Extreme Mechanics Letters最新文献_第10页

Secondary instability and evolution of straight-sided blisters in cylindrical film-substrate systems 圆柱形薄膜-衬底体系中直边泡的二次不稳定性和演化

IF 4.3 3区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Extreme Mechanics Letters

Pub Date : 2025-05-26 DOI: 10.1016/j.eml.2025.102360

Jiahui Zhang , Yi Sun , Linghui He , Yong Ni

The regulation of buckle delamination morphologies in compressed thin films is crucial for ensuring material stability, particularly in systems with curved substrates. While substrate curvature is known to influence surface instabilities, its specific role in governing buckle delamination remains insufficiently understood. This paper investigates the secondary instability and evolution of straight-sided blisters in cylindrical film-substrate systems with both positive and negative curvature through theoretical analysis and finite element simulations. Linear stability analysis elucidates the dependence of critical buckling stress and wavelength on the amplitude and sign of curvature and Poisson’s ratio, revealing distinct instability regimes. The calculated phase diagrams for secondary instability mode selection indicate that symmetric modes dominate at small curvature and low Poisson’s ratios, while antisymmetric modes prevail at larger values. Finite element simulations not only validate the linear stability predictions, but also capture nonlinear evolution of straight-sided blisters into dendritically branched morphologies with dimple-like structures beyond secondary instability. These findings provide new insights into the interplay between curvature, material properties, and instability modes in compressed film-substrate systems.

压缩薄膜中扣层脱层形态的调节对于确保材料稳定性至关重要，特别是在具有弯曲衬底的系统中。虽然已知基底曲率会影响表面不稳定性，但其在控制扣层脱层中的具体作用仍未得到充分了解。本文通过理论分析和有限元模拟，研究了正曲率和负曲率圆柱形薄膜-衬底系统中直边泡的二次失稳和演化过程。线性稳定性分析阐明了临界屈曲应力和波长与曲率和泊松比的幅度和符号的关系，揭示了不同的不稳定状态。计算的二次失稳模态选择相图表明，在小曲率和低泊松比下对称模态占优势，而在较大泊松比下反对称模态占优势。有限元模拟不仅验证了线性稳定性预测，而且还捕获了直边泡在二次不稳定性之外向具有韧窝状结构的枝状分支形态的非线性演化。这些发现为压缩薄膜-衬底系统中曲率、材料特性和不稳定模式之间的相互作用提供了新的见解。

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引用次数: 0

Frustrated domes: From planar metamaterials to load-bearing structures 受挫圆顶：从平面超材料到承重结构

IF 4.3 3区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Extreme Mechanics Letters

Pub Date : 2025-05-24 DOI: 10.1016/j.eml.2025.102352

Imtiar Niloy , Lucas Annink , Olivine Silier , Chiara Daraio , Paolo Celli

We show that non-periodic, planar metamaterials can be turned into pop-up dome structures that are up-scalable and load-bearing. We do so by introducing a pin-jointed variation of such metamaterials. We illustrate the pop-up mechanics of these structures – dominated by the non-periodicity-induced frustration of a mechanism motion – via numerical simulations and experiments. We then show that joining together boundary nodes leads to self-standing domes that can bear significant loads, at least 20 times their own weight. Finally, we show that our idea can be easily scaled up to the meter-scale, and we illustrate that one can play around with the geometrical shape of the structural elements to obtain different pop-up shapes. Our work shows how metamaterials-related ideas that work at the tabletop-scale can be turned into concepts for innovative shape-morphing, load-bearing structures.

我们展示了非周期性的平面超材料可以变成可伸缩和承重的弹出式圆顶结构。我们通过引入这种超材料的针状接头变体来实现这一目标。我们通过数值模拟和实验说明了这些结构的弹出机制-由机构运动的非周期性诱导的挫折主导。然后，我们展示了将边界节点连接在一起可以形成独立的圆顶，可以承受至少是其自重20倍的载荷。最后，我们展示了我们的想法可以很容易地扩展到米的尺度，我们说明了人们可以玩弄结构元素的几何形状来获得不同的弹出形状。我们的工作展示了在桌面尺度上工作的与超材料相关的想法如何转化为创新的形状变形和承重结构的概念。

引用次数: 0

Hexagonal tessellation-based mechanical metamaterials 基于六边形镶嵌的机械超材料

IF 4.3 3区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Extreme Mechanics Letters

Pub Date : 2025-05-21 DOI: 10.1016/j.eml.2025.102356

Reza Moghimimonfared, Andrea Spaggiari, Luigi Grasselli, Luke Mizzi

Mechanical metamaterials based on Euclidean polygonal tessellations represent a new class of architectured materials with the potential to exhibit a wide range of mechanical properties. In this work, we investigate a new class of systems based on the generic hexagonal tessellation with trigonal rotational symmetry and show how this tessellation has the potential to exhibit a wide range of Poisson’s ratios, including auxeticity, as well as a large spectrum of Young’s moduli whilst retaining transverse isotropy. The tessellation was characterized through geometric expressions in order to identify which combination of geometric parameters lead to realizable, concave or convex configurations and Finite Element simulations were used to evaluate the mechanical properties of these tessellations. Furthermore, three additively-manufactured prototypes, representative of the entire Poisson’s ratio range (i.e. negative, zero and positive Poisson’s ratio) were experimentally tested and analysed using Digital Image Correlation. The results obtained from both simulation and experimental approaches demonstrate the mechanical capabilities of these tessellations and indicate how new auxetic metamaterials may be found by exploring the vast design space afforded by Euclidean polygonal tilings.

基于欧几里得多边形镶嵌的机械超材料代表了一类具有广泛机械性能潜力的新型建筑材料。在这项工作中，我们研究了一类基于具有三角旋转对称的一般六边形镶嵌的新系统，并展示了这种镶嵌如何有潜力表现出广泛的泊松比，包括弹性，以及杨氏模的大谱，同时保持横向各向同性。通过几何表达式来表征镶嵌，以确定几何参数的组合导致可实现的凹或凸结构，并使用有限元模拟来评估这些镶嵌的力学性能。此外，三个可代表整个泊松比范围（即负泊松比、零泊松比和正泊松比）的加性制造原型进行了实验测试，并使用数字图像相关技术进行了分析。从模拟和实验方法中获得的结果证明了这些镶嵌的机械能力，并表明如何通过探索欧几里得多边形瓷砖提供的巨大设计空间来发现新的auxetic超材料。

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引用次数: 0

Molecular Velcro for characterizing hydrogel coating adhesion 表征水凝胶涂层附着力的分子魔术贴

IF 4.3 3区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Extreme Mechanics Letters

Pub Date : 2025-05-19 DOI: 10.1016/j.eml.2025.102357

Yuan Wang , Hui Yuan , Zhikun Miao , Junjie Liu , Xuxu Yang , Yecheng Wang

Rapid advances in hydrogel adhesion have enabled the development of hydrogel coating on various substrates for lubrication, drug delivery, and anti-fouling paints. The quality of adhesion between hydrogel coating and substrate is important in applications, but has been shown to be extremely challenging to assess. Here we develop a general approach to characterizing the adhesion of hydrogel coating, called the molecular Velcro. Such Velcro is a stiff layer, to which polymer chains are grafted through covalent interlinks, and adheres to hydrogel through non-covalent interlinks. We prepare a 35 μm-thick hydrogel coated on a rigid substrate, introduce a pre-cut crack to their interface, and use the molecular Velcro as backing layer to measure the adhesion toughness by 90-degree peel. As the non-covalent adhesion between the molecular Velcro and the hydrogel is instant and tough, and does not affect the mechanical properties of the hydrogel, the crack grows along the interface between the hydrogel and the substrate, or kinks into the hydrogel. Consequently, the adhesion between the hydrogel coating and the substrate is precisely characterized at various coating thicknesses, peel velocities, and crosslink densities. To show the robustness of our approach, we further measure the adhesion toughness of several types of 50 μm-thick hydrogels coated on the same substrate. This work will guide the characterization of adhesion of soft and wet coatings.

水凝胶粘附的快速发展使得水凝胶涂层在各种基材上的发展成为可能，用于润滑、药物输送和防污涂料。水凝胶涂层与基材之间的粘附质量在应用中很重要，但已被证明是极具挑战性的评估。在这里，我们开发了一种通用的方法来表征水凝胶涂层的附着力，称为分子魔术贴。这种尼龙搭扣是一种刚性层，聚合物链通过共价连接接枝，并通过非共价连接附着在水凝胶上。我们制备了一层35 μm厚的水凝胶包覆在刚性基体上，在其界面上引入预切裂缝，并使用分子维可牢作为衬底层，采用90度剥离法测量了水凝胶的粘附韧性。由于分子维可牢与水凝胶之间的非共价粘附是瞬间的、坚韧的，并且不影响水凝胶的力学性能，因此裂缝沿着水凝胶与底物之间的界面生长，或者扭入水凝胶。因此，在不同的涂层厚度、剥离速度和交联密度下，水凝胶涂层与基材之间的粘附性得到了精确的表征。为了证明我们方法的稳健性，我们进一步测量了几种50 μm厚的水凝胶涂覆在同一基底上的粘附韧性。这项工作将指导软性和湿性涂层的附着力表征。

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引用次数: 0

Implicit geometric descriptor-enabled ANN Framework for a unified structure-property relationship in architected nanofibrous materials 基于隐式几何描述符的人工神经网络框架用于构建纳米纤维材料的统一结构-性能关系

IF 4.3 3区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Extreme Mechanics Letters

Pub Date : 2025-05-17 DOI: 10.1016/j.eml.2025.102346

Bhanugoban Maheswaran, Komal Chawla, Abhishek Gupta, Ramathasan Thevamaran

Hierarchically architected nanofibrous materials, such as the vertically aligned carbon nanotube (VACNT) foams, draw their exceptional mechanical properties from the interplay of nanoscale size effects and inter-nanotube interactions within and across architectures. However, the distinct effects of these mechanisms, amplified by the architecture, on different mechanical properties remain elusive, limiting their independent tunability for targeted property combinations. Reliance on architecture-specific explicit design parameters further inhibits the development of a unified structure–property relationship rooted in those nanoscale mechanisms. Here, we introduce two implicit geometric descriptors — multi-component shape invariants (MCSI) — in an artificial neural network (ANN) framework to establish a unified structure–property relationship that governs diverse architectures. The MCSIs effectively capture the key nanoscale mechanisms that give rise to the bulk mechanical properties such as specific-energy absorption, peak stress, and average modulus. Exploiting their ability to predict mechanical properties for designs that are even outside of the training data, we propose generalized design strategies to achieve desired mechanical property combinations in architected VACNT foams. Such implicit descriptor-enabled ANN frameworks can guide the accelerated and tractable design of complex hierarchical materials for applications ranging from shock-absorbing layers in extreme environments to functional components in soft robotics.

分层结构的纳米纤维材料，如垂直排列的碳纳米管（VACNT）泡沫，从纳米尺度尺寸效应和结构内部和结构之间的纳米管相互作用的相互作用中获得了卓越的机械性能。然而，这些被结构放大的机制对不同机械性能的不同影响仍然难以捉摸，限制了它们对目标性能组合的独立可调性。依赖于特定于体系结构的显式设计参数进一步抑制了植根于这些纳米级机制的统一结构-性能关系的发展。本文在人工神经网络（ANN）框架中引入了两个隐式几何描述符——多分量形状不变量（MCSI），以建立统一的结构-属性关系来管理不同的体系结构。mcsi有效地捕获了产生体力学性能（如比能吸收、峰值应力和平均模量）的关键纳米尺度机制。利用其预测设计机械性能的能力，甚至在训练数据之外，我们提出了通用的设计策略，以实现在体系结构VACNT泡沫中所需的机械性能组合。这种隐式描述符支持的人工神经网络框架可以指导复杂分层材料的加速和易于处理的设计，应用范围从极端环境中的减震层到软机器人中的功能组件。

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引用次数: 0

Cylindrical cavity expansion for characterizing mechanical properties of soft materials 表征软质材料力学性能的圆柱腔膨胀

IF 4.3 3区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Extreme Mechanics Letters

Pub Date : 2025-05-14 DOI: 10.1016/j.eml.2025.102343

Jian Li , Zihao Xie , Hannah Varner , S. Chockalingam , Tal Cohen

The low elastic modulus of soft materials, combined with geometric nonlinearity and rate dependence, presents significant challenges in the characterization of their mechanical response. We introduce a novel method for measuring the mechanical properties of soft materials under large deformations via cylindrical cavity expansion. In this method, a cylindrical cavity is fabricated in the material and expanded by volume-controlled injection of an incompressible fluid with simultaneous measurement of the applied pressure at the cavity wall. The relationship between applied pressure and deformation at the cavity wall is then employed to characterize the nonlinear mechanical properties. This method improves traditional volume-controlled cavity expansion testing and other needle-induced cavity expansion methods by precisely controlling the geometry and size of the initial defect or cavity, significantly enhancing both the accuracy and repeatability of the experimental results. We demonstrate the feasibility of the proposed method and validate it by measuring the mechanical properties of synthetic polydimethylsiloxane (PDMS) and comparing with reported values in the literature. Results indicate that the cylindrical cavity expansion method effectively captures the response of PDMS over a wide range of stiffness (shear modulus ranging from 5 kPa to 300 kPa) and exhibit high repeatability. The proposed method overcomes limitations in characterization of ultra-soft materials using traditional testing methods, such as challenges with fabrication and clamping in uniaxial tension testing and friction and adhesion effects in compression and indentation testing, thus enabling accurate and precise characterization.

软质材料的低弹性模量，结合几何非线性和速率依赖性，对其力学响应的表征提出了重大挑战。介绍了一种利用圆柱空腔膨胀法测量软质材料大变形力学性能的新方法。在这种方法中，在材料中制造一个圆柱形腔，并通过体积控制注入不可压缩流体来膨胀，同时测量腔壁处的施加压力。然后利用施加压力与腔壁变形之间的关系来表征非线性力学性能。该方法通过精确控制初始缺陷或空腔的几何形状和尺寸，改进了传统的体积控制空腔扩展测试和其他针激空腔扩展方法，显著提高了实验结果的准确性和可重复性。我们通过测量合成聚二甲基硅氧烷（PDMS）的力学性能并与文献报道的值进行比较，证明了所提出方法的可行性。结果表明，柱腔扩展法能有效地捕捉PDMS在大刚度范围内（剪切模量从5 kPa到300 kPa）的响应，且具有较高的重复性。该方法克服了使用传统测试方法表征超软材料的局限性，例如单轴拉伸测试中的制造和夹紧挑战以及压缩和压痕测试中的摩擦和粘附效应，从而实现了准确和精确的表征。

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引用次数: 0

Mode-coupled infinite topological edge state in bulk-lattice-merged mechanical Su–Schrieffer–Heeger chain 块格融合机械Su-Schrieffer-Heeger链中模式耦合无限拓扑边态

IF 4.3 3区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Extreme Mechanics Letters

Pub Date : 2025-05-12 DOI: 10.1016/j.eml.2025.102334

Yeongtae Jang , Seokwoo Kim , Minkyung Kim , Guenil Kim , Eunho Kim , Junsuk Rho

Band topology has emerged as a powerful tool for designing mechanical engineering systems, from phononic crystals to metamaterials. Various design principles — whether bulk-based or lattice-based — have been proposed and successfully implemented according to unit cell structures. Here, we present a bulk-lattice merged Su–Schrieffer–Heeger (SSH) chain constructed from single-column woodpile metamaterials. This system consists of a lattice array of cylindrical particles, where each particle’s bulk dynamics exhibits local resonance-mode coupling with wave propagation. We demonstrate that topological edge states emerge in direct correspondence with these local resonance modes, manifesting as mode-coupled topological states. Experimentally, we observe the initial emergence of these mode-coupled topological edge states, with their frequencies accurately predicted by nonlinear characteristic equations rooted in continuum dynamics and topological symmetry. Additionally, the system’s weak nonlinearity enables simultaneous frequency shifts, allowing multivariate tunability in its topological states.

从声子晶体到超材料，带拓扑已经成为设计机械工程系统的有力工具。各种设计原则-无论是基于体的还是基于晶格的-已经根据单元胞结构提出并成功实施。在这里，我们提出了一个由单柱木桩超材料构建的体积-晶格合并Su-Schrieffer-Heeger （SSH）链。该系统由圆柱形粒子的晶格阵列组成，其中每个粒子的体动力学表现出与波传播的局部共振模式耦合。我们证明了拓扑边缘状态与这些局部共振模式直接对应，表现为模式耦合拓扑状态。实验中，我们观察到这些模式耦合拓扑边缘态的初始出现，其频率由基于连续统动力学和拓扑对称性的非线性特征方程精确预测。此外，系统的弱非线性使频移同时发生，允许其拓扑状态的多元可调性。

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引用次数: 0

An extended Euler-Bernoulli beam principle in multi-component metamaterial towards tunable Poisson’s ratio 面向泊松比可调的多组分超材料中欧拉-伯努利光束原理的扩展

IF 4.3 3区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Extreme Mechanics Letters

Pub Date : 2025-05-10 DOI: 10.1016/j.eml.2025.102347

Jingyi Zhang , Yuheng Liu , Haibao Lu , Ran Tao

In this paper, a multi-component mechanical metamaterial was proposed to achieve tunable nominal modulus and Poisson’s ratio to extend the potential and practical applications in smart materials and structures. Based on the Euler-Bernoulli beam theory, a universal model was formulated for the multi-component metamaterial to explore the constitutive relationship between the model parameters and mechanical properties. The theoretical model reveals that the Poisson’s ratio of the multi-component metamaterial could be quantitatively regulated over a broad range by manipulating the moduli of its constituent components. On this basis, a bi-component metamaterial composed of polylactic acid (PLA) and thermoplastic polyurethane (TPU), featuring distinct temperature-dependent moduli and geometric configurations, was manufactured and exhibited thermally tunable mechanical behavior. Parametric finite element simulations were conducted to investigate the synergistic effect of temperature-dependent moduli and geometric parameters on the stable mechanical behaviors of the bi-component metamaterial, with the results validated by experimental measurements. This study examines the design principle that combines material parameters (temperature-dependent moduli) and structural parameters (geometric parameters) for the multi-component mechanical metamaterial. The methodologies and insights presented in this paper provide new perspectives and technical approaches for the innovative applications of metamaterials in aerospace, biomedical, and microelectronic fields.

本文提出了一种多组分机械超材料，以实现可调的标称模量和泊松比，以扩大智能材料和结构的潜力和实际应用。基于欧拉-伯努利梁理论，建立了多组分超材料的通用模型，探讨了模型参数与力学性能之间的本构关系。理论模型表明，多组分超材料的泊松比可以通过控制其组成组分的模量在较宽的范围内进行定量调节。在此基础上，制备了一种由聚乳酸（PLA）和热塑性聚氨酯（TPU）组成的双组分超材料，该材料具有不同的温度依赖模量和几何构型，并表现出热可调的力学行为。通过参数化有限元模拟研究了温度相关模量和几何参数对双组分超材料稳定力学行为的协同效应，并通过实验验证了结果。本研究考察了多组分机械超材料的材料参数（温度相关模量）和结构参数（几何参数）相结合的设计原则。本文提出的方法和见解为超材料在航空航天、生物医学和微电子领域的创新应用提供了新的视角和技术途径。

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引用次数: 0

Kinematic folding propagation in degree-4 origami strips 4度折纸条的运动折叠传播

IF 4.3 3区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Extreme Mechanics Letters

Pub Date : 2025-05-09 DOI: 10.1016/j.eml.2025.102337

Rinki Imada , Akito Adachi , Shingo Terashima , Eiji Iwase , Tomohiro Tachi

Degree-4 origami strips, one-DOF mechanisms constructed by sequentially connecting degree-4 origami vertices, have inspired origami-based engineering design. However, thorough kinematic analyses were limited to a special subset of degree-4 origami strips that exhibit uniform folding along the sequence. In this study, we show how folding propagates non uniformly, i.e., gets attenuated or amplified, in a general degree-4 origami strip. We introduce the concept of kinematic folding propagation and analyze it by studying discrete dynamical systems. Our results reveal that, despite its simple structure, the strip exhibits diverse folding propagation behaviors, strongly influenced by design parameters such as sector angles and topology of the crease patterns. We show that the propagation behavior is topologically linear when adjacent vertices are connected via opposite creases. We compute and visualize folding motions, including strips that transition from a flat-folded state to a helical shape through uniform or nonuniform (attenuated/amplified) propagation upon actuation of the boundary crease. Additionally, we demonstrate folding propagation in physical models using 3D-printed prototypes with thick panels. Furthermore, we show that topologically nonlinear propagation emerges when adjacent creases are used to connect adjacent vertices. We also discuss folding propagation in curved-crease origami that is achieved by taking a continuum limit of the strip. Our findings establish kinematic folding propagation as a core functionality enabled by nonuniform folding, thereby laying the foundation for programmable origami.

四度折纸条是一种由四度折纸顶点顺序连接而成的单自由度机构，它启发了基于折纸的工程设计。然而，彻底的运动学分析仅限于一个特殊的4度折纸条子集，它们沿序列呈现均匀的折叠。在本研究中，我们展示了在一般程度为4的折纸带中，折叠如何非均匀传播，即衰减或放大。引入了运动学折叠传播的概念，并通过对离散动力系统的研究对其进行了分析。我们的研究结果表明，尽管其结构简单，但该条带表现出多种折叠传播行为，这些行为受到扇形角和折痕图拓扑等设计参数的强烈影响。我们证明，当相邻顶点通过相反的折痕连接时，传播行为是拓扑线性的。我们计算和可视化折叠运动，包括在边界折痕驱动下通过均匀或不均匀（衰减/放大）传播从平折叠状态过渡到螺旋形状的条带。此外，我们使用带有厚面板的3d打印原型在物理模型中演示折叠传播。此外，我们证明了当相邻的折痕用于连接相邻的顶点时，拓扑非线性传播会出现。我们还讨论了弯曲折痕折纸中的折叠传播，这是通过取条带的连续极限来实现的。我们的研究结果将运动折叠传播作为非均匀折叠的核心功能，从而为可编程折纸奠定了基础。

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引用次数: 0

Geometric dependence of curvature-induced rigidity

IF 4.3 3区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Extreme Mechanics Letters

Pub Date : 2025-05-09 DOI: 10.1016/j.eml.2025.102341

Hanzhang Mao , Thomas G.J. Chandler , Mark Han , Saverio E. Spagnolie

Bending the edge of a thin elastic material promotes rigidity far from its clamped boundary. However, this curvature-induced rigidity can be overwhelmed by gravity or other external loading, resulting in elastic buckling and large deformations. We consider the role of body geometry on this competition using experiments, numerical simulations, and reduced-order models. Finite element simulations are performed using a model nonlinear hyperelastic material, and a theoretical framework is proposed that incorporates small lateral curvatures, large longitudinal rotations, and a varying cross-sectional width. A particular focus is on the comparison between rectangular and triangular sheets, and trapezoidal sheets in between. Sheet geometry affects downward tip deflection by changing the relative importance of the sheet’s weight and the rigidity provided by curvature, often in subtle ways. In extreme cases, non-monotonic deflection is observed with increasing sheet length, and a region of hysteretic bistability emerges, becoming more pronounced with rectangular sheets and large imposed curvatures. These findings demonstrate the profound impact of geometry on the competition between curvature-induced rigidity and gravity-induced deformation in thin elastic materials.

弯曲薄型弹性材料的边缘可使其刚性远离其固定边界。然而，这种曲率引起的刚度可能被重力或其他外部载荷所淹没，导致弹性屈曲和大变形。我们使用实验、数值模拟和降阶模型来考虑身体几何在这种竞争中的作用。采用模型非线性超弹性材料进行了有限元模拟，并提出了一个包含小横向曲率，大纵向旋转和变截面宽度的理论框架。特别关注的是矩形和三角形板材之间的比较，以及两者之间的梯形板材。板的几何形状通过改变板的重量和曲率提供的刚度的相对重要性来影响向下的尖端挠度，通常以微妙的方式。在极端情况下，随着薄板长度的增加，观察到非单调偏转，并且出现了一个滞回双稳区域，在矩形薄板和大施加曲率时变得更加明显。这些发现表明几何形状对薄弹性材料中曲率诱导刚度和重力诱导变形之间的竞争有深远的影响。

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引用次数: 0