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An improved path integration method for the stochastic soft-impact systems 随机软冲击系统的改进路径积分法
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-08-08 DOI: 10.1016/j.ijnonlinmec.2024.104866

This paper presents an improved path integration method for a soft-impact system under stochastic excitation, which focuses on the response of the system on the impact surface. The system involves complex impact processes, including contact, deformation, recovery, and disengagement. To address the technical challenges posed by the system discontinuity at the moment of impact, we establish a mapping relation between impact events to solve the system response. Considering that the non-smooth moment of such systems exists only at the moment of contact with the impact surface, we chose to select the impact surface as a Poincaré cross-section. Two independent mappings were established to describe the transition of the oscillator from leaving the obstacle to the next contact with the obstacle, and from contacting the obstacle to leaving the obstacle. These two consecutive mappings were integrated into the plane to form a unified mapping. This method was employed to investigate the response probability density function of the system for autonomous and non-autonomous systems, respectively. The effectiveness of the methodology was validated by the use of Monte Carlo simulations, in addition to the discovery of the stochastic P-bifurcation phenomenon.

本文针对随机激励下的软撞击系统提出了一种改进的路径积分法,重点研究系统在撞击面上的响应。该系统涉及复杂的冲击过程,包括接触、变形、恢复和脱离。为了解决撞击瞬间系统不连续性带来的技术难题,我们建立了撞击事件之间的映射关系来解决系统响应问题。考虑到此类系统的非光滑力矩仅存在于与撞击面接触的瞬间,我们选择将撞击面选作波恩卡莱截面。我们建立了两个独立的映射来描述振荡器从离开障碍物到下一次接触障碍物的过渡,以及从接触障碍物到离开障碍物的过渡。这两个连续的映射被整合到平面上,形成一个统一的映射。利用这种方法分别研究了自主系统和非自主系统的响应概率密度函数。除了发现随机 P 分岔现象外,还利用蒙特卡罗模拟验证了该方法的有效性。
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引用次数: 0
General framework to implement isotropic and anisotropic hyperelastic biomaterials into finite element method 在有限元法中应用各向同性和各向异性超弹性生物材料的总体框架
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-08-06 DOI: 10.1016/j.ijnonlinmec.2024.104864

Hyperelastic models are extensively employed in the simulation of biological tissues under large deformation. While classical hyperelastic models are incorporated into certain finite element packages, new hyperelastic models for both isotropic and anisotropic materials are emerging in recent years for various soft materials. Fortunately, most hyperelastic models are formulated based on strain invariants, which provides a feasible way to directly implement these newly developed models into the numerical simulation. In this paper, we present a general framework for employing strain-invariant-based hyperelastic models in finite element analysis. We derive the general formulation for the Cauchy stress and elasticity tensor of both isotropic and anisotropic materials. By substituting the strain–energy density into these general forms, we are able to directly implement various hyperelastic models, such as the Fung–Demiray model and the Lopez-Pamies model for isotropic materials, and the Gasser–Ogden–Holzapfel model, the Merodio-Ogden model, and the Horgan-Saccomandi model for anisotropic materials, within the ABAQUS user-defined material subroutine, offering a numerical approach to implement materials not available through the built-in material models. To demonstrate the feasibility of our approach, we utilize these subroutines to compute several classic examples related to both homogeneous and inhomogeneous problems. The good agreement between the obtained results and the analytical or experimental solutions confirms the validity of developing these models by the proposed framework. The general framework and results presented in this study are useful for fast implementing newly developed hyperelastic models and are helpful to the finite element simulation of biological tissues.

超弹性模型被广泛应用于大变形条件下的生物组织模拟。虽然经典的超弹性模型已被纳入某些有限元软件包,但近年来针对各向同性和各向异性材料的新型超弹性模型也在各种软材料中不断涌现。幸运的是,大多数超弹性模型都是基于应变不变式制定的,这为将这些新开发的模型直接应用于数值模拟提供了可行的方法。本文提出了在有限元分析中采用基于应变不变式的超弹性模型的一般框架。我们推导了各向同性和各向异性材料的 Cauchy 应力和弹性张量的一般公式。通过将应变能量密度代入这些一般形式,我们能够在 ABAQUS 用户定义的材料子程序中直接实现各种超弹性模型,如各向同性材料的模型和模型,以及各向异性材料的模型、模型和模型,为实现内置材料模型无法实现的材料提供了一种数值方法。为了证明我们方法的可行性,我们利用这些子程序计算了几个与均质和非均质问题相关的经典示例。所获得的结果与分析或实验解之间的良好一致性证实了通过所建议的框架开发这些模型的有效性。本研究提出的总体框架和结果有助于快速实现新开发的超弹性模型,并有助于生物组织的有限元模拟。
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引用次数: 0
Stress-fractional model for clay based on yielding and hardening rules considering thermomechanical restriction 基于屈服和硬化规则的粘土应力-分数模型,考虑热力学限制因素
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-08-06 DOI: 10.1016/j.ijnonlinmec.2024.104870

This study presents the development of an isothermal model for characterising the stress-strain behaviour of clay, in the framework of thermomechanical restrictions. Clay is assumed to be a decoupled material, where the accumulation of the Helmholtz free energy can be decoupled into two components, elastic and plastic, that result in the explicit definitions of the shift and dissipative stress tensors, respectively. An anisotropic yielding function fulfilling the first and second laws of thermodynamics is then derived from the rate of plastic dissipation, where the loading tensor and fractional plastic flow tensor are also obtained. A compression-and-shearing hardening mechanism is introduced by further evaluating the thermodynamic restrictions of the rate of Helmholtz free energy at critical state. The developed model contains seven constitutive parameters, where the identification methods are discussed. Finally, an application of the developed model to simulate the drained and undrained stress-strain responses of different clays are provided.

本研究介绍了在热力学限制框架内,为描述粘土的应力-应变行为而开发的等温模型。粘土被假定为一种解耦材料,其中亥姆霍兹自由能的积累可解耦为弹性和塑性两个部分,从而分别明确定义了位移应力张量和耗散应力张量。然后,根据塑性耗散率推导出符合热力学第一和第二定律的各向异性屈服函数,并得到加载张量和分数塑性流动张量。通过进一步评估临界状态下赫尔姆霍兹自由能速率的热力学限制,引入了压缩剪切硬化机制。所建立的模型包含七个构成参数,并讨论了识别方法。最后,介绍了应用所建立的模型模拟不同粘土的排水和非排水应力-应变响应的情况。
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引用次数: 0
Nonlinear micromorphic Timoshenko beam modeling and vibration analysis of microstructured beams 非线性微形态季莫申科梁建模和微结构梁振动分析
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-08-06 DOI: 10.1016/j.ijnonlinmec.2024.104861

Generalized continuum theories can describe the mechanical behavior of microstructured materials more accurately than the classical Cauchy theory. In this manuscript, a micromorphic beam theory is developed for the efficient multiscale analysis of the linear and nonlinear deformation and vibration behavior of metamaterial beams. The proposed approach extends the conventional nonlinear Timoshenko beam theory by including three additional independent degrees of freedom, which allow to accurately capture four distinct microstrains for stretch, bending, and two types of shear behavior at the microscale level. The novel beam model is able to capture size effects and can accurately describe beams with only few unit cells through the thickness direction. However, consisting of 3 macro and 3 micro degrees of freedom, it is much more efficient than 2D or 3D micromorphic continuum models. It is demonstrated that the micromorphic material parameters can be identified from comparison studies with representative volume elements of the microstructure. For the numerical discretization of the governing equations for static deformations as well as vibrations, the differential quadrature method is employed here. The presented numerical examples show the accuracy of the method in obtaining deflections, linear eigenfrequencies, and nonlinear frequency responses for metamaterial beams with weakly separated macro and micro scales.

与经典的柯西理论相比,广义连续理论能更精确地描述微结构材料的力学行为。本手稿提出了一种微形态梁理论,用于对超材料梁的线性和非线性变形和振动行为进行高效的多尺度分析。所提出的方法扩展了传统的非线性季莫申科梁理论,增加了三个独立的自由度,从而可以在微尺度上准确捕捉拉伸、弯曲和两种剪切行为的四种不同微应变。这种新型梁模型能够捕捉尺寸效应,并能准确描述厚度方向上只有少数单元格的梁。然而,它由 3 个宏观和 3 个微观自由度组成,比二维或三维微观连续模型更有效。研究表明,通过与微观结构的代表性体积元素进行对比研究,可以确定微观材料参数。对于静态变形和振动控制方程的数值离散化,这里采用了微分正交法。所提供的数值示例表明,该方法能准确获得宏观和微观尺度弱分离的超材料梁的挠度、线性特征频率和非线性频率响应。
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引用次数: 0
Solutions to a two-phase mass flow model with generalized drag 具有广义阻力的两相质量流模型的解决方案
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-08-03 DOI: 10.1016/j.ijnonlinmec.2024.104860

Drag plays a dominant role in the interfacial momentum exchange in mixture mass flows. In this study, we examine a general two-phase mass flow model formulated by Pudasaini [1], which incorporates drag. This model describes the mass flow comprising a mixture of solid particles and viscous fluid moving downhill under the influence of gravity. We construct explicit, analytical, and numerical solutions to the model using the Lie symmetry method. These new solutions disclose the role of generalized drag in the dynamics of both solid particles and viscous fluid. The solutions show that solid and fluid phases undergo nonlinear evolution in a coupled manner. Additionally, the solutions demonstrate that increased drag results in a tighter binding between solid and fluid components. We also analyze the role of pressure gradients. The solutions reveal that when solid pressure dominates fluid pressure, solid velocity increases faster than fluid velocity. These findings align with our expectations, emphasizing the importance of analytical solution techniques in understanding the complex process of mixture mass transport in mountain slopes and valleys, thereby enhancing our understanding.

阻力在混合物质量流的界面动量交换中起着主导作用。在本研究中,我们研究了 Pudasaini [1] 提出的包含阻力的一般两相质量流模型。该模型描述了由固体颗粒和粘性流体组成的混合物在重力作用下向下运动的质量流。我们利用李对称法构建了该模型的显式、分析和数值解。这些新解揭示了广义阻力在固体颗粒和粘性流体动力学中的作用。求解结果表明,固相和流体相以耦合的方式经历了非线性演化。此外,解法还表明,阻力的增加会导致固体和流体成分之间的结合更加紧密。我们还分析了压力梯度的作用。求解结果表明,当固体压力主导流体压力时,固体速度的增加快于流体速度的增加。这些发现与我们的预期一致,强调了分析求解技术在理解山坡和山谷中混合物质量输运的复杂过程中的重要性,从而加深了我们的理解。
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引用次数: 0
Multiscale and microstructure-inspired constitutive models for soft materials. On the occasion of Giuseppe Saccomandi's 60th birthday 软材料的多尺度和微结构启发构成模型。纪念朱塞佩-萨科曼迪(Giuseppe Saccomandi)60 岁生日
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-08-02 DOI: 10.1016/j.ijnonlinmec.2024.104865
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引用次数: 0
Comprehensive analysis of electro-mechanical characteristics and new regression models of a novel slanted groove electrical connector 新型斜槽电气连接器的机电特性综合分析和新回归模型
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-07-31 DOI: 10.1016/j.ijnonlinmec.2024.104863

Electrical connectors are crucial electro-mechanical components, with insertion, withdrawal, and electrical contact characteristics serving as key indicators of their reliability. Studying the electro-mechanical characteristics and regression models of electrical connectors is vital to enhance their reliability. This work focuses on the M2-type electrical connector, investigating its electro-mechanical characteristics and developing a regression model. A withdrawal force calculation model is established using cantilever beam theory. Simulation and analysis provide data on insertion force, contact pressure, and contact resistance. Experiments on insertion, withdrawal, and electrical contact are conducted using an insertion force tester and a DC low-resistance instrument, comparing experimental results with simulations. The study reveals the fitting relationship between contact pressure and contact resistance for the M2-type connector. Key findings include a stable fluctuation in contact pressure with a relative error of 1.72% between simulated and tested values, an average discrepancy of 3.81% for insertion force, and 2.38% for withdrawal force, with insertion force slightly higher than withdrawal force. Contact resistance shows a U-shaped trend with pin displacement, with an average experimental error 3.70% and 1.16% lower than theoretical values (4.86%). The new regression model (quadratic polynomial fitting) demonstrates mean absolute percentage errors of 0.1458% for simulation values and 0.2219% for experimental values, significantly lower than those obtained using theoretical formulas (0.7046% and 0.3451%). These results provide theoretical guidance for studying electro-mechanical characteristics and designing experiments for electrical connectors, offering valuable insights for designing and ensuring the reliability of new types of electrical connectors.

电气连接器是重要的机电部件,其插入、拔出和电气接触特性是衡量其可靠性的关键指标。研究电气连接器的机电特性和回归模型对提高其可靠性至关重要。本研究以 M2 型电气连接器为重点,研究其电气机械特性并建立回归模型。利用悬臂梁理论建立了抽出力计算模型。模拟和分析提供了插入力、接触压力和接触电阻的数据。使用插入力测试仪和直流低电阻仪器对插入、退出和电接触进行了实验,并将实验结果与模拟结果进行了比较。研究揭示了 M2 型连接器的接触压力和接触电阻之间的拟合关系。主要发现包括:接触压力波动稳定,模拟值与测试值之间的相对误差为 1.72%;插入力的平均差异为 3.81%;抽出力的平均差异为 2.38%,插入力略高于抽出力。接触电阻随销轴位移呈 U 型趋势,平均实验误差为 3.70%,比理论值(4.86%)低 1.16%。新的回归模型(二次多项式拟合)显示,模拟值的平均绝对百分比误差为 0.1458%,实验值的平均绝对百分比误差为 0.2219%,明显低于使用理论公式得出的误差(0.7046% 和 0.3451%)。这些结果为研究电气连接器的机电特性和设计实验提供了理论指导,为设计和确保新型电气连接器的可靠性提供了宝贵的见解。
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引用次数: 0
Postbuckling and nonlinear free vibration of postbuckled porous functionally graded micro/nanotubes via nonlocal strain and velocity gradient theory 通过非局部应变和速度梯度理论研究后屈曲多孔功能分级微/纳米管的后屈曲和非线性自由振动
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-07-31 DOI: 10.1016/j.ijnonlinmec.2024.104862

Background

Vibration response analysis serves as a critical tool in investigating the behavior of micro/nanoscale structures operating in dynamic environments, offering valuable insights into their performance and ultimately refining the design of devices. Particularly, when these structures are deliberately engineered to function near or within the postbuckling regime, understanding their vibratory behavior in this state becomes essential. This study focuses on exploring the postbuckling behavior and nonlinear frequencies of simply supported buckled porous functionally graded (PFG) size-dependent tubes. Internal resonances are not considered in this analysis.

Method

The nonlocal strain and velocity gradient theory, within the framework of the Euler-Bernoulli beam hypothesis, is employed to derive the nonlinear partial differential equations of motion. It is assumed that the material properties are gradually graded in the radial direction. Additionally, two different porosity distribution patterns are used in the radial direction. The method of multiple scales is used to solve the system of nonlinear ordinary differential equations obtained by applying the Galerkin method.

Results

The closed expression for the i-th nonlinear frequency of buckled porous functionally graded size-dependent tubes is determined based on the amplitude of the vibration modes involved. The findings indicate that porous M/NTs exhibit a loss of static stability at lower compressive axial loads compared to their nonporous counterparts. Furthermore, the softening effects resulting from a uniform porosity distribution are more pronounced than those from an uneven porosity distribution. Interestingly, nonporous M/NTs display the lowest nonlinear postbuckling frequency among the studied configurations. Moreover, it is observed that the nonlinear frequency tends to increase with a rise in the compressive axial load, while it decreases with an increase in the excitation amplitude.

振动响应分析是研究微米/纳米级结构在动态环境中运行行为的重要工具,可为了解其性能提供宝贵的见解,并最终完善设备的设计。特别是当这些结构被刻意设计为在接近或在后屈曲状态下运行时,了解它们在这种状态下的振动行为就变得至关重要。本研究的重点是探索简单支撑的屈曲多孔功能分级管(PFG)的后屈曲行为和非线性频率。本分析未考虑内部共振。在欧拉-伯努利梁假设的框架内,采用非局部应变和速度梯度理论推导非线性偏微分运动方程。假设材料特性在径向逐渐分级。此外,在径向还采用了两种不同的孔隙率分布模式。多尺度法用于求解通过伽勒金法得到的非线性常微分方程系。根据相关振动模式的振幅,确定了多孔功能分级屈曲管的第 i 个非线性频率的封闭表达式。研究结果表明,与无孔材料相比,多孔 M/NT 在较低的压缩轴向载荷下会失去静态稳定性。此外,均匀孔隙率分布产生的软化效应比不均匀孔隙率分布产生的软化效应更为明显。有趣的是,在所研究的结构中,无孔 M/NT 的非线性后屈曲频率最低。此外,还观察到非线性频率随着压缩轴向载荷的增加而增加,而随着激励振幅的增加而降低。
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引用次数: 0
Periodic response and stability analysis of a bistable viscoelastic von Mises truss 双稳态粘弹性 von Mises 桁架的周期响应和稳定性分析
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-07-30 DOI: 10.1016/j.ijnonlinmec.2024.104858

This paper examines the effect of viscoelasticity on the periodic response of a lumped parameter viscoelastic von Mises truss. The viscoelastic system is described by a second-order equation that governs the mechanical motion coupled to a first-order equation that governs the time evolution of the viscoelastic forces. The viscoelastic force evolves at a much slower rate than the elastic oscillations in the system. This adds additional time scales and degrees of freedom to the system compared to its viscous counterparts. The focus of this study is on the system’s behavior under harmonic loading, which is expected to show both regular and chaotic dynamics for certain combinations of forcing frequency and amplitude. While the presence of chaos in this system has already been demonstrated, we shall concentrate only on the periodic solutions. The presence of the intrawell and interwell periodic oscillations is revealed using the Harmonic Balance method. The study also looks at the influence of parameter changes on the system’s behavior through bifurcation diagrams, which enable us to identify optimal system parameters for maximum energy dissipation. Lastly, we formulate an equivalent viscous system using an energy-based approach. We observe that a naive viscous model fails to capture the behavior accurately depending on the system and excitation parameters, as well as the type of excitation. This underscores the necessity to study the full-scale viscoelastic system.

本文研究了粘弹性对总参数粘弹性 von Mises 桁架周期性响应的影响。粘弹性系统由一个控制机械运动的二阶方程和一个控制粘弹力时间演化的一阶方程来描述。粘弹力的演变速度比系统中的弹性振荡慢得多。与粘滞力相比,粘弹力为系统增加了额外的时间尺度和自由度。本研究的重点是谐波加载下的系统行为,预计在某些强迫频率和振幅组合下,系统会显示出规则和混乱的动态。虽然已经证明了该系统中存在混沌现象,但我们将只集中研究周期解。利用谐波平衡法揭示了井内和井间周期振荡的存在。本研究还通过分岔图研究了参数变化对系统行为的影响,从而确定了实现最大能量耗散的最佳系统参数。最后,我们使用基于能量的方法制定了一个等效粘性系统。我们观察到,根据系统和激励参数以及激励类型的不同,简单的粘性模型无法准确捕捉行为。这凸显了研究全尺度粘弹性系统的必要性。
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引用次数: 0
Machine learning prediction models for investigating vibration properties of epoxy resin under moisture conditions 用于研究环氧树脂在潮湿条件下振动特性的机器学习预测模型
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-07-26 DOI: 10.1016/j.ijnonlinmec.2024.104857

Epoxy resins used in engineering applications are commonly exposed to wet environment during intended service life, which causes vibration property degradation and increasing risk of structural failure. In this work, vibration properties of epoxy resin plate under different moisture conditions are predicted with various sizes and boundary conditions using developed machine learning (ML) models. The dataset of epoxy vibration is established first, where values in the dataset are calculated with five moisture contents using previously developed meshless model. The dataset from meshless simulation is used to train ML models of epoxy vibration using six different algorithms, including support vector machine, decision tree, random forest, gradient boosting decision tree, extreme gradient boosting, and artificial neural network. It is found that the prediction model developed using extreme gradient boosting algorithm shows the highest accuracy of 99.9% and strong reliability. Using this model, vibration properties of epoxy resin with a series of sizes and boundary conditions are predicted under various moisture contents from dry case to saturated case, which deepens the understanding of the effects of wet environments on the vibration responses of epoxy resins. The results could be used for analysis of durability of epoxy resin, and the developed ML prediction models contribute to investigating vibration property of epoxy resin under different moisture conditions, which is crucial for ensuring durability of epoxy resin in wet environment.

工程应用中使用的环氧树脂在预期使用寿命内通常会暴露在潮湿的环境中,从而导致振动性能下降,增加结构失效的风险。在这项工作中,利用开发的机器学习(ML)模型,预测了环氧树脂板在不同湿度条件下的振动特性,包括各种尺寸和边界条件。首先建立环氧树脂振动数据集,利用之前开发的无网格模型计算数据集中五种水分含量的值。利用无网格模拟的数据集,使用六种不同的算法训练环氧树脂振动的 ML 模型,包括支持向量机、决策树、随机森林、梯度提升决策树、极端梯度提升和人工神经网络。结果发现,使用极梯度提升算法建立的预测模型准确率最高,达到 99.9%,可靠性强。利用该模型,可以预测一系列尺寸和边界条件的环氧树脂在从干燥到饱和的不同含水量条件下的振动特性,加深了人们对潮湿环境对环氧树脂振动响应影响的理解。这些结果可用于分析环氧树脂的耐久性,所开发的 ML 预测模型有助于研究环氧树脂在不同湿度条件下的振动特性,这对于确保环氧树脂在潮湿环境中的耐久性至关重要。
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引用次数: 0
期刊
International Journal of Non-Linear Mechanics
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