we proposed a CPG-based controller utilizing the tension of soft pneumatic artificial muscles (PAMs). Musculoskeletal quadruped robots driven by PAMs are so soft, which prevents over-tilting of the trunk because the soft leg acts like a suspension. In addition, tension, one of the proprioceptive information of PAMs, exhibits high sensitivity to changes in trunk posture because the soft body's motion easily is affected by over-tilting of the trunk. To validate the efficacy of the proposed controller, we conducted numerical simulations with a simple quadruped model and experiments with a musculoskeletal quadruped robot. As a result, the tension feedback is not effective for posture stabilization on flat terrain whereas it is effective on uneven terrain. Moreover, the tension feedback improved the running velocity over uneven terrain. These results will enhance the locomotion capability of musculoskeletal quadruped robots, advancing their practical application.

基于中央模式发生器(CPG)的控制器可增强四足运动的适应性,例如通过控制躯干姿势。传统的基于中央模式发生器的姿态控制控制器通常利用姿态角度作为反馈信息。但是,如果机器人的身体像肌肉骨骼结构一样柔软,它就可以根据肌肉的本体感觉信息来测量躯干的过度倾斜。一般来说,肌肉张力等本体感觉信息比姿势角度信息变化更快。因此,基于本体感觉信息的反馈回路在应对在不平坦地形上运动时发生的突然干扰方面具有巨大潜力。在这项研究中,我们提出了一种基于 CPG 的控制器,利用软气动肌(PAM)的张力。由 PAM 驱动的肌肉骨骼四足机器人非常柔软,可在一定程度上防止腿部过度伸展和躯干过度倾斜。此外,PAM 的本体感觉信息之一--张力对躯干姿势的变化表现出高度敏感性,因为软体的运动很容易因躯干过度倾斜而发生变化。为了验证所提控制器的有效性,我们用一个简单的四足机器人模型进行了数值模拟,并用一个肌肉骨骼四足机器人进行了实验。结果表明,当机器人的运动受到干扰时,张力反馈能有效地稳定姿态。此外,张力反馈还能有效提高机器人在不平坦地形上的奔跑速度。这些结果将提高肌肉骨骼四足机器人的运动能力,推动其实际应用。
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引用次数: 0
3D printed feathers with embedded aerodynamic sensing. 嵌入空气动力传感技术的 3D 打印羽毛。
IF 3.1 3区 计算机科学 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2024-11-06 DOI: 10.1088/1748-3190/ad87a0
Ruowen Tu, Rémy A Delplanche, Bret W Tobalske, Daniel J Inman, Henry A Sodano

Bird flight is often characterized by outstanding aerodynamic efficiency, agility and adaptivity in dynamic conditions. Feathers play an integral role in facilitating these aspects of performance, and the benefits feathers provide largely derive from their intricate and hierarchical structures. Although research has been attempted on developing membrane-type artificial feathers for bio-inspired aircraft and micro air vehicles (MAVs), fabricating anatomically accurate artificial feathers to fully exploit the advantages of feathers has not been achieved. Here, we present our 3D printed artificial feathers consisting of hierarchical vane structures with feature dimensions spanning from 10-2to 102mm, which have remarkable structural, mechanical and aerodynamic resemblance to natural feathers. The multi-step, multi-scale 3D printing process used in this work can provide scalability for the fabrication of artificial feathers tailored to the specific size requirements of aircraft wings. Moreover, we provide the printed feathers with embedded aerodynamic sensing ability through the integration of customized piezoresistive and piezoelectric transducers for strain and vibration measurements, respectively. Hence, the 3D printed feather transducers combine the aerodynamic advantages from the hierarchical feather structure design with additional aerodynamic sensing capabilities, which can be utilized in future biomechanical studies on birds and can contribute to advancements in high-performance adaptive MAVs.

鸟类飞行的特点通常是在动态条件下具有出色的气动效率、灵活性和适应性。羽毛在促进这些方面的性能方面发挥着不可或缺的作用,而羽毛所带来的益处主要来自于其错综复杂的分层结构。虽然人们已经尝试为生物启发飞机和微型飞行器(MAVs)开发膜式人工羽毛,但还没有制造出解剖精确的人工羽毛来充分发挥羽毛的优势。在此,我们展示了由分层叶片结构组成的三维打印人工羽毛,其特征尺寸从 10-2 毫米到 102 毫米不等,在结构、机械和空气动力学方面与天然羽毛极为相似。这项工作中使用的多步骤、多尺度三维打印工艺可为制造符合飞机机翼特定尺寸要求的人造羽毛提供可扩展性。此外,我们还通过集成定制的压阻和压电传感器,使打印的羽毛具有嵌入式空气动力传感能力,分别用于应变和振动测量。因此,三维打印羽毛传感器结合了分层羽毛结构设计的空气动力学优势和额外的空气动力学传感能力,可用于未来的鸟类生物力学研究,并有助于推动高性能自适应无人飞行器的发展。
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引用次数: 0
The passive recording of the click trains of a beluga whale (Delphinapterus leucas) and the subsequent creation of a bio-inspired echolocation model. 被动记录白鲸(Delphinapterus leucas)的点击序列,并随后创建生物启发回声定位模型。
IF 3.1 3区 计算机科学 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2024-11-05 DOI: 10.1088/1748-3190/ad8f22
Xin Qing, Yuncong Wang, Zhi Xia, Songzuo Liu, Suleman Mazhar, Yibo Zhao, Wangyi Pu, Gang Qiao

A beluga-like model of click train signal is developed by observing beluga's sound recording. To reproduce the feature of the biosonar signal, this paper uses a signal extracting method with a correction factor of inter-click interval to acquire the parameter of click trains. The extracted clicks were analyzed in the time and frequency domain. Furthermore, a joint pulse-frequency representation was undertaken in order to provide a 2D energy distribution for an echolocation click train. The results from joint pulse-frequency representation indicate that click train can be adjusted its energy distribution by using a multi-component signal structure. To evaluate the capability of the click train to inform the whale of relevant target information perception for the click train, a finite element model is built to reproduce target discrimination by the bio-inspired click train. Numerical results indicate that the bio-inspired click train could enhance the echo-response by concentrating energy into the frequency bins for extracting target feature effectively. This proof-of-concept study suggests that the model of click train could be dynamically controlled to match the target properties, and show a promising way to use various types of echolocation click train to interrogate different features of the target by man-made sonar.

通过观察白鲸的声音记录,建立了类似白鲸的点击列车信号模型。为了再现生物声纳信号的特征,本文采用了一种信号提取方法,并加入了点击间隔修正因子,以获取点击列车的参数。本文对提取的点击信号进行了时域和频域分析。此外,为了提供回声定位点击序列的二维能量分布,还采用了脉冲-频率联合表示法。脉冲-频率联合表示法的结果表明,点击序列可以通过使用多分量信号结构调整其能量分布。为了评估点击列车向鲸鱼提供相关目标信息感知的能力,建立了一个有限元模型来再现生物启发点击列车的目标识别能力。数值结果表明,生物启发的点击列车可以通过将能量集中到频段来增强回声响应,从而有效提取目标特征。这项概念验证研究表明,可以动态控制点击列车的模型以匹配目标特性,并为利用各种类型的回声定位点击列车通过人造声纳询问目标的不同特征提供了一种可行的方法。
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引用次数: 0
Robotic feet modeled after ungulates improve locomotion on soft wet grounds. 仿照蹄类动物的机器人脚改善了在松软潮湿地面上的运动能力。
IF 3.1 3区 计算机科学 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2024-11-04 DOI: 10.1088/1748-3190/ad839c
S Godon, A Ristolainen, M Kruusmaa

Locomotion on soft yielding grounds is more complicated and energetically demanding than on hard ground. Wet soft ground (such as mud or snow) is a particularly difficult substance because it dissipates energy when stepping and resists extrusion of the foot. Sinkage in mud forces walkers to make higher steps, thus, to spend more energy. Yet wet yielding terrains are part of the habitat of numerous even-toed ungulates (large mammals with split hooves). We hypothesized that split hooves provide an advantage on wet grounds and investigated the behavior of moose legs on a test rig. We found that split hooves of a moose reduce suction force at extrusion but could not find conclusive evidence that the hoof reduces sinkage. We then continued by designing artificial feet equipped with split-hoof-inspired protuberances and testing them under different conditions. These bio-inspired feet demonstrate an anisotropic behavior enabling reduction of sinkage depth up to 46.3%, suction force by 47.6%, and energy cost of stepping on mud by up to 70.4%. Finally, we mounted these artificial feet on a Go1 quadruped robot moving in mud and observed 38.7% reduction of the mechanical cost of transport and 55.0% increase of speed. Those results help us understand the physics of mud locomotion of animals and design better robots moving on wet terrains. We did not find any disadvantages of the split-hooves-inspired design on hard ground, which suggests that redesigning the feet of quadruped robots improves their overall versatility and efficiency on natural terrains.

在松软的地面上运动比在坚硬的地面上运动更加复杂,对能量的要求也更高。湿软地面(如泥地或雪地)是一种特别困难的物质,因为它在迈步时会耗散能量并阻碍脚的挤出。泥浆中的沉降迫使步行者迈出更高的步子,从而消耗更多的能量。然而,潮湿的屈服地形是许多偶蹄类动物(大型哺乳动物,蹄分裂)的栖息地之一。我们假设分蹄在潮湿的地面上具有优势,并在试验台上对驼鹿腿的行为进行了调查。我们发现,驼鹿的分蹄能减少挤压时的吸力,但找不到分蹄能减少下沉的确凿证据。随后,我们继续设计了装有受裂蹄启发的突起的人造脚,并在不同条件下对其进行了测试。这些受生物启发的脚表现出了各向异性的行为,使下沉深度降低了 46.3%,吸力降低了 47.6%,踩泥的能量成本降低了 70.4%。最后,我们将这些人造足安装在泥浆中移动的 Go1 四足机器人上,观察到运输的机械成本降低了 38.7%,速度提高了 55.0%。这些结果有助于我们理解动物在泥浆中运动的物理原理,并设计出在潮湿地形上运动的更好的机器人。我们没有发现分蹄式设计在坚硬地面上有任何缺点,这表明重新设计四足机器人的脚可以提高它们在自然地形上的整体通用性和效率。
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引用次数: 0
Designing efficient bird-like flapping-wing aerial vehicles: insights from aviation perspective. 设计高效的类鸟拍翼飞行器:从航空角度看问题。
IF 3.1 3区 计算机科学 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2024-11-01 DOI: 10.1088/1748-3190/ad88c4
Dongfu Ma, Bifeng Song, Shijin Gao, Dong Xue, Jianlin Xuan

Bird-like flapping-wing aerial vehicles (BFAVs) have attracted significant attention due to their advantages in endurance, range, and load capacity. For a long time, biologists have been studying the enigma of bird flight to understand its mechanism. In contrast, aviation designers focus more on bionic flight systems. This paper presents a comprehensive review of the development of BFAV design. The study aims to provide insights into building a flyable model from the perspective of aviation designers, focusing on the methods in the process of overall design, flapping wing design and drive system design. The review examines the annual progress of flight-capable BFAVs, analyzing changes in prototype size and performance over the years. Additionally, the paper highlights various applications of these vehicles. Furthermore, it discusses the challenges encountered in BFAV design and proposes several possible directions for future research, including perfecting design methods, improving component performance, and promoting practical application. This review will provide essential guidelines and insights for designing BFAVs with higher performance.

生物启发飞行系统;类鸟拍翼飞行器;拍翼飞行;机翼设计;机构设计;多模式运动。
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引用次数: 0
Brain-body-task co-adaptation can improve autonomous learning and speed of bipedal walking. 大脑-身体-任务协同适应可以提高自主学习能力和双足行走的速度。
IF 3.1 3区 计算机科学 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2024-10-24 DOI: 10.1088/1748-3190/ad8419
Darío Urbina-Meléndez, Hesam Azadjou, Francisco J Valero-Cuevas

Inspired by animals that co-adapt their brain and body to interact with the environment, we present a tendon-driven and over-actuated (i.e.njoint,n+1 actuators) bipedal robot that (i) exploits its backdrivable mechanical properties to manage body-environment interactions without explicit control,and(ii) uses a simple 3-layer neural network to learn to walk after only 2 min of 'natural' motor babbling (i.e. an exploration strategy that is compatible with leg and task dynamics; akin to childsplay). This brain-body collaboration first learns to produce feet cyclical movements 'in air' and, without further tuning, can produce locomotion when the biped is lowered to be in slight contact with the ground. In contrast, training with 2 min of 'naïve' motor babbling (i.e. an exploration strategy that ignores leg task dynamics), does not produce consistent cyclical movements 'in air', and produces erratic movements and no locomotion when in slight contact with the ground. When further lowering the biped and making the desired leg trajectories reach 1 cm below ground (causing the desired-vs-obtained trajectories error to be unavoidable), cyclical movements based on either natural or naïve babbling presented almost equally persistent trends, and locomotion emerged with naïve babbling. Therefore, we show how continual learning of walking in unforeseen circumstances can be driven by continual physical adaptation rooted in the backdrivable properties of the plant and enhanced by exploration strategies that exploit plant dynamics. Our studies also demonstrate that the bio-inspired co-design and co-adaptations of limbs and control strategies can produce locomotion without explicit control of trajectory errors.

受共同调整大脑和身体以与环境互动的动物的启发,我们提出了一种腱驱动和过度致动(即 n 个关节、n+1 个致动器)的双足机器人,(i) 利用其可反向驱动的机械特性来管理身体与环境的互动,而无需显式控制;(ii) 使用简单的 3 层神经网络,在仅 2 分钟的 "自然 "运动咿呀学语(即一种与腿部和任务动态相容的探索策略;类似于儿童游戏)后学会行走。这种脑-体协作首先学会在 "空中 "进行脚部周期性运动,然后无需进一步调整,就能在双足降低到与地面轻微接触时进行运动。与此相反,通过 2 分钟的 "原始 "运动咿呀训练(即忽略腿部任务动态的探索策略),并不能在 "空中 "产生一致的周期性运动,而且在与地面轻微接触时会产生不稳定的运动,也不会产生运动。当进一步降低双足并使所需的腿部轨迹低于地面 1 厘米时(使所需与所获轨迹的误差不可避免),基于自然咿呀学语或天真咿呀学语的周期性运动呈现出几乎相同的持续趋势,而天真咿呀学语则出现了运动。因此,我们展示了在不可预见的情况下如何通过持续的物理适应来学习行走,这种适应植根于植物的可逆向驱动特性,并通过利用植物动态的探索策略得到加强。我们的研究还证明,生物启发的肢体和控制策略的共同设计和共同适应可以在不明确控制轨迹误差的情况下产生运动。
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引用次数: 0
One-shot manufacturable soft-robotic pump inspired by embryonic tubular heart. 受胚胎管状心脏启发的一次性可制造软机器人泵。
IF 3.1 3区 计算机科学 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2024-10-22 DOI: 10.1088/1748-3190/ad839f
Kyoung Jin Lee, Jung Chan Lee

Soft peristaltic pumps, which use soft ring actuators instead of mechanical pistons or rollers, offer advantages in transporting liquids with non-uniform solids, such as slurry, food, and sewage. Recent advances in 3D printing with flexible thermoplastic polyurethane (TPU) present the potential for single-step fabrication of these pumps, distinguished from handcrafted, multistep traditional silicone casting methods. However, because of the relatively high hardness of TPU, TPU-based soft peristaltic pumps contract insufficiently and thus cannot perform as well as silicone-based ones. Improving the performance is crucial for fully automated, one-step manufactured soft pumps to lead to industrial use. This study aims to enhance TPU-based soft pumps through bioinspired design. Specifically, it proposed a design inspired by embryonic tubular hearts, in contrast to previous studies that mimicked digestive tracts. The new design facilitated long-axis stretching of an elliptical lumen during non-concentric contractile motion, akin to embryonic tubular hearts. The design was optimized for ring actuators and pumps 3D-printed with shore hardness 85 A TPU filament. The ring actuator achieved over 99% lumen closure with the best designs. The soft pumps transported water at flow rates of up to 218 ml min-1and generated a maximum discharge pressure of 355 mm Hg, comparable to the performance of blood pumps used in continuous renal replacement therapy.

软蠕动泵使用软环执行器代替机械活塞或滚轴,在输送含有不均匀固体的液体(如泥浆、食品和污水)方面具有优势。最近在使用柔性热塑性聚氨酯(TPU)进行三维打印方面取得的进展,为单步制造这些泵提供了可能,有别于手工制作、多步骤的传统硅胶铸造方法。然而,由于热塑性聚氨酯的硬度相对较高,基于热塑性聚氨酯的软蠕动泵收缩不足,因此性能不如基于硅胶的软蠕动泵。本研究旨在通过生物启发设计来提高基于热塑性聚氨酯的软蠕动泵的性能。具体来说,它提出了一种设计灵感来自胚胎管状心脏,与之前模仿消化道的研究不同。这种新设计有助于在非同心收缩运动中实现椭圆形管腔的长轴拉伸,与胚胎管状心脏类似。该设计针对环形致动器和泵进行了优化,使用邵氏硬度为 85A 的热塑性聚氨酯长丝进行 3D 打印。在最佳设计中,环形致动器实现了 99% 以上的管腔闭合。软泵输送水的流速高达 218 毫升/分钟,产生的最大排出压力为 355 毫米汞柱,与连续肾脏替代疗法中使用的血泵性能相当。
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引用次数: 0
Corrigendum: Aerodynamic efficiency of gliding birds vs comparable UAVs: a review (2021Bioinspir. Biomim.16 031001). 更正:滑翔鸟类与同类无人驾驶飞行器的空气动力效率对比:综述(2021Bioinspir. Biomim.16 031001)。
IF 3.1 3区 计算机科学 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2024-10-11 DOI: 10.1088/1748-3190/ad7082
Christina Harvey, Daniel J Inman
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引用次数: 0
A biomimetic fruit fly robot for studying the neuromechanics of legged locomotion. 用于研究腿部运动神经力学的仿生果蝇机器人。
IF 3.1 3区 计算机科学 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2024-10-09 DOI: 10.1088/1748-3190/ad80ec
Clarus A Goldsmith, Moritz Haustein, Ansgar Büschges, Nicholas S Szczecinski

For decades, the field of biologically inspired robotics has leveraged insights from animal locomotion to improve the walking ability of legged robots. Recently, 'biomimetic' robots have been developed to model how specific animals walk. By prioritizing biological accuracy to the target organism rather than the application of general principles from biology, these robots can be used to develop detailed biological hypotheses for animal experiments, ultimately improving our understanding of the biological control of legs while improving technical solutions. In this work, we report the development and validation of the robot Drosophibot II, a meso-scale robotic model of an adult fruit fly,Drosophila melanogaster. This robot is novel for its close attention to the kinematics and dynamics ofDrosophila, an increasingly important model of legged locomotion. Each leg's proportions and degrees of freedom have been modeled afterDrosophila3D pose estimation data. We developed a program to automatically solve the inverse kinematics necessary for walking and solve the inverse dynamics necessary for mechatronic design. By applying this solver to a fly-scale body structure, we demonstrate that the robot's dynamics fit those modeled for the fly. We validate the robot's ability to walk forward and backward via open-loop straight line walking with biologically inspired foot trajectories. This robot will be used to test biologically inspired walking controllers informed by the morphology and dynamics of the insect nervous system, which will increase our understanding of how the nervous system controls legged locomotion.

几十年来,受生物启发的机器人学领域一直在利用从动物运动中获得的启示来提高腿部机器人的行走能力。最近,"仿生 "机器人被开发出来,以模拟特定动物的行走方式。通过优先考虑目标生物的生物学精确性,而不是应用生物学的一般原理,这些机器人可用于为动物实验开发详细的生物学假设,最终提高我们对腿部生物控制的理解,同时改进技术解决方案。在这项工作中,我们报告了机器人 Drosophibot II 的开发和验证情况,这是一种中尺度的成年果蝇(黑腹果蝇)机器人模型。该机器人的新颖之处在于它密切关注果蝇的运动学和动力学,而果蝇是一种日益重要的腿部运动模型。每条腿的比例和自由度都是根据果蝇的三维姿势估计数据建模的。我们开发了一个程序,可以自动求解行走所需的逆运动学,并求解机电一体化设计所需的逆动力学。通过将该求解器应用于苍蝇尺度的身体结构,我们证明机器人的动力学符合苍蝇的模型。我们验证了机器人通过开环直线行走和生物脚轨迹向前和向后行走的能力。该机器人将用于测试受昆虫神经系统形态和动力学启发的生物行走控制器,这将加深我们对神经系统如何控制腿部运动的理解。
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引用次数: 0
Role of viscoelasticity in the adhesion of mushroom-shaped pillars. 粘弹性在蘑菇状支柱粘附中的作用。
IF 3.1 3区 计算机科学 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2024-10-04 DOI: 10.1088/1748-3190/ad839d
Guido Violano, Savino Dibitonto, Luciano Afferrante

The contact behaviour of mushroom-shaped pillars has been extensively studied for their superior adhesive properties, often inspired by natural attachment systems observed in insects. Typically, pillars are modeled with linear elastic materials in the literature; in reality, the soft materials used for their fabrication exhibit a rate-dependent constitutive behaviour. Additionally, conventional models focus solely on the detachment phase of the pillar, overlooking the analysis of the attachment phase. As a result, they are unable to estimate the energy loss during a complete loading-unloading cycle. This study investigates the role of viscoelasticity in the adhesion between a mushroom-shaped pillar and a rigid flat countersurface. Interactions at the interface are assumed to be governed by van der Waals forces, and the material is modeled using a standard linear solid model. Normal push and release contact cycles are simulated at different approaching and retracting speeds. Results reveal that, in the presence of an interfacial defect, a monotonically increasing trend in the pull-off force with pulling speed is observed. The corresponding change in the contact pressure distribution suggests a transition from short-range to long-range adhesion, corroborating recent experimental and theoretical investigations. Moreover, the pull-off force remains invariant to the loading history due to our assumption of a flat-flat contact interface. Conversely, in the absence of defects and under the parameters used in this study, detachment occurs after reaching the theoretical contact strength, and the corresponding pull-off force is found to be rate independent. Notably, the hysteretic loss exhibits a peak at intermediate detachment speeds, where viscous dissipation occurs, which holds true in both the presence and absence of a defect. However, the presence of a defect shifts the region where the majority of viscous dissipation takes place.

蘑菇状支柱的接触行为因其卓越的粘附特性而受到广泛研究,其灵感往往来自于在昆虫中观察到的自然粘附系统。文献中通常使用线性弹性材料对支柱进行建模;而实际上,用于制造支柱的软材料表现出与速率相关的构成行为。此外,传统模型只关注支柱的脱离阶段,忽略了对附着阶段的分析。因此,这些模型无法估算出在一个完整的加载-卸载循环过程中的能量损失。假定界面上的相互作用力受范德华力支配,并使用标准线性固体模型对材料进行建模。结果表明,在存在界面缺陷的情况下,拉拔力随拉拔速度呈单调递增趋势。接触压力分布的相应变化表明,短程粘附过渡到了长程粘附,这与最近的实验和理论研究相吻合。相反,在没有缺陷和本研究使用的参数下,达到理论接触强度后就会发生脱离,相应的拉脱力与速率 无关。值得注意的是,滞后损失在中间脱离速度处显示出一个峰值,此时会出现粘性耗散,这在存在和不存在缺陷时都是正确的。然而,缺陷的存在会移动大部分粘性耗散发生的区域。
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引用次数: 0
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