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Gradient metamaterials with tunable compression-twist coupling deformation 具有可调压扭耦合变形的梯度超材料
IF 2.3 3区 工程技术 Q2 MECHANICS Pub Date : 2024-11-26 DOI: 10.1007/s00707-024-04159-8
Xiaobin Zhang, Zhifang Liu, Jianyin Lei, Shiqiang Li

Compression-twist metamaterials exhibit unique properties of compression-induced twisting, presenting new possibilities for the development of smart materials. However, achieving multifunctionality solely through conventional configuration design and parametric studies of individual cells is relatively constrained. Gradient metamaterials, which are characterized by continuous spatial variation in physical and mechanical properties through the gradient design of geometric parameters, offer a promising approach for development multifunctional and smart materials. In this study, a novel 3D gradient compression-twist metamaterial (GCTMM) is proposed, with its mechanical properties and deformation mechanisms under in-plane compression investigated by theoretical analysis, experiment, and numerical simulations. The experimental and simulation results demonstrate a nonlinear relationship between the twist angle and compressive displacement. The height and number of cell layers influence the overall stiffness of the GCTMM and affect the deformation coordination between layers. The structure’s compression-twist coupling properties are significantly reduced due to the plastic yield of the inclined rods. Analytical models were developed to describe the twist angle and initial yield displacement, accurately predicting the nonlinear variation in compression-twist coupling behavior and the degradation of the mechanical performance. To enhance structural reliability, an improved GCTMM with protective support columns was designed and analyzed through numerical simulations. The results indicate that the maximum stress within the structure remains below the material’s yield strength, ensuring its reliability and durability. These findings offer valuable insights for the design of gradient buffer materials, the development of mechanical signal enhancement or conversion devices, and the creation of multistage signal transmission sensors.

压缩扭曲超材料表现出独特的压缩诱导扭曲特性,为智能材料的发展提供了新的可能性。然而,仅仅通过传统的配置设计和单个细胞的参数化研究来实现多功能是相对受限的。梯度超材料通过几何参数的梯度设计,其物理力学性能具有连续的空间变化特征,为开发多功能和智能材料提供了一条很有前途的途径。本文提出了一种新型的三维梯度压缩-扭转超材料(GCTMM),通过理论分析、实验和数值模拟研究了其在平面压缩下的力学性能和变形机理。实验和仿真结果表明,扭转角与压缩位移之间存在非线性关系。单元格层的高度和层数影响GCTMM的整体刚度,影响层间的变形协调。由于斜杆的塑性屈服,结构的压扭耦合性能显著降低。建立了描述扭角和初始屈服位移的解析模型,准确预测了压扭耦合行为的非线性变化和力学性能的退化。为了提高结构的可靠性,设计了一种带有保护支撑柱的改进GCTMM,并进行了数值模拟分析。结果表明,结构内部的最大应力保持在材料屈服强度以下,保证了结构的可靠性和耐久性。这些发现为梯度缓冲材料的设计、机械信号增强或转换装置的开发以及多级信号传输传感器的创建提供了有价值的见解。
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引用次数: 0
Influence of dynamic fiber volume fraction on Love wave velocity in PFRC plate imperfectly bonded with piezoelectric-viscoelastic substrate 动态纤维体积分数对非完美粘结PFRC板-压电粘弹性基板Love波速的影响
IF 2.3 3区 工程技术 Q2 MECHANICS Pub Date : 2024-11-25 DOI: 10.1007/s00707-024-04147-y
Mahargha Biswas, Sayantan Guha

To overcome certain limitations like shape control and high acoustic impedance of monolithic piezoelectric materials, piezoelectric fiber-reinforced composites (PFRCs) and piezoelectric-viscoelastic (PV) composites have emerged as obvious and amazing replacements. Particularly in PFRCs, piezoelectric fibers are surrounded by non-piezoelectric materials, and the effective material properties of PFRCs are dependent on both the constituent materials and the amount of piezoelectric fibers (fiber volume fraction) present in the elementary units of the composite. The present research article focuses on the transference of Love-type surface acoustic waves in a PFRC layer sandwiched between a viscoelastic polymer layer and a functionally graded piezoelectric-viscoelastic (FGPV) substrate. The effective material properties of the PFRC layer obtained by the rule of mixtures along with the strength of materials approach are used for mathematical computation. The interface between PFRC and FGPV substrate is mechanically and dielectrically imperfect. The material properties of the FGPV substrate vary along the structure’s depth. Dispersion relations have been obtained for both electroded and non-electroded states. Parametric responses of fiber volume fraction, mechanical and electrical imperfections, viscosity, and functional grading on dispersion traits of Love-type wave are demonstrated through graphical plotting. The outcomes of the study can be utilized to theoretically understand the dispersion in PFRCs.

为了克服单片压电材料的形状控制和高声阻抗等局限性,压电纤维增强复合材料(PFRCs)和压电粘弹性复合材料(PV)成为明显而令人惊叹的替代品。特别是在PFRCs中,压电纤维被非压电材料包围,PFRCs的有效材料性能取决于组成材料和复合材料基本单元中存在的压电纤维的数量(纤维体积分数)。本文主要研究了粘弹性聚合物层和功能梯度压电粘弹性(FGPV)基板之间的PFRC层中love型表面声波的传递。利用混合规律和材料强度法得到的PFRC层的有效材料性能进行了数学计算。PFRC和FGPV衬底之间的界面在机械和介电方面都不完美。FGPV衬底的材料特性沿着结构的深度变化。得到了电态和非电态的色散关系。通过图形化的方法,展示了纤维体积分数、机械和电缺陷、粘度和功能分级等参数对love型波色散特性的响应。研究结果可用于从理论上理解PFRCs中的分散。
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引用次数: 0
An improved line contact model for elastic–plastic rough surfaces 弹塑性粗糙表面的改进线接触模型
IF 2.3 3区 工程技术 Q2 MECHANICS Pub Date : 2024-11-25 DOI: 10.1007/s00707-024-04151-2
S. H. Wang, W. K. Yuan, X. M. Liang, G. F. Wang

In contacts of rough surfaces, the real contact area is much smaller and thus the contact pressure can be far beyond the yield strength of solids. Therefore, the influence of plastic deformation should be quite considerable in practice. In this paper, an improved incremental contact model is proposed to examine the elastic–plastic contact between a self-affine fractal rough surface and a rigid flat under the plane strain condition. For different rough surfaces with various material properties, the load-contact area relations predicted by the present model are in accordance with direct finite element simulations, and show a linear dependence within 15% contact fraction. Compared with the solution of purely elastic contact, the existence of plastic deformation results in a lower mean contact pressure over the real contact area. For rough surface with a small yield strain, the mean contact pressure rises with the yield stress in a power law: P/(E*Ac) ∝ (σy/E*)0.89. This study provides an efficient method for contact evaluation of elastic–plastic solids with highly anisotropic rough surfaces.

在粗糙表面的接触中,实际接触面积要小得多,因此接触压力可以远远超过固体的屈服强度。因此,在实际应用中塑性变形的影响应该是相当大的。本文提出了一种改进的增量接触模型,用于研究平面应变条件下自仿射分形粗糙表面与刚性平面之间的弹塑性接触。对于具有不同材料性能的不同粗糙表面,该模型预测的载荷-接触面积关系与直接有限元模拟基本一致,且在15%的接触分数范围内呈线性相关关系。与纯弹性接触解相比,塑性变形的存在使实际接触面积上的平均接触压力降低。对于屈服应变较小的粗糙表面,平均接触压力随屈服应力呈幂律上升:P/(E*Ac)∝(σy/E*)0.89。本研究为具有高各向异性粗糙表面的弹塑性固体的接触评价提供了一种有效的方法。
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引用次数: 0
Combined vibration control of flexible cantilever beam driven by MFC actuators and rotary motor MFC作动器与旋转电机驱动柔性悬臂梁的组合振动控制
IF 2.3 3区 工程技术 Q2 MECHANICS Pub Date : 2024-11-24 DOI: 10.1007/s00707-024-04140-5
Zhipeng Lyu, Chaofeng Li, Tichang Jia

This paper proposed a novel combined vibration control method, designed to rapidly stabilize the flexible cantilever beam driven by MFC actuators and rotary motor. Firstly, the dynamic model of the flexible cantilever beam system, incorporating MFC actuators and a rotary motor, was established based on the Euler–Bernoulli beam theory and Hamilton’s principle, using orthogonal polynomials as mode shapes. Then, the voltage applied to the MFC actuators and the rotation angle of the rotary motor, both serving as inputs, have a phase delay relative to the elastic deformation deflection of the flexible cantilever beam to achieve combined control. Moreover, convergence analysis and model effectiveness verification were conducted. Finally, the effects of the phase delay coefficient, voltage control gain, and rotation angle control gain on vibration control effectiveness and system energy were studied. The results show that compared to the individual action of either the MFC actuators or the rotary motor alone, the combined action of the MFC actuators and the rotary motor can achieve superior vibration control effectiveness. These results confirm the feasibility of applying the combined vibration control to suppress the vibration of the flexible cantilever beam and provide a new approach to vibration control for flexible cantilever structures.

本文提出了一种新的组合振动控制方法,旨在快速稳定由MFC执行器和旋转电机驱动的柔性悬臂梁。首先,基于欧拉-伯努利梁理论和Hamilton原理,以正交多项式为模态振型,建立了包含MFC驱动器和旋转电机的柔性悬臂梁系统的动力学模型;然后,将施加在MFC执行器上的电压和旋转电机的转角作为输入,使其相对于柔性悬臂梁的弹性变形挠度具有相位延迟,从而实现组合控制。并进行了收敛性分析和模型有效性验证。最后,研究了相位延迟系数、电压控制增益和转角控制增益对振动控制效果和系统能量的影响。结果表明,与MFC致动器单独作用或旋转电机单独作用相比,MFC致动器与旋转电机联合作用能达到更好的振动控制效果。这些结果证实了采用组合振动控制来抑制柔性悬臂梁振动的可行性,为柔性悬臂梁结构的振动控制提供了一种新的途径。
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引用次数: 0
Non-local response prediction for FGP sandwich microbeam with 2D PSH network subjected to adatoms-substrate interactions and exited by magnetic intensity 具有二维PSH网络的FGP夹层微束在ad原子-衬底相互作用下的非局部响应预测
IF 2.3 3区 工程技术 Q2 MECHANICS Pub Date : 2024-11-22 DOI: 10.1007/s00707-024-04149-w
Yahia Maiza, Hicham Bourouina

The present research contribution investigates a molecular resonant system’s adsorption-induced relative resonant frequency shift, considering the quality of distributed adatoms, the effect of shear distortion, and small-scale effects using non-local elasticity theory. We considered the structure’s several properties of perforation, sandwich, FGM, and porosity. The nanobeam structure can be considered a one-dimensional multi-property system. Using Eringen’s theory of elasticity, small-scale behaviour is modelled. To find the total energy transformation, the substrate-adatom energy and the adatom-adatom energy were calculated based on the van der Waals (vdW) interactions in the framework of the Morse potential and the Lennard–Jones (6–12) potential. The shear beam model (SBM) and the Euler beam model (EBM) were deduced by relying on the mechanical equations and modifying the coupled system equations. Computation was analysed analytically via the Navier-Type solution and numerically using the differential quadrature method. The SBM and EBM yield distinct relative frequency shifts, highlighting the importance of considering shear effects. The results indicate a significant dependency of the resonant frequency shift on the nanobeam’s structural properties and external conditions. This study provides a comprehensive understanding of the dynamic behaviour of multi-property nanobeams under various conditions. The findings can be applied to the design of advanced detection microdevices and microsensors.

本研究利用非局部弹性理论,考虑了分子共振系统中分布原子的质量、剪切畸变的影响和小尺度效应,研究了吸附引起的分子共振系统的相对共振频移。我们考虑了该结构的射孔、夹层、FGM和孔隙度等几个特性。纳米梁结构可以看作是一个一维多属性体系。利用Eringen的弹性理论,模拟了小尺度的行为。为了得到总能量转换,在Morse势和Lennard-Jones(6-12)势的框架下,基于范德华(vdW)相互作用计算了基底-adatom能和adatom-adatom能。基于力学方程和修正耦合系统方程,推导出剪力梁模型和欧拉梁模型。计算采用纳维尔型解析法和微分正交法进行了解析分析。SBM和EBM产生明显的相对频移,突出了考虑剪切效应的重要性。结果表明,谐振频移与纳米梁的结构特性和外部条件密切相关。本研究提供了对不同条件下多性能纳米梁动态行为的全面理解。研究结果可应用于先进检测微器件和微传感器的设计。
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引用次数: 0
Scattering of plane waves from an interface crack between the 1D hexagonal quasicrystals coating and the elastic substrate 一维六方准晶涂层与弹性衬底界面裂纹对平面波的散射
IF 2.3 3区 工程技术 Q2 MECHANICS Pub Date : 2024-11-22 DOI: 10.1007/s00707-024-04153-0
Yuanyuan Ma, Yueting Zhou, Juan Yang, Shaonan Lu, Xuefen Zhao, Shenghu Ding

Interface cracks are an important structural defect across various engineering domains. Based on Bak’s model, this paper explores the scattering problem of an interface crack between a 1D hexagonal quasicrystals (QCs) coating and an elastic substrate under harmonic plane waves. The Fourier transform method has been used to obtain the Cauchy singular integral equations (CSIEs) of the second kind in which the unknown variables are the dislocation density functions. The Jacobi polynomials have been used to reduce the CSIE into a system of linear algebraic equations. By taking the limit of the stress field near the crack tip, dynamic stress intensity factors (DSIFs) and crack opening displacements (CODs) are obtained. Finally, numerical results investigate the DSIFs for various wave types, material combinations, crack sizes, incident angles, and coupling coefficients of the phonon-phason field. The research findings provide valuable insights into using integral equation methods to address practical engineering issues related to crack detection and prediction.

界面裂缝是各种工程领域的重要结构缺陷。基于Bak模型,研究了一维六边形准晶涂层与弹性衬底界面裂纹在谐波平面波作用下的散射问题。利用傅里叶变换方法,得到了未知变量为位错密度函数的第二类柯西奇异积分方程。利用雅可比多项式将CSIE简化为一个线性代数方程组。通过取裂纹尖端附近应力场的极限,得到了动应力强度因子(DSIFs)和裂纹张开位移(CODs)。最后,数值结果研究了不同波型、材料组合、裂纹尺寸、入射角和声子-相场耦合系数下的声子-相场的dssifs。研究结果为利用积分方程方法解决与裂纹检测和预测相关的实际工程问题提供了有价值的见解。
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引用次数: 0
A multi-scale constitutive model for analyzing the tensile deformation of eutectic high-entropy alloys 用多尺度本构模型分析共晶高熵合金的拉伸变形
IF 2.3 3区 工程技术 Q2 MECHANICS Pub Date : 2024-11-18 DOI: 10.1007/s00707-024-04144-1
Yingying Wang, Yao Yao

The increase of Al percentage x transforms the crystalline structure of (FeCoNiCrMn)100-xAlx high-entropy alloys (HEAs) from single face-centered cubic (FCC) phase to FCC + body-centered cubic (BCC) two phase, which affects subsequent mechanical properties. Therefore, it is necessary to develop a constitutive model that can establish the relationship between microstructure and macro-mechanical properties. In the current study, Mori–Tanaka homogenization method is adopted to describe the evolution of microstructure with increasing Al concentration, which assumes that BCC inhomogeneity is embedded in FCC matrix as a reinforcement phase. A dislocation density-based crystal plasticity theory is employed to simulate the plastic deformation of both FCC and BCC phases. By coupling the influence of Al concentration into the constitutive model, the model is able to predict the plastic deformation of the FCC phase. The multi-scale constitutive theory, implemented into subroutine, is applied to describe the tensile behavior of HEAs. The numerical simulation matches well with the experimental data. The proposed model can accurately predict the tensile deformation of (FeCoNiCrMn)100-xAlx HEAs and provide valuable theoretical guidance for optimizing the mechanical performance of HEAs by adjusting the proportion of the components.

随着Al含量x的增加,(FeCoNiCrMn)100-xAlx高熵合金(HEAs)的晶体结构由单面心立方(FCC)相转变为FCC +体心立方(BCC)两相,影响了后续的力学性能。因此,有必要建立一种能够建立微观组织与宏观力学性能关系的本构模型。本研究采用Mori-Tanaka均质化方法描述随着Al浓度的增加微观结构的演变,假设BCC不均匀性作为增强相嵌入FCC基体中。采用基于位错密度的晶体塑性理论模拟了FCC相和BCC相的塑性变形。通过将Al浓度的影响耦合到本构模型中,该模型能够预测FCC相的塑性变形。将多尺度本构理论实现到子程序中,用于描述HEAs的拉伸行为。数值模拟结果与实验数据吻合较好。该模型能够准确预测(FeCoNiCrMn)100-xAlx HEAs的拉伸变形,为通过调整构件比例优化HEAs的力学性能提供了有价值的理论指导。
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引用次数: 0
Electrostriction and modelling of finitely deformable dielectrics 有限变形介质的电致伸缩和建模
IF 2.3 3区 工程技术 Q2 MECHANICS Pub Date : 2024-11-15 DOI: 10.1007/s00707-024-04113-8
Claudio Giorgi, Angelo Morro

The paper investigates models of electrostriction by following a new approach though within the basic laws of continuum mechanics. Three general requirements are considered. Firstly, in a three-dimensional setting the balance of angular momentum implies a symmetry condition for the Cauchy stress tensor, the electric field and the electric polarization. By checking the thermodynamic consistency it is observed that constitutive equations with a separate dependence on the deformation gradient and the electric field does not satisfy the symmetry condition. Instead the symmetry is shown to hold for variables involving jointly the deformation gradient and the electric field or the polarization. This scheme in turn is found to satisfy both the thermodynamic consistency and the objectivity principle. Next electrostriction is examined by determining the deformation of an isotropic elastic solid induced by an electric field. Furthermore, it is shown that a proper dependence on the polarization or on the electric field results in elongations or contractions just as it is observed in real materials.

本文在连续介质力学的基本定律范围内,采用一种新的方法来研究电致伸缩模型。考虑了三个一般要求。首先,在三维环境下,角动量平衡意味着柯西应力张量、电场和电极化的对称条件。通过热力学一致性检验,发现单独依赖于变形梯度和电场的本构方程不满足对称条件。相反,对于共同涉及变形梯度和电场或极化的变量,对称性是成立的。结果表明,该方案既满足热力学一致性,又满足客观性原则。接下来,通过确定由电场引起的各向同性弹性固体的变形来检验电致伸缩。此外,还表明,适当地依赖于极化或电场会产生伸长或收缩,就像在实际材料中观察到的那样。
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引用次数: 0
A novel probabilistic analysis method for long-term dynamical response analysis 长期动力响应分析的一种新的概率分析方法
IF 2.3 3区 工程技术 Q2 MECHANICS Pub Date : 2024-11-12 DOI: 10.1007/s00707-024-04137-0
Jingwei Meng, Yanfei Jin

Uncertainty propagation and quantification analysis in nonlinear systems are among the most challenging issues in engineering practice. Probabilistic analysis methods, based on the statistical information (i.e., mean and variance) of random variables, can account for uncertainties in the dynamical analysis of nonlinear systems. The statistical information of responses obtained by the Polynomial chaos expansion (PCE) method for nonlinear systems with random uncertainties deteriorates as the time history increases. Thus, the significant difficulty arises in analyzing the stochastic responses and long-term uncertainty propagation of nonlinear dynamical systems. To solve this problem, this paper proposes the PCE-HHT method by embedding a classical signal decomposition technique named Hilbert–Huang transform (HHT) in the PCE. Firstly, the HHT technique decomposes the multi-component response of a nonlinear system into a sum of several single vibration components and a trend component. Secondly, the PCE employs Hermite polynomials to approximate the instantaneous amplitudes and phases of each vibration component and the trend component, thereby establishing a coupled model of the system response, which can be used to determine the mean and variance of the dynamical response. Finally, considering parameter uncertainties in the Duffing–Van der Pol oscillator, the rigid double pendulum, and the spatially rigid-flexible crank-slider mechanism, the effectiveness of the PCE-HHT method is validated. Numerical results demonstrate that the PCE-HHT method exhibits desirable computational accuracy in the long-term random dynamical analysis of nonlinear systems.

非线性系统的不确定性传播和量化分析是工程实践中最具挑战性的问题之一。概率分析方法基于随机变量的统计信息(即均值和方差),可以解释非线性系统动态分析中的不确定性。对于具有随机不确定性的非线性系统,多项式混沌展开(PCE)方法得到的响应统计信息随着时间历程的增加而退化。因此,对非线性动力系统的随机响应和长期不确定性传播进行分析是一个非常困难的问题。为了解决这一问题,本文提出了PCE-HHT方法,该方法将经典的信号分解技术Hilbert-Huang变换(HHT)嵌入到PCE中。HHT技术首先将非线性系统的多分量响应分解为多个单振动分量和一个趋势分量;其次,PCE采用Hermite多项式逼近各振动分量和趋势分量的瞬时幅值和相位,从而建立系统响应的耦合模型,用于确定动力响应的均值和方差;最后,考虑Duffing-Van der Pol振荡器、刚性双摆和空间刚柔曲柄滑块机构参数的不确定性,验证了PCE-HHT方法的有效性。数值结果表明,PCE-HHT方法在非线性系统的长期随机动力分析中具有良好的计算精度。
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引用次数: 0
A novel modified nonlocal strain gradient theory for comprehensive analysis of functionally graded nanoplates 一种用于功能梯度纳米片综合分析的修正非局部应变梯度理论
IF 2.3 3区 工程技术 Q2 MECHANICS Pub Date : 2024-11-12 DOI: 10.1007/s00707-024-04131-6
Pham Van Vinh

In this study, a novel theory, called the modified nonlocal strain gradient theory, is established for the analysis of functionally graded nanoplates. This theory integrates the nonlocal effects through classical stress tensors, the deviatoric part of the symmetric couple stress tensor, dilatation gradient and deviatoric stretch gradient tensors. This combination ensures compatibility for investigating a wide range of structures, from nano- to macro-scales. Some comparative studies are performed to establish the precision and reliability of the proposed theory in specific cases. Furthermore, a massive parametric study is organized to illustrate the influence of several coefficients on the bending, free vibration and buckling behaviors of the functionally graded nanoplates. The proposed theory provides a robust theoretical foundation for future investigations into various small-scale structures situated within multi-physical environments. This establishing approach not only enhances the understanding of micro- and nanoscale mechanics but also paves the way for advanced applications in mechanical engineering.

在本研究中,建立了一个新的理论,称为修正非局部应变梯度理论,用于分析功能梯度纳米板。该理论通过经典应力张量、对称耦合应力张量的偏微分部分、膨胀梯度和偏微分拉伸梯度张量集成了非局部效应。这种组合确保了研究从纳米到宏观尺度的广泛结构的兼容性。本文还进行了一些比较研究,以确定所提出的理论在具体情况下的准确性和可靠性。此外,还组织了大量的参数研究,以说明几个系数对功能梯度纳米板的弯曲、自由振动和屈曲行为的影响。所提出的理论为未来研究位于多物理环境中的各种小规模结构提供了坚实的理论基础。这种建立方法不仅提高了对微纳米尺度力学的理解,而且为机械工程的高级应用铺平了道路。
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引用次数: 0
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