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New Insight into the Flexoelectricity in the View of Mechanics of Materials: Prismatic Beams Subjected to Bending 材料力学视角下的柔电新见解:受弯曲影响的棱柱梁
IF 2 3区 工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2024-07-11 DOI: 10.1007/s10338-024-00495-3
Xu Yang, Lingling Chen, Shengyou Yang

Flexoelectricity is a fascinating electromechanical phenomenon that occurs in non-homogeneously deformed dielectric materials. Unlike piezoelectricity, the flexoelectric effect is highly dependent on both the material scale and the deformation gradient. Although several theoretical models have been proposed to explain the mechanism of flexoelectricity, these models can be rather complicated for those who are interested in studying the topic. This paper aims to simplify the understanding of flexoelectricity by focusing on the bending behavior of a prismatic dielectric beam from a mechanics of material perspective. We avoid using complicated mathematical formulations based on continuum mechanics, including advanced tensor algebra and calculus of variations. Our formulation clearly explains how inhomogeneous deformations and material size affect the electromechanical coupling, changing the effective bending stiffness, deflection, and rotation angles of a bending beam. We hope this paper can help undergraduate students and researchers, who are unfamiliar with the electromechanical coupling in flexoelectricity, to develop an understanding of this phenomenon and encourage further research in this area.

挠电是一种迷人的机电现象,发生在非均匀变形的介电材料中。与压电不同,挠电效应高度依赖于材料尺度和变形梯度。虽然已经提出了一些理论模型来解释挠电效应的机理,但对于有兴趣研究该课题的人来说,这些模型可能相当复杂。本文从材料力学的角度出发,重点研究棱柱形介电梁的弯曲行为,旨在简化对挠性电动现象的理解。我们避免使用基于连续介质力学的复杂数学公式,包括高级张量代数和变分微积分。我们的公式清楚地解释了不均匀变形和材料尺寸如何影响机电耦合,从而改变弯曲梁的有效弯曲刚度、挠度和旋转角度。我们希望这篇论文能帮助不熟悉挠性电中机电耦合的本科生和研究人员理解这一现象,并鼓励他们在这一领域开展进一步的研究。
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引用次数: 0
Preface to the Special Issue in Celebration of Professor Shouwen Yu’s 85th Birthday 庆祝余寿文教授 85 岁诞辰特刊序言
IF 2 3区 工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2024-07-03 DOI: 10.1007/s10338-024-00496-2
Xi-Qiao Feng, Qunyang Li
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引用次数: 0
Effect of Tacticity on the Dynamic Response of Chiral Mechanical Metamaterials 手性对手性机械超材料动态响应的影响
IF 2 3区 工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2024-07-01 DOI: 10.1007/s10338-024-00505-4
Pengcheng Zhao, Zhigang Wang, Xiaojun Zhu, Tingting Wang, Kai Zhang

In this work, a tacticity strategy is proposed to adjust the mechanical properties of chiral mechanical metamaterials for vibration isolation. By applying the finite element method, the impact of tacticity on tensile deformations, band structures, and vibration transmission spectra of chiral metamaterials is investigated. The axial deformations of isotactic configuration and syndiotactic configuration are similar under tensile loads, but rotational deformation occurs in the isotactic configuration. With the same geometric and material parameters, the first band gap of the syndiotactic configuration is lower than that of the isotactic configuration. The vibration suppression performance of chiral mechanical metamaterials is verified by numerical simulations and experiments. Parametric analysis of the band gap provides valuable insights for the manipulation and expansion of vibration reduction. Gradient design based on parametric analysis achieves an extended range of vibration suppression.

本研究提出了一种触变策略,用于调整手性机械超材料的机械特性,以达到隔振效果。通过应用有限元方法,研究了触变对手性超材料的拉伸变形、带状结构和振动传输谱的影响。在拉伸载荷作用下,等轴构型和双轴构型的轴向变形相似,但等轴构型出现了旋转变形。在几何和材料参数相同的情况下,辛迪拉构型的第一带隙低于异构构型。数值模拟和实验验证了手性机械超材料的振动抑制性能。对带隙的参数分析为操纵和扩展振动抑制提供了有价值的见解。基于参数分析的梯度设计实现了更大范围的振动抑制。
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引用次数: 0
Hysteresis Analysis on Origami Energy Dissipation Braces with Local Miura Units 带有局部三浦单元的折纸消能支架的滞后分析
IF 2 3区 工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2024-06-28 DOI: 10.1007/s10338-024-00503-6
Ya Zhou, Xu Li, Yuting Zhang, Jian Feng, Jianguo Cai

A local design scheme for origami energy dissipation braces was proposed by combining local Miura units at both ends and a straight segment in the middle. This design was implemented to address the issue of uneven axial stiffness observed in global origami braces. Globally and locally designed origami braces were simulated and compared under cyclic loading to validate the advantages of the proposed design scheme in terms of hysteretic properties. Additionally, an analysis was conducted on the designed braces with varying straight segment lengths, geometric angles, and origami plate thicknesses for comparison. Results indicate that the local design significantly increases the tensile bearing load, enhances the anti-buckling capability, and improves the energy dissipation performance compared to the global design. The positive impact on bearing capacity and energy dissipation performance was observed with increased straight segment length, geometric angles, and origami plate thickness. However, excessively large parameter values result in brace buckling under compression, diminishing energy dissipation capacity.

通过将两端的局部三浦单元和中间的直线段结合起来,提出了一种折纸消能支架的局部设计方案。采用这种设计是为了解决在全局折纸支撑中观察到的轴向刚度不均匀的问题。对整体和局部设计的折纸支架进行了模拟,并在循环载荷下进行了比较,以验证所提设计方案在滞后特性方面的优势。此外,还对不同直线段长度、几何角度和折纸板厚度的设计支架进行了分析比较。结果表明,与整体设计相比,局部设计大大提高了拉伸承载力,增强了抗屈曲能力,并改善了能量耗散性能。随着直线段长度、几何角度和折纸板厚度的增加,对承载能力和能量耗散性能产生了积极影响。然而,过大的参数值会导致支撑在压缩时发生屈曲,从而降低能量耗散能力。
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引用次数: 0
Enhanced Flexoelectricity in Barium Titanate-Cellulose Composite Thin Films 增强钛酸钡-纤维素复合薄膜的柔电性能
IF 2 3区 工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2024-06-26 DOI: 10.1007/s10338-024-00493-5
Wensi Xing, Hongyu Cao, Xin Zhang, Xu Liang, Jianwei Song, Shengping Shen

Biopolymers, the potential flexoelectric materials, are environment-friendly, degradable, lightweight, cost-effective, and possess remarkable processing properties catering to the requirements of advanced devices. However, the flexoelectric coefficient of biopolymers is normally much weaker than that of ceramic materials, limiting their potential applications for designing high-performance green electromechanical coupling devices. To improve the flexoelectric response in biopolymers, we composited barium titanate (BTO) with 2,2,6,6-tetramethylpiperidine-1-oxyl -oxidized cellulose nanofibrils (TOCNF) to enhance the flexoelectric response of TOCNF. Owing to the high permittivity and flexoelectric effect of BTO, the relative dielectric constant and flexoelectric coefficient of 33.3 wt% BTO-TOCNF films reached 30.94 @ 1 kHz and 50.05 ± 1.88 nC/m @ 1 Hz, which were almost 172 times and 27 times higher than those of TOCNF, respectively. The composite thin film contains high dielectric constant and flexoelectric coefficient, as well as excellent flexibility. Our study provided a straightforward and efficient method for improving the flexoelectric effect of biopolymers, and demonstrated its great potential applications in flexoelectric-based devices.

生物聚合物是一种潜在的挠电材料,具有环境友好、可降解、重量轻、成本低等特点,并具有显著的加工性能,可满足先进设备的要求。然而,生物聚合物的挠电系数通常比陶瓷材料的挠电系数弱得多,这限制了它们在设计高性能绿色机电耦合器件方面的潜在应用。为了改善生物聚合物的挠电响应,我们将钛酸钡(BTO)与 2,2,6,6- 四甲基哌啶-1-氧代氧化纤维素纳米纤维(TOCNF)复合,以增强 TOCNF 的挠电响应。由于 BTO 的高介电常数和挠电效应,33.3 wt% BTO-TOCNF 薄膜的相对介电常数和挠电系数分别达到 30.94 @ 1 kHz 和 50.05 ± 1.88 nC/m @ 1 Hz,分别是 TOCNF 的近 172 倍和 27 倍。复合薄膜具有较高的介电常数和柔电系数,以及优异的柔韧性。我们的研究为改善生物聚合物的挠电效应提供了一种简单有效的方法,并证明了其在基于挠电的器件中的巨大应用潜力。
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引用次数: 0
Preface to the “Theory and Applications of Flexoelectricity” Special Issue of Acta Mechanica Solida Sinica Mechanica Solida Sinica》"柔电理论与应用 "特刊序言
IF 2 3区 工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2024-06-19 DOI: 10.1007/s10338-024-00499-z
Qian Deng, Yue Zheng, Shengping Shen
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引用次数: 0
Total Internal Reflection (TIR) Behavior of Heterogeneous Interface Shear Waves in Layered Soft Structure 层状软结构中异质界面剪切波的全内反射 (TIR) 行为
IF 2 3区 工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2024-06-18 DOI: 10.1007/s10338-024-00497-1
Ming Zhao, Wentao Jiang, Qingyuan Wang, Ying Liang, Haidong Fan, Xiaobao Tian

The total internal reflection (TIR) behavior of interface shear waves is crucial for ensuring the reliability of dielectric elastomer (DE) devices. However, due to the complex force-electric coupling and large deformation of DEs, the TIR behavior of shear waves in heterogeneous force-electric interface models is still unclear. This study modeled an elastic/DE bi-material interface to analyze the trajectory of out-of-plane shear waves. Employing Dorfmann and Ogden’s nonlinear electroelastic framework and the related linear small incremental motion theory, a method has been developed to control the TIR behavior of interface shear waves. It has been found that the TIR behavior is significantly influenced by the strain-stiffening effect induced by biasing fields. Consequently, a biasing field principle involving preset electric displacement and pre-stretch has been proposed for TIR occurrence. By controlling the pre-stretch and preset electric displacement, active regulation of TIR behavior can be achieved. These results suggest a potential method for achieving autonomous energy shielding to improve the reliability of DE devices.

界面剪切波的全内反射(TIR)行为对于确保介电弹性体(DE)器件的可靠性至关重要。然而,由于介电弹性体复杂的力-电耦合和较大的变形,在异质力-电界面模型中剪切波的 TIR 行为仍不清楚。本研究建立了弹性/DE 双材料界面模型,以分析平面外剪切波的轨迹。利用 Dorfmann 和 Ogden 的非线性电弹性框架和相关的线性小增量运动理论,开发了一种控制界面剪切波 TIR 行为的方法。研究发现,界面剪切波的 TIR 行为受偏置场诱导的应变加固效应影响很大。因此,针对 TIR 的发生,提出了涉及预设电位移和预拉伸的偏置场原理。通过控制预拉伸和预设电位移,可以实现对 TIR 行为的主动调节。这些结果为实现自主能量屏蔽以提高 DE 器件的可靠性提供了一种潜在的方法。
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引用次数: 0
Size and Interface Effects on Tensile Strength of Polymers with Nano/Micro Particle Inclusions 尺寸和界面对含有纳米/微粒夹杂物的聚合物拉伸强度的影响
IF 2 3区 工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2024-06-12 DOI: 10.1007/s10338-024-00498-0
R. Yuan, X. Ma, L. H. Liang, Y. Wei

Polymers with particle inclusions have wide applications, and the mechanical properties of polymer composites affect their reliability in service. The strength of these composites is dependent on factors such as particle fraction, size, distribution, and interface interaction between the two phases, in addition to the properties of the polymers and particles. The size effect of particles and interface damage play an important role and thus draw considerable attention. In this paper, the size- and interface-dependent strength of polypropylene (PP) with nano/micro silica (SiO2) particles of different fractions is studied through a combination of tensile experiments on a series of samples and corresponding three-dimensional (3D) finite element modeling. The results indicate that PP with 2% SiO2 nanoparticles of 50 nm exhibits relatively higher tensile strength, shedding light on the microstructure mechanism where smaller particle sizes lead to better interface bonding. Furthermore, the particle size and interface coupling effect is analyzed based on the size-dependent elastic modulus model and the interface-cohesive model. The simulation demonstrates the local interface damage evolution around a particle of the composites in tension. These findings are beneficial for designing polymer composites with nanoparticle inclusions.

含有颗粒夹杂物的聚合物应用广泛,而聚合物复合材料的机械性能会影响其在使用中的可靠性。除了聚合物和颗粒的特性外,这些复合材料的强度还取决于颗粒的组分、尺寸、分布以及两相之间的界面相互作用等因素。颗粒的尺寸效应和界面破坏起着重要作用,因此备受关注。本文结合一系列样品的拉伸实验和相应的三维(3D)有限元建模,研究了含有不同比例纳米/微硅(SiO2)粒子的聚丙烯(PP)的尺寸和界面强度。结果表明,含有 2% 50 nm SiO2 纳米颗粒的聚丙烯具有相对较高的拉伸强度,这揭示了微观结构机制,即较小的颗粒尺寸会导致更好的界面结合。此外,基于粒度相关弹性模量模型和界面粘合模型分析了粒度和界面耦合效应。模拟展示了复合材料在拉伸状态下颗粒周围的局部界面损伤演变。这些发现有助于设计含有纳米颗粒夹杂物的聚合物复合材料。
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引用次数: 0
Linear and Nonlinear Formulation of Phase Field Model with Generalized Polynomial Degradation Functions for Brittle Fractures 带有广义多项式退化函数的脆性断裂相场模型的线性和非线性公式化
IF 2 3区 工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2024-06-11 DOI: 10.1007/s10338-024-00501-8
Ala Tabiei, Li Meng

The classical phase field model has wide applications for brittle materials, but nonlinearity and inelasticity are found in its stress–strain curve. The degradation function in the classical phase field model makes it a linear formulation of phase field and computationally attractive, but stiffness reduction happens even at low strain. In this paper, generalized polynomial degradation functions are investigated to solve this problem. The first derivative of degradation function at zero phase is added as an extra constraint, which renders higher-order polynomial degradation function and nonlinear formulation of phase field. Compared with other degradation functions (like algebraic fraction function, exponential function, and trigonometric function), this polynomial degradation function enables phase in [0, 1] (should still avoid the first derivative of degradation function at zero phase to be 0), so there is no (Gamma ) convergence problem. The good and meaningful finding is that, under the same fracture strength, the proposed phase field model has a larger length scale, which means larger element size and better computational efficiency. This proposed phase field model is implemented in LS-DYNA user-defined element and user-defined material and solved by the Newton–Raphson method. A tensile test shows that the first derivative of degradation function at zero phase does impact stress–strain curve. Mode I, mode II, and mixed-mode examples show the feasibility of the proposed phase field model in simulating brittle fracture.

经典相场模型广泛应用于脆性材料,但其应力-应变曲线存在非线性和非弹性。经典相场模型中的退化函数使其成为一种线性相场公式,在计算上具有吸引力,但即使在低应变时也会发生刚度降低。本文研究了广义多项式降解函数来解决这一问题。退化函数在零相位的一阶导数被添加为一个额外的约束条件,这使得高阶多项式退化函数和相位场的非线性表述成为可能。与其他降维函数(如代数分数函数、指数函数和三角函数)相比,该多项式降维函数使相位在 [0, 1] 内(仍应避免降维函数在零相位的一阶导数为 0),因此不存在 (Gamma ) 收敛问题。一个有意义的发现是,在相同的断裂强度下,所提出的相场模型具有更大的长度尺度,这意味着更大的元素尺寸和更好的计算效率。该相场模型在 LS-DYNA 用户自定义元素和用户自定义材料中实现,并采用 Newton-Raphson 方法求解。拉伸试验表明,零相退化函数的一阶导数确实会影响应力应变曲线。模式 I、模式 II 和混合模式实例表明了所提出的相场模型在模拟脆性断裂方面的可行性。
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引用次数: 0
Size-Dependent Analysis of Piezoelectric–Elastic Bilayer Microbeams Based on General Strain Gradient Theory 基于一般应变梯度理论的压电弹性双层微梁尺寸依赖性分析
IF 2 3区 工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2024-06-06 DOI: 10.1007/s10338-024-00492-6
Kanghui Wu, Shenjie Zhou, Zhenjie Zhang, Juanjuan Li

The classical piezoelectric theory fails to capture the size-dependent electromechanical coupling behaviors of piezoelectric microstructures due to the lack of material length-scale parameters. This study presents the constitutive relations of a piezoelectric material in terms of irreducible transversely isotropic tensors that include material length-scale parameters. Using these relations and the general strain gradient theory, a size-dependent bending model is proposed for a bilayer cantilever microbeam consisting of a transversely isotropic piezoelectric layer and an isotropic elastic layer. Analytical solutions are provided for bilayer cantilever microbeams subjected to force load and voltage load. The proposed model can be simplified to the model incorporating only partial strain gradient effects. This study examines the effect of strain gradient by comparing the normalized electric potentials and deflections of different models. Numerical results show that the proposed model effectively captures size effects in piezoelectric microbeams, whereas simplified models underestimate size effects due to ignoring partial strain gradient effects.

由于缺乏材料长度尺度参数,经典压电理论无法捕捉压电微结构的尺寸依赖性机电耦合行为。本研究通过包含材料长度尺度参数的不可还原横向各向同性张量,提出了压电材料的构成关系。利用这些关系和一般应变梯度理论,为由横向各向同性压电层和各向同性弹性层组成的双层悬臂微梁提出了与尺寸有关的弯曲模型。为承受力载荷和电压载荷的双层悬臂微梁提供了分析解决方案。提出的模型可简化为只包含部分应变梯度效应的模型。本研究通过比较不同模型的归一化电动势和挠度来研究应变梯度的影响。数值结果表明,提出的模型能有效捕捉压电微梁的尺寸效应,而简化模型由于忽略了部分应变梯度效应而低估了尺寸效应。
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引用次数: 0
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Acta Mechanica Solida Sinica
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