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The deflection limit of slab-like topologically interlocked structures 板状拓扑互锁结构的挠度极限
IF 2.6 4区 工程技术 Q2 MECHANICS Pub Date : 2023-07-03 DOI: 10.1115/1.4063345
Silvan Ullmann, David S. Kammer, Shai Feldfogel
Topologically Interlocked Structures (TIS) are structural assemblies that achieve stability and carrying capacity through the geometric arrangement of interlocking blocks, relying solely on contact and friction forces for load transfer. Unlike beam-like TIS, whose deflection never exceeds the height of the blocks, the deflection of slab-like TIS often does. Yet, the upper limit of deflection of slab-like TIS, a key parameter defining their loading energy capacity, remains unexplored. Here, we establish a theoretical upper bound for the deflection capacity of slab-like TIS and outline a systematic design strategy to approach this upper bound. This strategy is based on engineering the contact interfaces such that the non-central blocks are more engaged in the structural response, leading to a more global and holistic deformation mode with higher deflections. We demonstrate the application of this strategy in a numerical case study on a typical slab-like TIS and show that it leads to a 350% increase in deflection, yielding a value closer to the upper bound than previously reported in the literature. We find that the resulting deflection mode engages all the blocks equally, avoids localized sliding modes, and resembles that of monolithic equivalents. Lastly, we show that the strategy not only maximizes TIS' deflection capacity but also its loading energy capacity.
拓扑联锁结构(TIS)是通过联锁块的几何布置实现稳定性和承载能力的结构组件,仅依靠接触力和摩擦力进行荷载传递。与梁状TIS不同,板状TIS的挠度通常不会超过砌块的高度。然而,板状TIS的挠度上限,这是定义其加载能量容量的关键参数,仍有待探索。在这里,我们建立了板状TIS挠度能力的理论上限,并概述了一个接近该上限的系统设计策略。该策略基于对接触界面进行工程设计,使非中心块体更多地参与结构响应,从而导致具有更高挠度的更全局和整体的变形模式。我们在一个典型的板状TIS的数值案例研究中证明了这种策略的应用,并表明它会导致350%的挠度增加,产生一个比文献中先前报道的更接近上限的值。我们发现,由此产生的偏转模式平等地接合所有块体,避免了局部滑动模式,并且类似于单片等效的偏转模式。最后,我们证明了该策略不仅使TIS的偏转能力最大化,而且使其加载能量能力最大化。
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引用次数: 3
The General Gauss Principle of Least Constraint 一般高斯最小约束原理
IF 2.6 4区 工程技术 Q2 MECHANICS Pub Date : 2023-07-03 DOI: 10.1115/1.4062887
F. Udwadia
This paper develops a general form of Gauss's Principle of Least Constraint, which deals with the manner in which Nature appears to orchestrate the motion of constrained mechanical systems. The theory of constrained motion has been at the heart of classical mechanics since the days of Lagrange, and it is used in various areas of science and engineering like analytical dynamics, quantum mechanics, statistical physics, and nonequilibrium thermodynamics. The new principle permits the constraints on any mechanical system to be inconsistent and shows that Nature handles these inconsistent constraints in the least squares sense. This broadening of Gauss's original principle leads to two forms of the General Gauss Principle obtained in this paper. They explain why the motion that Nature generates is robust with respect to inaccuracies with which constraints are often specified in modeling naturally occurring and engineered systems since their specification in dynamical systems are often only approximate, and many physical systems may not exactly satisfy them at every instant of time. An important byproduct of the new principle is a refinement of the notion of what constitutes a virtual displacement, a foundational concept in classical mechanics.
本文发展了高斯最小约束原理的一般形式,它处理自然似乎协调受约束机械系统运动的方式。自拉格朗日以来,约束运动理论一直是经典力学的核心,它被应用于科学和工程的各个领域,如分析动力学、量子力学、统计物理和非平衡热力学。新原理允许任何机械系统上的约束是不一致的,并表明大自然在最小二乘意义上处理这些不一致的约束。对高斯原原理的扩展,得到了两种形式的一般高斯原理。它们解释了为什么自然产生的运动相对于在自然发生和工程系统建模中经常指定的约束的不准确性是健壮的,因为它们在动力系统中的规范通常只是近似的,许多物理系统可能并不完全满足它们在每个时刻。新原理的一个重要副产品是对构成虚位移的概念的改进,虚位移是经典力学中的一个基本概念。
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引用次数: 0
Shock Isolation of an Orthogonal Six DOFs Platform with High-Static-Low-Dynamic Stiffness 高静低动刚度正交六自由度平台的隔震
IF 2.6 4区 工程技术 Q2 MECHANICS Pub Date : 2023-07-03 DOI: 10.1115/1.4062886
Rong-Biao Hao, Ze-Qi Lu, H. Ding, Liqun Chen
A novel approach to enhance the shock vibration environment of multi-directions using a high-static-low-dynamic stiffness supported orthogonal six degree-of-freedoms (DOFs) nonlinear vibration isolation (OSNVI) system is presented in this paper. By combining spring positive stiffness and magnetic negative stiffness, the proposed system achieves high-static-low-dynamic stiffness. Under the multi-directions half-sine vibration, the dynamic equation of the OSNVI is obtained. Both dynamic and static analysis methods are utilized to explore the effect of various parameters on the shock isolation performance of the OSNVI from both the time and frequency domains. The results indicate that the proposed OSNVI can efficiently suppress multi-direction shocks at the cost of only one second. Although a nonlinear jump is usually not expected, the nonlinear jump of the OSNVI could improve the load capacity by increasing the spring stiffness without changing the shock isolation frequency band. Finally, a shock experiment is employed through a three-axis shaker platform to validate the shock isolation performance of the orthogonal six-DOFs nonlinear vibration isolator. The proposed OSNVI provides a promising approach to suppress the multi-directional shock vibrations.
本文提出了一种利用高静态低动态刚度支撑的正交六自由度非线性隔振系统来增强多方向冲击振动环境的新方法。该系统将弹簧正刚度和磁负刚度相结合,实现了高静态低动态刚度。在多方向半正弦振动下,得到了OSNVI的动力学方程。采用动态和静态分析方法,从时域和频域两个角度探讨了各种参数对OSNVI隔振性能的影响。结果表明,所提出的OSNVI可以有效地抑制多方向冲击,只需1秒的时间。虽然通常不会出现非线性跳跃,但OSNVI的非线性跳跃可以在不改变隔振频带的情况下通过增加弹簧刚度来提高承载能力。最后,通过三轴振动台进行了冲击实验,验证了正交六自由度非线性隔振器的隔振性能。所提出的OSNVI为抑制多向冲击振动提供了一种很有前途的方法。
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引用次数: 2
A novel efficient energy absorber with necking-expansion of foam sandwich tubes 一种新型泡沫夹层管颈胀式高效吸能器
IF 2.6 4区 工程技术 Q2 MECHANICS Pub Date : 2023-06-28 DOI: 10.1115/1.4062843
Haoyuan Guo, Jianxun Zhang
Foam sandwich tube is composed of two tubes and a lightweight foam core possessing various advantages, i.e. low density, excellent mitigation performance and energy absorption, etc. With the hope of enhancing the load bearing and energy absorption capacity of energy absorbers, a novel efficient energy absorber composing of axial necking-expansion deformation mode for sandwich circular tube with metal foam core (SCMF-Tube) by an inner-outer conical-cylindrical die is proposed. Considering deformation modes including necking, stretching, bending and strain hardening of metal tubes as well as densification of the metal foam core, we established an analytical model of necking-expansion deformation for the SCMF-Tube. Then, FE simulations are conducted. Analytical deformation modes, load-displacement curves and bending radii all agree well with the FE results. Effects of material property and geometry on the necking-expansion deformation of SCMF-Tubes are discussed in detail based on the validated analytical model. Adjusting parameters, such as the wall thickness ratio of the inner tube to the outer tube and the maximum diameter of the die can improve the load bearing and energy absorption capacity of the novel energy absorber. Finally, the specific energy absorption (SEA) of the SCMF-Tube under necking-expansion deformation is 68% higher than that of the circular metal tube under expansion deformation.
泡沫夹层管由两根管和一个轻质泡沫芯组成,具有密度低、缓冲性能好、吸能等优点。为了提高吸能器的承载能力和吸能能力,提出了一种由内外锥形圆柱模具组成的金属泡沫芯夹芯圆管(SCMF-Tube)轴向结胀型高效吸能器。考虑金属管的颈缩、拉伸、弯曲和应变硬化变形模式以及金属泡沫芯的致密化,建立了scmf管的颈缩-膨胀变形解析模型。然后进行了有限元模拟。解析变形模式、荷载-位移曲线和弯曲半径与有限元结果吻合较好。在验证的解析模型基础上,详细讨论了材料性能和几何形状对scmf管颈胀变形的影响。调节内管与外管壁厚比、模具最大直径等参数,可以提高新型吸能器的承载和吸能能力。最后,SCMF-Tube在颈部膨胀变形下的比能吸收(SEA)比圆形金属管在膨胀变形下的比能吸收(SEA)高68%。
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引用次数: 0
Effective mechanical properties of auxetic materials: Numerical predictions using variational asymptotic method based homogenization 增减材料的有效力学性能:基于均质化的变分渐近方法的数值预测
IF 2.6 4区 工程技术 Q2 MECHANICS Pub Date : 2023-06-28 DOI: 10.1115/1.4062845
Chetna Srivastava, V. M., P. Pitchai, P. Guruprasad, N. Petrinic, F. Scarpa, D. Harursampath, Sathiskumar Anusuya Ponnusami
In this work, the variational asymptotic method (VAM) based homogenization framework is used for the first time to determine the equivalent elastic stiffness tensor of auxetic materials. The proposed method allows the structural elements of the auxetic unit cell to naturally incorporate rotational degrees of freedom, without any ad-hoc assumptions. The overall macroscale homogenized response of the unit-cells is considered to be fully anisotropic; specific possible responses, representative of orthotropy or transverse isotropy naturally emerge from the VAM-based homogenization, due to the arrangements of the structural elements making up the unit-cell. For all the auxetic unit cell geometries considered in this study, the predictions obtained from the in-house python-based implementation of the VAM-based homogenization framework are validated using commercial finite element software (Abaqus) and open literature. The results demonstrate the versatility and the computational efficiency of the VAM-based homogenization framework to describe auxetic metamaterials.
本文首次利用变分渐近方法(VAM)的均匀化框架确定了塑性材料的等效弹性刚度张量。所提出的方法允许辅助单元胞的结构元素自然地结合旋转自由度,而不需要任何特别的假设。单元胞整体宏观均匀响应被认为是完全各向异性的;由于构成单元胞的结构元素的排列,从基于vam的均质化中自然产生了具有代表性的正交异性或横向各向同性的特定可能响应。对于本研究中考虑的所有缺陷单元格几何形状,利用商业有限元软件(Abaqus)和公开文献验证了基于vam的均质化框架的内部python实现所获得的预测。结果表明,基于vam的均匀化框架在描述生长性超材料方面具有通用性和计算效率。
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引用次数: 1
Axisymmetric peeling of thin elastic films: A perturbation solution 弹性薄膜轴对称剥落:微扰解
IF 2.6 4区 工程技术 Q2 MECHANICS Pub Date : 2023-06-26 DOI: 10.1115/1.4062831
E. Chen, Zhaohe Dai
We study the mechanical behavior of a thin elastic film that is affixed to a rigid substrate and subjected to a transverse force using a shaft with a finite radius. This scenario, also referred to as axisymmetric peeling, is encountered frequently in conventional blister tests as well as in our daily lives when removing an adhesive film from a substrate. Our primary objective is to gain a quantitative understanding of how the shaft's radius influences the relationships between force and displacement, as well as between force and delamination areas. These relationships can serve as a dependable method to determine both the film's elastic modulus and the adhesion strength between the film and its substrate. In this work, we provide a simple perturbation solution to this geometrically nonlinear problem while avoiding any use of ad hoc assumptions that were previously required in the literature. As a result, our results are in excellent agreement with numerical simulations and offer improved accuracy compared to analytical solutions available in the literature.
我们研究了粘在刚性基材上的弹性薄膜的力学行为,并使用有限半径的轴施加横向力。这种情况,也被称为轴对称剥落,在传统的泡罩测试中经常遇到,以及在我们的日常生活中,当从基材上去除胶膜时。我们的主要目标是定量了解轴的半径如何影响力和位移之间的关系,以及力和分层区域之间的关系。这些关系可以作为一种可靠的方法来确定薄膜的弹性模量和薄膜与基材之间的粘附强度。在这项工作中,我们为这个几何非线性问题提供了一个简单的摄动解决方案,同时避免了以往文献中所要求的任何临时假设的使用。因此,我们的结果与数值模拟非常一致,并且与文献中可用的解析解决方案相比,提供了更高的准确性。
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引用次数: 1
Full field solution for remotely loaded one side completely debonded short rigid line inclusion embedded in soft matrix: 2D Analytical and Experimental insights 嵌入软基质的远程加载单侧完全脱粘短刚性线夹杂物的全场解决方案:2D分析和实验见解
IF 2.6 4区 工程技术 Q2 MECHANICS Pub Date : 2023-06-21 DOI: 10.1115/1.4062771
Swapnil Patil, S. Khaderi, Ramji Manoharan, Vishwanath Chinthapenta
The problem of a completely debonded short fiber (rigid line inclusion/anticrack) embedded in a 2D isotropic elastic soft-matrix subjected to the remote loading condition is of fundamental interest. The current work investigates completely debonded anticrack embedded in a soft (isotropic) matrix using Kolosov Muskhelisvili's complex potential framework. Here two configurations are studied: debonded inclusion oriented (i) parallel and (ii) perpendicular to the loading direction. In particular, the potentials take the form of a non-homogeneous Riemann - Hilbert equation for the given problem. Upon solving analytical forms of potentials, the stress fields were obtained. The stress field for the fully debonded anticrack exhibited oscillatory singular behavior between r^(-3/4) and r^(-1/4) with the dependence on the oscillatory index e and material constants. The correctness of the analytical solution was validated using numerical simulation and experiments based on the digital photoelasticity technique. The analytical results were in good agreement with the experimental and numerically obtained stress fields confirming the accuracy of it. The magnitude of singularity is quantified by defining a complex stress intensity factor at the tip of the discontinuity and compared with the experimentally estimated value. So far in the literature, no full-field analytical solution exists for the completely debonded rigid inclusion embedded in an isotropic soft matrix. The solution obtained in the present work is of fundamental importance in developing the constitutive properties of short fiber reinforced thermoplastic (SFRT) composites.
在二维各向同性弹性软基体中嵌入完全脱粘的短纤维(刚性线夹杂物/抗裂物)在远程加载条件下的问题是一个重要的研究课题。目前的工作使用Kolosov Muskhelisvili的复杂势框架研究嵌入在软(各向同性)矩阵中的完全脱粘裂纹。这里研究了两种构型:与加载方向平行(i)和垂直(ii)的脱粘包涵体。特别地,对于给定的问题,势采用非齐次黎曼-希尔伯特方程的形式。通过求解势的解析形式,得到了应力场。完全脱粘裂纹应力场在r^(-3/4)和r^(-1/4)之间表现出振荡奇异行为,与振荡指数e和材料常数有关。基于数字光弹性技术的数值模拟和实验验证了解析解的正确性。分析结果与实验和数值计算的应力场吻合较好,证实了该方法的准确性。通过在不连续点尖端定义一个复杂应力强度因子来量化奇异性的大小,并与实验估计值进行比较。在文献中,对于嵌入在各向同性软矩阵中的完全脱粘刚性包体,还没有完整的场解析解。研究结果对研究短纤维增强热塑性塑料(SFRT)复合材料的本构性能具有重要意义。
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引用次数: 0
Dramatic amplification of the flexoelectric effect in snapping surfaces 挠性表面的挠性电效应的急剧放大
IF 2.6 4区 工程技术 Q2 MECHANICS Pub Date : 2023-06-21 DOI: 10.1115/1.4062777
Lingling Chen, Xinyu Xing, Chuo Zhao, Shengyou Yang
Flexoelectricity exists in all inhomogeneously deformed dielectric materials and is greatly interesting in engineering science, especially in manufacturing microelectromechanical systems. However, the flexoelectricity is relatively small compared to the commonly known piezoelectricity. How to produce a considerably large flexoelectric effect and how to apply the effect to a large scale have concerned people for a long time. In this paper, we creatively enlarge the flexoelectric effect without decreasing the structure scale by harnessing the electromechanical instability—the snap-through instability—of a curved dielectric plate subjected to a concentrated load. We formulate the electrostatic energy of the system and obtain the governing equations by taking the first variation of the free energy. In the analysis, we find that the thickness of the plate and the initial configuration affect the onset of the snap-through. Beyond that, we notice that flexoelectricity can lower the critical load of the snap-through instability. Importantly, we find that a large flexoelectricity can be generated by harnessing the instability. For a dielectric plate with thickness 2 × 10−7 m, the effective electromechanical coefficient is equal to 35 pC/N in the beginning; however, by using the instability, the coefficient can be increased to as high as 740 pC/N, which is 21 times higher after the instability. In the end, we tune the electromechanical behaviors by designing the curved plate's thickness and configuration. This paper contributes to our understanding of the amplification of flexoelectric effects by harnessing snapping surfaces.
挠性电存在于所有非均匀变形的介质材料中,是工程科学,特别是制造微机电系统中非常有趣的问题。然而,与众所周知的压电相比,挠性电相对较小。如何产生相当大的挠电效应以及如何大规模应用挠电效应一直是人们关注的问题。在本文中,我们创造性地利用弯曲介质板在集中载荷作用下的机电不稳定性——卡通不稳定性,在不减小结构尺度的情况下扩大了挠性电效应。我们给出了系统的静电能,并通过自由能的一阶变化得到了控制方程。在分析中,我们发现板的厚度和初始配置影响卡通的发生。除此之外,我们还注意到,柔性电可以降低卡通不稳定性的临界负载。重要的是,我们发现利用不稳定性可以产生大量的柔性电力。对于厚度为2 × 10−7 m的介质板,初始有效机电系数为35 pC/N;而利用失稳后,系数可提高到740 pC/N,失稳后系数提高了21倍。最后,通过设计弯曲板的厚度和结构,对其机电性能进行了调整。这篇论文有助于我们理解利用断裂表面放大柔性电效应。
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引用次数: 0
Analytical and numerical investigations of circular metal foam sandwich tube under free inversion 自由反演下圆形金属泡沫夹层管的解析与数值研究
IF 2.6 4区 工程技术 Q2 MECHANICS Pub Date : 2023-06-21 DOI: 10.1115/1.4062772
Jinwen Bai, Jianxun Zhang
The foam sandwich tube contains inner and outer tubes and filling foam. The foam sandwich tube is widely used in engineering, due to the lightweight, high specific strength, energy absorption and other excellent characteristics. In this paper, the free inversion of the circular metal foam sandwich tube (CMFST) under axial loading is studied analytically and numerically. The plastic deformation occurs in the CMFST, and its main deformation modes include circumferential expansion, radial bending of the CMFST and compression of the metal sandwich foam. An analytical model for the free inversion of the CMFST under axial loading is established, considering metal tube expansion, the radial bending of metal circular tube wall, and metal foam compression. The commercial ABAQUS software is adopted to numerically study the free inversion behavior of the CMFST. The analytical predications agree well with the numerical ones. It is shown that the specific energy absorption (SEA) of the CMFST under free inversion is significantly better than the empty tube. When the non-dimensional foam strength is 0.05, the SEA of the CMFST under free inversion is 107.68% higher than the empty tube. Thus, the metal foam sandwich tube under free inversion is an excellent energy-absorbing device.
泡沫夹芯管包括内管、外管和填充泡沫。泡沫夹层管由于具有重量轻、比强度高、吸能等优良特性,在工程上得到了广泛的应用。本文对圆形金属泡沫夹层管(CMFST)在轴向载荷作用下的自由反演问题进行了分析和数值研究。塑性变形发生在CMFST中,其主要变形模式包括CMFST的周向膨胀、径向弯曲和金属夹层泡沫的压缩。考虑金属管膨胀、金属圆管壁径向弯曲和金属泡沫压缩,建立了轴向载荷作用下CMFST自由变形的解析模型。采用商用ABAQUS软件对CMFST的自由反演行为进行了数值研究。解析预测与数值预测吻合较好。结果表明,自由倒置下CMFST的比能吸收(SEA)明显优于空管。当无因次泡沫强度为0.05时,自由倒置下CMFST的SEA比空管高107.68%。因此,自由倒置下的金属泡沫夹层管是一种优良的吸能装置。
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引用次数: 0
Perspective: Large Language Models in Applied Mechanics 透视:应用力学中的大语言模型
IF 2.6 4区 工程技术 Q2 MECHANICS Pub Date : 2023-06-21 DOI: 10.1115/1.4062773
Neal R. Brodnik, Samuel Carton, Caelin Muir, Satanu Ghosh, Doug Downey, M. Echlin, T. Pollock, S. Daly
Large language models (LLMs), such as ChatGPT and PaLM, are able to perform sophisticated text comprehension and generation tasks with little or no training. Alongside their broader societal impacts, these capabilities carry great promise for the physical sciences, including applied mechanics. We present a summary of recent developments in these models, their application to mechanics and adjacent fields, and a perspective on their future use in applied mechanics, taking into account their limitations and the unique challenges of the field.
大型语言模型(LLM),如ChatGPT和PaLM,能够在很少或没有训练的情况下执行复杂的文本理解和生成任务。除了更广泛的社会影响外,这些能力对包括应用力学在内的物理科学也有很大的前景。我们总结了这些模型的最新发展,它们在力学和邻近领域的应用,并展望了它们在应用力学中的未来应用,同时考虑到它们的局限性和该领域的独特挑战。
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引用次数: 2
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Journal of Applied Mechanics-Transactions of the Asme
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