International Journal of Engineering Science最新文献_第9页

Experimental validation of Lamb wave dispersion curves using the Scaled Boundary Finite Element Method (SBFEM) 尺度边界有限元法（SBFEM）对Lamb波色散曲线的实验验证

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-09-16 DOI: 10.1016/j.ijengsci.2025.104370

Carlos A. Galán Pinilla , Jorge Gosálbez , Darío Yesid Peña Ballesteros , Adan Y. León , Jabid Eduardo Quiroga

Dispersion curves are essential for characterizing Lamb wave propagation. A key challenge in estimating these curves is ensuring both computational efficiency and agreement with experimental results, particularly in complex, multilayered materials. This study focuses on bilayer structures, specifically metallic substrates with viscoelastic coatings, and employs the Scaled Boundary Finite Element Method (SBFEM) to generate dispersion curves. SBFEM discretizes the waveguide cross-section using high-order spectral finite elements and a Gauss–Lobatto–Legendre (GLL) node distribution, assigning a single spectral element per material layer. To validate the SBFEM curves, estimation is compared with experimental data obtained from metallic plates and bilayer structures consisting of viscoelastic coatings on steel substrates. The strong correlation between numerical predictions and experimental results highlights the effectiveness of SBFEM in accurately capturing Lamb wave behavior in bilayer waveguides with viscoelastic coatings while maintaining computational efficiency. These findings reinforce the method’s applicability for the analysis of wave propagation in complex, layered, and dissipative materials.

色散曲线是表征兰姆波传播的关键。估计这些曲线的一个关键挑战是确保计算效率和与实验结果的一致性，特别是在复杂的多层材料中。本研究针对双层结构，特别是粘弹性涂层的金属基底，采用缩放边界有限元法（SBFEM）生成色散曲线。SBFEM采用高阶光谱有限元和Gauss-Lobatto-Legendre （GLL）节点分布对波导截面进行离散化，为每层材料分配单个光谱单元。为了验证SBFEM曲线的有效性，将估计结果与金属板和由粘弹性涂层组成的钢基双层结构的实验数据进行了比较。数值预测与实验结果之间的强相关性表明了SBFEM在保持计算效率的同时准确捕获粘弹性涂层双层波导中兰姆波行为的有效性。这些发现加强了该方法在复杂、分层和耗散材料中波传播分析的适用性。

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引用次数: 0

Multi-scale non-affine mechanics of electro-magneto-active elastomers: Taut domain exploitable convolution of polymer chain crosslinks, entanglements and finite extensibility 电磁活性弹性体的多尺度非仿射力学：聚合物链交联、缠结和有限可扩展性的紧域可开发卷积

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-09-16 DOI: 10.1016/j.ijengsci.2025.104378

Aman Khurana , Susmita Naskar , M.M. Joglekar , Tanmoy Mukhopadhyay

Actuation devices fabricated using smart polymers often exhibit wrinkling and pull-in instability when they are subjected to external stimulation. These instabilities can disrupt the intended functionality of the actuation devices and hinder their reliability. The underlying reason for these instabilities is the complicated architecture of the polymer network, which results in a complex and chaotic arrangement of crosslinks and entanglements in smart elastomer membranes. This convoluted structure significantly influences the mechanical behavior of the polymers when external forces are applied. To better understand and characterize these instability phenomena, the present study develops a physics-based non-affine material model incorporating the effects of critical factors like polymer chain crosslinks, entanglements, and finite extensibility. By considering the intricate interplay among these factors, the model provides fundamental insights into the mechanisms behind the instability phenomena in smart polymers. Subsequently, the study explores the relationship between the applied electromagnetic field and the taut domains. The findings reveal that the size of the taut domains can be effectively altered by manipulating the levels of polymer chain crosslinks, entanglements, and finite extensibility. It is observed that, for a given level of applied electromagnetic field, increasing the entanglement and crosslink parameter leads to a larger taut domain. Conversely, an increase in the finite extensibility of the polymer chain diminishes the taut domain under the same level of electromagnetic loading. These understandings open up new avenues for optimizing actuation devices by adjusting the intricate properties of polymer chains to enhance stability and performance by unlocking the full multi-physical potential of smart elastomers.

使用智能聚合物制造的驱动装置在受到外部刺激时经常表现出起皱和拉入不稳定性。这些不稳定性可能会破坏致动装置的预期功能，并阻碍其可靠性。这些不稳定性的根本原因是聚合物网络的复杂结构，导致智能弹性体膜中交联和缠结的复杂和混乱排列。当施加外力时，这种卷曲的结构显著影响聚合物的力学行为。为了更好地理解和表征这些不稳定现象，本研究开发了一个基于物理的非仿射材料模型，该模型结合了聚合物链交联、纠缠和有限可扩展性等关键因素的影响。通过考虑这些因素之间错综复杂的相互作用，该模型为智能聚合物中不稳定现象背后的机制提供了基本的见解。随后，研究了外加电磁场与紧绷畴之间的关系。研究结果表明，通过控制聚合物链交联、缠结和有限可扩展性的水平，可以有效地改变绷紧结构域的大小。我们观察到，对于给定的外加电磁场水平，增加纠缠和交联参数会导致更大的拉紧域。相反，在相同水平的电磁载荷下，聚合物链有限可扩展性的增加减少了张力域。这些认识为优化驱动装置开辟了新的途径，通过调整聚合物链的复杂特性，通过释放智能弹性体的全部多物理潜力来提高稳定性和性能。

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引用次数: 0

Elastohydrodynamic instabilities in pressure-driven flow through a poroelastic channel 孔隙弹性通道中压力驱动流体的弹性水动力不稳定性

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-09-15 DOI: 10.1016/j.ijengsci.2025.104379

Ramkarn Patne

The linear stability analysis of a pressure-driven flow through a saturated poroelastic channel sandwiched between two impermeable rigid walls is carried out in the present study. Mixture theory is employed to describe the dynamics of the interstitial fluid and elastic solid matrix. The resulting eigenvalue problem is solved using the pseudo-spectral method. Without the poroelastic solid matrix, the flow under consideration reduces to the classical plane Poiseuille flow for which the linear stability analysis predicts critical Reynolds number,

R e_{c} = 5772

. However, the present study, predicts that

R e_{c}

could be as low as 5 for the flow under consideration owing to the deformability of the solid matrix. Further analysis reveals the existence of three new modes of instability. For low

R e

, mode I dominates the instability, while at high

R e

, mode III dominates the instability with characteristic scaling

Γ_{c} \sim 1 / R e

where

Γ_{c}

is a measure of the deformability of the solid matrix. The driving mechanism of the predicted instability is found to be the coupling between the fluid and solid due to the pressure perturbation. The energy exchange between the base state velocity gradient and normal velocity perturbation via the convection term in the linearised Navier–Stokes equation plays a supporting role to the pressure perturbations in introducing unstable modes.

本文对夹在两个不透水刚性壁面之间的饱和孔弹性通道进行了压力驱动流动的线性稳定性分析。混合理论用于描述间隙流体和弹性固体基质的动力学。利用伪谱法求解得到的特征值问题。在没有孔隙弹性固体基体的情况下，所考虑的流动可以简化为经典的平面泊泽维尔流动，线性稳定性分析预测其临界雷诺数Rec=5772。然而，本研究预测，由于固体基体的可变形性，所考虑的流动的Rec可能低至5。进一步分析表明存在三种新的不稳定模态。对于低Re， I型主导不稳定性，而在高Re时，III型主导不稳定性，其特征标度为Γc ~ 1/Re，其中Γc是固体基体变形能力的度量。发现预测的不稳定性的驱动机制是由于压力扰动引起的流体与固体之间的耦合。线性化Navier-Stokes方程中基态速度梯度与法向速度扰动之间通过对流项的能量交换对引入不稳定模态的压力扰动起支持作用。

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引用次数: 0

Lagrangian theory of extensible elastica with arbitrary undeformed shape 任意不变形可扩展弹性的拉格朗日理论

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-09-12 DOI: 10.1016/j.ijengsci.2025.104383

Alessandro Taloni , Daniele Vilone , Giuseppe Ruta

This work presents a consistent formulation of the Lagrangian function for slender elastic bodies with arbitrary initial geometries, within a dynamic framework and under finite displacements. Building upon and extending previous research, we develop a rigorous expression for the kinetic energy, thereby completing the Lagrangian formulation. Our approach ensures consistency across geometric and dynamic nonlinearities. Furthermore, we derive pattern solutions for representative benchmark problems, illustrating the applicability and versatility of the proposed framework. These results open new avenues for the application of our formulation across various domains in applied science and engineering.

这项工作提出了具有任意初始几何形状的细长弹性体的拉格朗日函数的一致公式，在动态框架内和有限位移下。在前人研究的基础上，我们提出了一个严谨的动能表达式，从而完成了拉格朗日公式。我们的方法确保了几何非线性和动态非线性的一致性。此外，我们推导了典型基准问题的模式解决方案，说明了所提出框架的适用性和通用性。这些结果为我们的公式在应用科学和工程的各个领域的应用开辟了新的途径。

引用次数: 0

Effective field methods vs finite element models for microgeometries with ellipsoidal inclusions. Theory and application 椭球形夹杂微观几何的有效场方法与有限元模型。理论与应用

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-09-11 DOI: 10.1016/j.ijengsci.2025.104373

E. Polyzos, L. Pyl

This study compares the predictions of analytical and numerical models employing ellipsoidal inclusions to determine the effective properties of composite materials. Three groups of factors influencing homogenization accuracy are investigated: the type of homogenization problem (elasticity, expansion, and conductivity), the material phase characteristics (isotropy, inclusion orientation, and inclusion aspect ratio), and the modeling methodologies, where effective field methods (EFMs) – including the Non-Interaction, the Mori–Tanaka and Maxwell methods – are evaluated against the pseudo grain decomposition method (PGDM) and numerical finite element (FE) models in a parametric study. The study considers ellipsoidal inclusions with aspect ratios ranging from 0.2 to 5 and orientation scattering from completely random to fully aligned. The results indicate that the type of homogenization problem does not significantly affect the prediction accuracy of EFMs and that the Mori–Tanaka and Maxwell methods show excellent agreement with FE models for all properties. The PGDM is shown to yield reliable results only for certain elastic properties (e.g.,

E_{11}

) for composites with inclusions of aspect ratios greater than 1. Therefore, it is concluded that the Mori–Tanaka and the Maxwell methods serve as the most suitable analytical alternatives to computationally intensive FE models.

本研究比较了采用椭球体夹杂物的解析模型和数值模型的预测结果，以确定复合材料的有效性能。研究了影响均质精度的三组因素：均质化问题的类型（弹性、膨胀和电导率）、材料相特性（各向同性、夹杂取向和夹杂长宽比）以及建模方法，其中有效的场方法(efm) -包括非相互作用、Mori-Tanaka和Maxwell方法-在参数化研究中对伪颗粒分解方法（PGDM）和数值有限元（FE）模型进行了评估。研究考虑椭球状包裹体，其纵横比为0.2 ~ 5，取向散射从完全随机到完全排列。结果表明，均匀化问题的类型对efm的预测精度没有显著影响，Mori-Tanaka和Maxwell方法在所有性质上都与有限元模型具有很好的一致性。对于长径比大于1的复合材料，PGDM仅对某些弹性性能（例如E11）产生可靠的结果。因此，Mori-Tanaka和Maxwell方法是计算密集型有限元模型的最合适的分析选择。

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引用次数: 0

A geometric one-fluid model of superfluid helium-4 超流体氦-4的几何单流体模型

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-09-11 DOI: 10.1016/j.ijengsci.2025.104377

Nadine Suzan Cetin , Michal Pavelka , Emil Varga

A standard description of superfluid helium-4 is based on the concept of two components (superfluid and normal), which leads to the so called two-fluid models. However, as there are no two kinds of atoms in helium-4, the two components cannot be separated. Superfluid helium-4 is not a mixture of two components, being rather a single fluid with two motions. Here, we present a geometric one-fluid model of superfluid helium-4, which is based on the Hamiltonian formulation of fluid mechanics. The model is derived from the kinetic theory of excitations (treated as an ideal Bose gas under the temperature

1.3 K

) and average particle motions. It can be simplified to the Hall–Vinen–Bekharevich–Khalatnikov (HVBK) two-fluid model, where it removes one fitting parameter from the HVBK model, but it also gives extra terms beyond the HVBK model. Actually, we show that the two-fluid models are problematic in case of higher counter-flow velocities, where the usual splitting of total momentum to the superfluid and normal component becomes impossible. Finally, we show how vortex line density may be added to the state variables. The one-fluid model can be seen as a generalization of the two-fluid models that is geometrically consistent, fully compressible, with non-zero superfluid vorticity, and compatible with classical experiments.

超流体氦-4的标准描述是基于两组分（超流体和正常）的概念，这导致了所谓的双流体模型。然而，由于氦-4中没有两种原子，这两种成分不能分开。超流体氦-4不是两种成分的混合物，而是一种具有两种运动的单一流体。本文提出了一个基于流体力学哈密顿公式的超流体氦-4的几何单流体模型。该模型由激发态（在温度1.3K下作为理想玻色气体）和平均粒子运动的动力学理论推导而来。它可以简化为Hall-Vinen-Bekharevich-Khalatnikov （HVBK）双流体模型，其中它从HVBK模型中删除了一个拟合参数，但它也给出了超出HVBK模型的额外项。实际上，我们表明，双流体模型在较高逆流速度的情况下是有问题的，在这种情况下，通常的总动量向超流体和法向分量的分裂变得不可能。最后，我们展示了如何将涡线密度添加到状态变量中。单流体模型可以看作是双流体模型的推广，它几何上一致，完全可压缩，具有非零超流体涡量，并且与经典实验相兼容。

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引用次数: 0

Torsional vibration of a coupled cylinder 耦合圆柱的扭转振动

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-09-09 DOI: 10.1016/j.ijengsci.2025.104374

Igor Istenes , Daniel Peck , Yuriy Protserov , Natalya Vaysfeld , Zinaida Zhuravlova

The torsion loading of a coupled cylinder, comprising distinct upper and lower cylindrical sections potentially made of different materials, is considered. The bottom of the cylinder is fixed in place, and induces the cylinder vibration. The torsion is applied via an arbitrary loading on the upper face. Three forms of coupling condition between the upper and lower cylinders are outlined: ideal, soft (weak), and rigid (hard/ stiff) contact. The resulting displacements and tangential stresses are obtained using the finite Hankel transform, and a Green’s function representation of the displacement. Numerical results are provided, and the impact of the differing coupling conditions investigated for a range of cylinder geometries, material properties and vibration rates. The resonance frequencies of the coupled cylinder are determined. A method for using the coupled cylinder model to approximate the displacement of a cylinder containing a damaged region via a weak interfacial layer is outlined. The properties of the weak interface layer needed for this approximation are determined, and the advantages of its use in non-destructive testing are discussed.

考虑了一个耦合圆柱体的扭转载荷，该圆柱体包括不同的上下圆柱体部分，可能由不同的材料制成。气缸底部固定到位，引起气缸振动。扭转是通过上表面的任意载荷施加的。概述了上下气缸之间的三种形式的耦合条件：理想、软（弱）和刚性（硬/硬）接触。利用有限汉克尔变换和位移的格林函数表示得到了位移和切向应力。给出了数值结果，并研究了不同耦合条件对一系列圆柱体几何形状、材料性能和振动速率的影响。确定了耦合圆柱的谐振频率。提出了一种利用耦合柱体模型通过弱界面层逼近含有损伤区域的柱体位移的方法。确定了这种近似所需的弱界面层的性质，并讨论了其在无损检测中的优点。

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引用次数: 0

Effect of periodic lamellar inclusions on interface integrity 周期性层状夹杂物对界面完整性的影响

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-09-05 DOI: 10.1016/j.ijengsci.2025.104380

Chao Tang , Fei Su , Wen Zhao , Jingyu Zhang , Biao Wang , Lifeng Ma

The bond strength between dissimilar solids is highly sensitive to defects near or within the interface. Interfacial inclusions, which are ubiquitous in materials engineering, play a critical role in determining the local and global integrity of materials or structures. In this article, we propose a theoretical model for periodic rectangular lamellar inclusions at the interface of dissimilar solids. In view of the concept of line inclusion, the Kolosov–Muskhelishvili complex potentials for the homogeneous periodic inclusion problem are derived based on the Green’s function method within the framework of plane elasticity. The explicit analytical solution of the stress field of the inhomogeneous periodic rectangular lamellar inclusion problem with arbitrary eigenstrain distribution is derived with the aid of the equivalent eigenstrain principle. A new stress concentration factor (SCF) is consequently defined to assess the interface strength. The influence of the size and material of rectangular lamellar inclusions on the SCF is analyzed. The accuracy of the theoretical results is further verified by finite element simulations. The analytical formulae established in this study offer a straightforward yet effective approach for various inhomogeneous and homogeneous interfacial inclusion problems encountered in engineering practice.

不同固体之间的结合强度对界面附近或界面内的缺陷高度敏感。界面夹杂物在材料工程中无处不在，在决定材料或结构的局部和整体完整性方面起着至关重要的作用。本文提出了不同固体界面上周期性矩形片层夹杂物的理论模型。考虑到线包含的概念，在平面弹性的框架下，基于格林函数方法，导出了齐次周期包含问题的Kolosov-Muskhelishvili复势。利用等效本征应变原理，导出了具有任意本征应变分布的非均匀周期性矩形片层夹杂问题应力场的显式解析解。因此，定义了一个新的应力集中系数（SCF）来评估界面强度。分析了矩形层状夹杂物的尺寸和材料对SCF的影响。通过有限元仿真进一步验证了理论结果的准确性。本研究建立的解析公式为工程实践中遇到的各种非均匀和均匀界面夹杂问题提供了一个简单而有效的方法。

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引用次数: 0

Topology optimization of 2D chiral metamaterials with dilatation-shear and shear-shear coupling capabilities 具有膨胀-剪切和剪切-剪切耦合能力的二维手性超材料拓扑优化

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-09-04 DOI: 10.1016/j.ijengsci.2025.104367

Mohamed Shaat , Xin-Lin Gao

Metamaterials with chiral microstructures exhibit unique mechanical coupling among various deformation modes. Traditional approaches for designing such materials rely heavily on discrete models and unit cells with predefined architectures, and hence it has been challenging to develop methodologies that can explore a broad range of chiral configurations and optimize the mechanical coupling behavior without being constrained by specific unit cell geometries. In the current study, a new multi-objective topology optimization (TO) method is developed for designing 2D chiral metamaterials with prescribed mechanical coupling among dilatation and two distinct shear deformation modes. The new method incorporates material symmetry constraints (including the

C_{2}

and

C_{4}

symmetries) into the TO process. A strain energy-based homogenization approach is adopted to determine the effective elastic stiffness matrix for each periodic chiral metamaterial. The TO process begins with maximizing the trace of the stiffness matrix to avoid cases with vanishing bulk or shear moduli, which is followed by maximizing/minimizing a selected off-diagonal component to optimize the dilatation-shear or shear-shear coupling. The proposed method successfully identifies optimal topologies that exhibit chiral layouts consistent with the imposed material symmetry constraints, and it maximizes mechanical coupling among dilatation and shear deformation modes. This newly developed method enables the exploration of diverse chiral material configurations, achieving optimized mechanical coupling without relying on a specific unit cell architecture.

具有手性微结构的超材料在各种变形模式之间表现出独特的力学耦合。设计此类材料的传统方法严重依赖于具有预定义架构的离散模型和单元格，因此开发能够探索广泛的手性配置并优化机械耦合行为的方法一直具有挑战性，而不受特定单元格几何形状的限制。在本研究中，提出了一种新的多目标拓扑优化（TO）方法，用于设计具有规定的膨胀和两种不同剪切变形模式之间的力学耦合的二维手性超材料。新方法将材料对称约束（包括C2和C4对称）纳入到TO工艺中。采用基于应变能的均匀化方法确定了各周期手性超材料的有效弹性刚度矩阵。TO过程首先最大化刚度矩阵的轨迹，以避免体积模量或剪切模量消失的情况，然后最大化/最小化选定的非对角线分量，以优化膨胀-剪切或剪切-剪切耦合。该方法成功地识别出符合材料对称约束的手性布局的最优拓扑结构，并最大限度地提高了膨胀和剪切变形模式之间的力学耦合。这种新开发的方法可以探索不同的手性材料结构，实现优化的机械耦合，而不依赖于特定的单元胞结构。

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引用次数: 0

Micromechanism-based electrochemo-mechanical model for double polarization-actuation of PVC gel-based electronic electroactive polymer 聚氯乙烯胶基电子电活性聚合物双极化驱动的微观电化学-力学模型

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-09-02 DOI: 10.1016/j.ijengsci.2025.104375

Li Zhang , Yiqi Mao , Wenyang Liu , Shujuan Hou

The polyvinyl chloride gel (PVCG)-based electroactive polymer exhibits tunable stiffness and achieves large strains with rapid response at moderate drive voltages (200–3000 V), making it suitable for versatile engineering applications. The electric actuation response of PVCG involves a strong micromechanism-characterized coupling between the electrochemical mobility of the plasticizer and the electro-modulus of PVC chain. Specifically, plasticizer polarization-induced electromigration generates polarization stress and osmotic stress, which act as the active driving forces for high actuation strain in PVCG, while polymer skeleton polarization-induced conformational transformation influences the electro-modulus of PVCG, impeding the deformation process. This work formulates an electrochemo-mechanical model to unravel the double polarization-induced actuation mechanism of PVCG under a thermodynamically consistent large deformation frame. First, we solve the polarization and dynamic evolution of a single polymer chain under electric excitation, as well as a single plasticizer molecule. The total free energy function of PVCG is then integrated through statistical mechanics in line with the full-network model. Subsequently, micromechanism-based constitutive relations are simplified following the core principles of the eight-chain model, incorporating effective stretch and electric field through average directions analytically. The finite element implementation is realized and the model is calibrated through a series of tests. Double polarization-induced actuation properties and the memory effect of PVCG under cyclic activation are analyzed. Additionally, a telescopic driver and a self-sensing variable stiffness artificial muscle model are simulated to showcase the wider applicability of our numerical simulation capability. This work provides theoretical understanding and design guidelines for PVCG at macro/micro scales in the actuation field.

基于聚氯乙烯凝胶（PVCG）的电活性聚合物具有可调的刚度，并且在中等驱动电压（200-3000 V）下实现快速响应的大应变，使其适用于多种工程应用。PVCG的电致动响应涉及增塑剂的电化学迁移率与PVC链的电模量之间的强微观机制耦合。其中，增塑剂极化诱导的电迁移产生极化应力和渗透应力，这是PVCG中高驱动应变的主动驱动力，而聚合物骨架极化诱导的构象转变影响了PVCG的电模量，阻碍了变形过程。本文建立了一个电化学-力学模型，揭示了PVCG在热一致大变形框架下的双极化致动机理。首先，我们求解了电激发下单个聚合物链的极化和动态演化，以及单个增塑剂分子。然后根据全网络模型，通过统计力学对PVCG的总自由能函数进行积分。随后，根据八链模型的核心原理，对基于微观机制的本构关系进行简化，通过平均方向解析纳入有效拉伸和电场。实现了有限元实现，并通过一系列试验对模型进行了标定。分析了双极化致动特性和循环活化下PVCG的记忆效应。此外，还对伸缩驱动器和自感知变刚度人工肌肉模型进行了仿真，以展示我们的数值模拟能力的广泛适用性。本研究为PVCG在驱动领域的宏/微尺度提供了理论认识和设计指导。

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引用次数: 0