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Multiscale modeling of transient problems in periodic Cauchy materials: Asymptotic and spectro-hierarchical homogenization 周期柯西材料瞬态问题的多尺度建模:渐近和光谱层次均匀化
IF 5.7 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2026-01-10 DOI: 10.1016/j.ijengsci.2025.104460
Alessandro Fortunati , Francesca Fantoni , Andrea Bacigalupo
This work presents a detailed and systematic analytical investigation of the transient elastic wave propagation in two-dimensional periodic heterogeneous composites. The study is conducted through two complementary methodologies: asymptotic homogenization and a recently proposed spectro-hierarchical approach, specifically designed to resolve higher-order microstructural effects. The asymptotic homogenization method derives effective macroscopic equations that accurately capture the averaged behavior of the periodic microstructure, providing a reduced-order but reliable representation of long-wave and low-frequency dynamics. In parallel, the spectro-hierarchical approach systematically reconstructs microstructural fluctuations using a combination of truncated Fourier expansions and a hierarchical sequence of differential problems, allowing the recovery of both first-order homogenized responses and higher-order corrections due to local heterogeneities. The analysis considers both zero and non-zero initial conditions, enabling the study of general transient excitations, including short-time dynamics and localized disturbances, rather than merely steady-state or frequency-limited responses.
本文对二维周期性非均质复合材料中的瞬态弹性波传播进行了详细而系统的分析研究。该研究通过两种互补的方法进行:渐近均质化和最近提出的光谱分层方法,专门用于解决高阶微观结构效应。渐近均匀化方法导出了有效的宏观方程,准确地捕捉了周期微观结构的平均行为,提供了一个降阶但可靠的长波和低频动力学表示。同时,光谱分层方法系统地重建微观结构波动,使用截断傅立叶展开和微分问题的分层序列相结合,允许恢复一阶均匀响应和由于局部异质性引起的高阶修正。该分析考虑了零和非零初始条件,使研究一般瞬态激励,包括短时动力学和局部扰动,而不仅仅是稳态或频率有限的响应。
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引用次数: 0
Mechanical characterization and visco-hyperelastic modeling of epithelial cells: Pressure-rate dependency of the apparent elastic modulus 上皮细胞的力学特性和粘弹性建模:表观弹性模量的压力-速率依赖性
IF 5.7 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2026-01-08 DOI: 10.1016/j.ijengsci.2025.104459
Enzo Brito , Claudio García-Herrera , Blanca González-Bermúdez , Gustavo R. Plaza , Diego Celentano , Bernardo J. Krause , Aldo Abarca-Ortega
In this study, an experimental and numerical characterization of the viscohyperelastic behavior of suspended epithelial ARPE-19 cells is carried out using the micropipette aspiration technique, with particular emphasis on the evaluation of two viscoelastic models with different mathematical formulations, which were implemented in an in-house finite element code. The tests, conducted under one and two-ramp aspiration protocols, revealed variations in the measured mechanical properties of the cells, which are first sensitive to the applied pressure levels; This dependency is attributed to the internal organization of subcellular components. Second, the aspiration tests show that the apparent elastic modulus is dependent to the applied pressure rate. Two visco-hyperelastic models were evaluated to replicate the experimentally observed behavior. Although both models successfully fit the results, the LM model proved to be more efficient, requiring fewer parameters and enabling a clearer physical interpretation of the viscoelastic properties. In the numerical calculations, a time- and geometry-dependent load function was implemented, which optimally replicated the experimental observations while maintaining low computational cost.
在本研究中,使用微管抽吸技术对悬浮上皮ARPE-19细胞的粘超弹性行为进行了实验和数值表征,特别强调了两种具有不同数学公式的粘弹性模型的评估,这些模型在内部有限元代码中实现。在单坡和双坡抽吸方案下进行的测试揭示了所测细胞的机械特性的变化,它们首先对施加的压力水平敏感;这种依赖性归因于亚细胞成分的内部组织。其次,吸入试验表明,表观弹性模量与施加压力速率有关。评估了两个粘超弹性模型以复制实验观察到的行为。虽然两种模型都成功地拟合了结果,但LM模型被证明更有效,需要更少的参数,并且能够更清晰地解释粘弹性特性。在数值计算中,实现了与时间和几何相关的载荷函数,在保持较低计算成本的同时,最优地复制了实验观测结果。
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引用次数: 0
On the classical and constrained theories for preventing self-intersection in orthotropic nonlinear elasticity 正交各向异性非线性弹性中防止自交的经典理论和约束理论
IF 5.7 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2026-01-08 DOI: 10.1016/j.ijengsci.2025.104452
Adair R. Aguiar , Thomas J. Pence , Lucas A. Rocha
We investigate the local injectivity requirement detF>0, where F is the deformation gradient, in the context of both the classical nonlinear elasticity theory and a constrained energy minimization theory with the explicit constraint detFɛ, where 0<ɛ<1. In the classical theory, the condition detF>0 is guaranteed by Ball’s theorem provided that appropriate growth conditions are satisfied. For orthotropic hyperelastic solids, we consider equilibrated states of finite plane strain for which the principal axes of strain align with the axes of orthotropic symmetry. Two materials are considered: an orthotropic St. Venant–Kirchhoff material as considered in previous work, and an orthotropic compressible Mooney–Rivlin material. Basic issues are revealed by considering homogeneous plane strain deformation with applied in-plane uniaxial loading. In the absence of the condition detF>0, the St. Venant–Kirchhoff material permits complete volume loss, and hence material overlap, at zero applied load. The Mooney–Rivlin material has no such issue, although it exhibits stress–strain nonmonotonicity for certain parameter values. Material overlap for the St. Venant–Kirchhoff material is remedied by imposing the constraint detFɛ and many features of the corresponding stress–strain behavior are then found to mirror that of the unconstrained Mooney–Rivlin material. The homogeneous deformation study serves as a prelude to the investigation of a nonhomogeneous deformation problem, that of a radially reinforced annular disk that is fixed on its inner radius and subjected to uniform pressure on its outer radius. The problem is solved both as a boundary value problem using a phase-plane technique and via direct minimization using nonlinear programming tools. For each material model, the two procedures give indistinguishable results. Sufficiently high applied pressures yield non-smooth deformations inside the disk. Solutions for the unconstrained Mooney–Rivlin material obtain close agreement with those for the constrained St. Venant material as ɛ tends to zero.
本文在经典非线性弹性理论和约束能量最小化理论的背景下,研究了局部注入性要求detF>;0,其中F为变形梯度,其中detF≥,其中0<;在经典理论中,只要满足适当的生长条件,条件detF>;0由Ball定理保证。对于正交各向异性超弹性固体,我们考虑了应变主轴与正交各向异性对称轴对齐的有限平面应变的平衡状态。本文考虑了两种材料:一种是之前研究过的正交各向异性St. Venant-Kirchhoff材料,另一种是正交各向异性可压缩Mooney-Rivlin材料。通过考虑施加平面内单轴载荷的均匀平面应变变形,揭示了基本问题。在没有条件detF>;0的情况下,St. Venant-Kirchhoff材料允许在零载荷下完全体积损失,因此材料重叠。Mooney-Rivlin材料没有这样的问题,尽管它在某些参数值下表现出应力-应变非单调性。St. Venant-Kirchhoff材料的材料重叠通过施加约束detF≥i来弥补,然后发现相应的应力-应变行为的许多特征反映了无约束的Mooney-Rivlin材料的特征。均匀变形研究是研究非均匀变形问题的前奏,非均匀变形问题是指径向增强的环形圆盘,其内半径固定,外半径承受均匀压力。利用相平面技术和非线性规划工具的直接最小化来求解边值问题。对于每种材料模型,这两种方法给出的结果难以区分。施加足够高的压力会使圆盘内部产生非光滑变形。无约束Mooney-Rivlin材料的解与有约束St. Venant材料的解在趋近于零时非常接近。
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引用次数: 0
Inclined mode-I elliptic crack problem in one-dimensional hexagonal quasicrystals 一维六边形准晶体的倾斜i型椭圆裂纹问题
IF 5.7 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2026-01-08 DOI: 10.1016/j.ijengsci.2025.104458
Haining Liu , Ruifeng Zheng , Zichen Deng , Haimin Yao
This article investigates an inclined elliptic crack problem in one-dimensional (1D) hexagonal quasicrystals (QCs). The crack lies in a plane perpendicular to the transversely isotropic plane, and its orientation (the major axis of the ellipse) forms an arbitrary angle with the quasi-periodic axis of the QCs. A pair of uniform normal loading is applied symmetrically on the crack surfaces. Using the potential theory method, the governing equation is established and the phonon–phason field is obtained in terms of simple integrals. The fracture parameters including the crack opening displacement (COD) and the stress intensity factor (SIF) are derived. Numerical results validate the solutions and investigate the effects of the phason field, inclination angle and eccentricity on the fracture parameters. A simplified explicit expression for the SIF is developed via symbolic regression. This machine learning-based model offers an efficient and accurate computational alternative to complex theoretical solutions. As a model problem within the framework of QC elasticity theory, the present study offers insights into the fracture behavior of 1D hexagonal QCs and is expected to provide a theoretical reference for structural integrity evaluation and fracture-resistant design of QC materials.
本文研究了一维六方准晶体(QCs)中的一个倾斜椭圆裂纹问题。裂纹位于垂直于横各向同性平面的平面上,其方向(椭圆长轴)与qc的准周期轴成任意角度。在裂纹表面对称施加一对均匀法向载荷。利用势理论的方法,建立了控制方程,用简单积分的形式得到了声子-相场。推导了包括裂纹张开位移(COD)和应力强度因子(SIF)在内的断裂参数。数值结果验证了上述解的正确性,并研究了相场、倾角和偏心距对裂缝参数的影响。通过符号回归得到了SIF的简化显式表达式。这种基于机器学习的模型为复杂的理论解决方案提供了一种高效、准确的计算替代方案。作为QC弹性理论框架下的模型问题,本研究深入了解了一维六边形QC的断裂行为,有望为QC材料的结构完整性评价和抗断裂设计提供理论参考。
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引用次数: 0
Asymptotic continualisation of high-contrast lattices and the interpretation of gradient elasticity 高对比格的渐近连续化与梯度弹性的解释
IF 5.7 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2026-01-08 DOI: 10.1016/j.ijengsci.2025.104456
J. Kaplunov , L. Nazarenko , H. Altenbach
The basic concepts of gradient elasticity are interpreted by developing an asymptotic continualisation procedure for high-contrast lattices. As an example, a two-spring axial lattice supporting both direct and indirect interactions is considered, assuming the stiffness of the string related to the latter is much greater. In this case, the length scale of gradient phenomena considerably exceeds the distance between lattice nodes ensuring a continuous approximation. At leading order, it is given by a fourth-order singular perturbed equation degenerating to a second-order one, which is typical of the canonical asymptotic setup. It is shown that the gradient behaviour may also be incorporated by imposing effective boundary conditions for the mentioned second-order equation. The accuracy of the derived continuous framework is illustrated by comparison with the exact discrete solution.
梯度弹性的基本概念是通过发展高对比度格的渐近连续化过程来解释的。作为一个例子,考虑了支持直接和间接相互作用的双弹簧轴向晶格,假设与后者相关的弦的刚度要大得多。在这种情况下,梯度现象的长度尺度大大超过晶格节点之间的距离,以确保连续逼近。在首阶,它由退化为二阶的四阶奇异摄动方程给出,这是典型的正则渐近建立。结果表明,通过对上述二阶方程施加有效的边界条件,也可以纳入梯度行为。通过与精确离散解的比较,说明了导出的连续框架的准确性。
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引用次数: 0
Weakly nonlinear dynamics of a thin aerogel coating governed by Rajagopal’s continuum model Rajagopal连续统模型下薄气凝胶涂层的弱非线性动力学
IF 5.7 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2026-01-07 DOI: 10.1016/j.ijengsci.2025.104451
Weibo Xiong , Danila Prikazchikov , Rasul Abdusalamov , Mikhail Itskov
This paper addresses a dynamic problem for a thin aerogel layer with one face fixed and a time-harmonic vertical displacement prescribed on the opposite face. The constitutive relations rely on Rajagopal’s nonlinear implicit model. To validate the material parameters, we conduct uniaxial compression experiments on organic–inorganic hybrid silica aerogels, confirming the predictive capability of the proposed model. A weakly nonlinear asymptotic analysis is conducted and the associated two-term approximate solution is obtained, for both the one-dimensional problem for transverse displacement and the plane-strain problem. Comparisons with numerical solutions are performed, highlighting the importance of the nonlinear corrector. The integrated approach involving asymptotic analysis, numerical investigations, and experimental characterization advances the understanding of the dynamic behaviour of aerogels and paves the way for the design of aerogel-based insulation applications.
本文研究了一面固定,另一面规定时谐垂直位移的薄气凝胶层的动力学问题。本构关系依赖于Rajagopal的非线性隐式模型。为了验证材料参数,我们对有机-无机杂化二氧化硅气凝胶进行了单轴压缩实验,证实了所提出模型的预测能力。对一维横向位移问题和平面应变问题进行了弱非线性渐近分析,得到了相应的两项近似解。与数值解进行了比较,突出了非线性校正器的重要性。包括渐近分析、数值研究和实验表征在内的综合方法促进了对气凝胶动态行为的理解,并为气凝胶基绝缘应用的设计铺平了道路。
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引用次数: 0
Poroelasticity in the presence of active fluids 活性流体存在时的孔隙弹性
IF 5.7 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2026-01-06 DOI: 10.1016/j.ijengsci.2025.104457
R. Cavuoto , S. Scala , A. Cutolo , G. Mensitieri , M. Fraldi
This work presents a model for characterizing porous, deformable media embedded with magnetorheological fluids (MRFs). These active fluids exhibit tunable mechanical and rheological properties that can be controlled through the application of a magnetic field, which induces a phase transition from a liquid to a solid-like state. This transition profoundly affects both stress transmission and fluid flow within the composite, leading to a behaviour governed by a well-defined threshold that depends on the ratio between the pore size and the characteristic size of clusters of magnetic particles, and can be triggered by adjusting the magnetic field intensity. These effects were confirmed through an experimental campaign conducted on a prototype composite obtained by imbibing a selected MRF into commercial sponges. To design and optimize this new class of materials, a linear poroelastic formulation is proposed and validated through comparison with experimental results. The constitutive relationships, i.e. overall elastic constitutive tensor and permeability, of the model are updated from phenomenological observations, exploiting the experimental data obtained for both the pure fluid and the composite material. The findings demonstrate that the proposed simplified formulation is sufficiently robust to predict and optimize the behaviour of porous media containing MRFs. Such materials hold significant promise for a wide range of engineering applications, including adaptive exosuits for human tissue and joint rehabilitation, as well as innovative structural systems.
这项工作提出了一个模型来表征嵌入磁流变流体(mrf)的多孔、可变形介质。这些活性流体表现出可调节的机械和流变特性,可以通过施加磁场来控制,从而诱导从液体到类固体状态的相变。这种转变对复合材料内部的应力传递和流体流动都产生了深远的影响,导致了一种由一个定义明确的阈值控制的行为,该阈值取决于孔隙大小与磁性颗粒簇的特征尺寸之间的比例,并且可以通过调节磁场强度来触发。通过将选定的MRF吸入商业海绵中获得的原型复合材料的实验活动,证实了这些效果。为了设计和优化这种新型材料,提出了一种线性孔弹性公式,并通过与实验结果的比较验证了该公式的正确性。利用纯流体和复合材料的实验数据,根据现象学观测更新了模型的本构关系,即整体弹性本构张量和渗透率。研究结果表明,所提出的简化公式具有足够的鲁棒性,可以预测和优化含有MRFs的多孔介质的行为。这些材料在广泛的工程应用中具有重要的前景,包括用于人体组织和关节康复的自适应外骨骼,以及创新的结构系统。
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引用次数: 0
Numerical reproduction of physiological flow conditions in complex vessel system of cerebral arteries with a porosity based method 基于孔隙度方法的脑动脉复杂血管系统生理流动条件的数值再现
IF 5.7 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2026-01-02 DOI: 10.1016/j.ijengsci.2025.104455
Michał Tomaszewski , Michał Kucewicz , Radosław Rzepliński , Marcin Paturalski , Jerzy Małachowski , Bogdan Ciszek
This paper introduces an innovative approach to modelling boundary conditions for blood flow simulations in arteries with highly complex geometries and multiple outlets. In cases where the arterial cross-section varies significantly, employing analytical models like Windkessel to represent tissue resistance becomes particularly challenging. In this study, we propose a novel approach that combines a porosity model, which induces a pressure drop, with physiological outlet pressures to achieve realistic hemodynamic conditions in blood vessels. The total proportion of blood flow through the perforators was approximately 7.2 % for the BA and 11.6 % for the MCA, while maintaining physiological velocity values in the subsequent branches. The proposed method stands out for its relative simplicity in determining porous body parameters for outlets of varying diameters by quasi-iteratively adjusting two key values of the Power Law model. A major advantage of this approach is its accessibility to non-experts in fluid mechanics, as it does not require complex model reductions to 1D. The study also examines key parameters influencing artery remodelling processes, specifically wall shear stress divergence (WSSD). Furthermore, preliminary histopathological analyses confirm that regions with low WSSD exhibit structural changes in the vessel wall, leading changes similar to intimal hyperplasia. The original data such as DICOM images, artery geometry and domain mesh for the individual representations, together with UDF files for the initial boundary conditions, have been included in the Mendeley database: DOI: 10.17632/5vxtmcwr64.3 and basilar artery model in DOI: 10.17632/ng9mrrn2r7.3.
本文介绍了一种创新的方法来模拟具有高度复杂几何形状和多个出口的动脉血流模拟的边界条件。在动脉横截面变化显著的情况下,采用Windkessel等分析模型来表示组织阻力变得特别具有挑战性。在这项研究中,我们提出了一种新的方法,将孔隙率模型与生理出口压力相结合,以实现血管中真实的血流动力学条件。通过穿支的总血流比例在BA约为7.2%,MCA约为11.6%,同时在随后的分支中保持生理速度值。该方法通过准迭代调整幂律模型的两个关键值来确定不同直径出口的多孔体参数,其特点是相对简单。这种方法的一个主要优点是它不需要将复杂的模型简化为一维,因此对于非流体力学专家来说也很容易使用。该研究还研究了影响动脉重构过程的关键参数,特别是壁剪切应力散度(WSSD)。此外,初步的组织病理学分析证实,低WSSD区域的血管壁发生结构变化,导致类似内膜增生的变化。原始数据,如DICOM图像、动脉几何形状和用于单独表示的域网格,以及用于初始边界条件的UDF文件,已包含在Mendeley数据库中:DOI: 10.17632/5vxtmcwr64.3,基底动脉模型包含在DOI: 10.17632/ng9mrrn2r7.3。
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引用次数: 0
Investigation of hemodynamics in bypass grafts for left anterior descending coronary artery revascularization: Biaxial tension tests and fluid-structure interaction simulation 左冠状动脉前降支血运重建术旁路移植术血流动力学研究:双轴张力试验和流固耦合模拟
IF 5.7 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2026-01-02 DOI: 10.1016/j.ijengsci.2025.104462
Alireza Behrouz Jazi, Aisa Rassoli
Coronary artery occlusion is one of the most common cardiovascular diseases. In severe cases, bypass surgery is employed as a treatment, wherein a vessel is used as a bypass graft to restore blood flow by connecting the graft to the area beyond the coronary artery blockage. However, since these vessels are prone to reocclusion over time, investigating the hemodynamics of bypass flow is essential. In this study, samples of the three most common grafts, namely the saphenous vein, mammary artery, and radial artery, were obtained. Biaxial tension tests were performed on them to extract their anisotropic hyperelastic properties, which were then used in fluid-structure interaction (FSI) simulations. The results of the biaxial tension tests indicated that the saphenous vein exhibited significant stiffness compared to the other two grafts. The simulations also showed better wall shear stress distribution and higher blood flow velocities within the mammary artery. The saphenous vein exhibited large stresses and displacements at critical attachment points in both the fluid and solid domains, which may, over time, cause damage to the graft attachment and disrupt graft performance. The time average wall shear stress (TAWSS) in the toe region of the attachment area was 7.21 Pa for the saphenous vein, 5.99 Pa for the radial artery, and 3.05 Pa for the mammary artery. Additionally, the maximum displacement in the saphenous vein was 0.416 mm, 0.323 mm in the mammary artery, and 0.157 mm in the radial artery. The results of this research have potential applications in clinical cardiovascular studies and contribute to the development of practical treatment approaches.
冠状动脉闭塞是最常见的心血管疾病之一。在严重的情况下,旁路手术是一种治疗方法,其中血管被用作旁路移植物,通过将移植物连接到冠状动脉阻塞以外的区域来恢复血液流动。然而,由于这些血管随着时间的推移容易再闭塞,研究旁路血流动力学是必要的。在本研究中,获得了三种最常见的移植物样本,即隐静脉、乳腺动脉和桡动脉。对其进行双轴拉伸试验,提取其各向异性超弹性特性,然后将其用于流固耦合(FSI)模拟。双轴张力测试结果表明,与其他两种移植物相比,隐静脉表现出明显的刚度。模拟还显示了更好的壁剪切应力分布和乳腺动脉内更高的血流速度。隐静脉在流体和固体领域的关键附着点都表现出较大的应力和位移,随着时间的推移,这可能会导致移植物附着点损伤并破坏移植物的性能。趾部附着区时间平均壁剪切应力(TAWSS)隐静脉为7.21 Pa,桡动脉为5.99 Pa,乳腺动脉为3.05 Pa。隐静脉最大位移0.416 mm,乳腺动脉最大位移0.323 mm,桡动脉最大位移0.157 mm。本研究结果在临床心血管研究中具有潜在的应用价值,并有助于开发实用的治疗方法。
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引用次数: 0
Dynamics of curved domain walls in hexagonal magnetostrictive materials with nonlinear dissipation and Rashba effects 具有非线性耗散和Rashba效应的六方磁致伸缩材料弯曲畴壁动力学
IF 5.7 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2025-12-31 DOI: 10.1016/j.ijengsci.2025.104461
Ambalika Halder , Sharad Dwivedi , Shruti Dubey
This study presents an analytical investigation of the dynamics of curved domain walls in a bilayer magnetostrictive–piezoelectric heterostructure, using the extended Landau–Lifshitz–Gilbert equation. The system comprises a thin magnetostrictive layer perfectly bonded to the upper surface of a thick piezoelectric layer. We consider a transversely isotropic hexagonal class of magnetostrictive materials that exhibit structural inversion asymmetry. Our analysis accounts for the coupled effects of external magnetic fields, spin-polarized electric currents, magnetoelastic interactions, magnetocrystalline anisotropy, Rashba spin–orbit fields, and nonlinear viscous-dry friction dissipation mechanisms. Employing the reductive perturbation technique, we derive explicit analytical expressions for key dynamic parameters, such as the velocity, mobility, threshold, and breakdown conditions of the domain wall motion in the steady state. Our results reveal the intricate interplay between mean curvature, Rashba field, magnetoelastic coupling, and nonlinear dissipation, which collectively govern the propagation of domain walls in the magnetostrictive layer. Further, we numerically illustrate the analytical results obtained for curved domain walls on constant-curvature surfaces, such as planes, spheres, and cylinders. The results derived here demonstrate good qualitative alignment with recent studies.
本文利用扩展的Landau-Lifshitz-Gilbert方程对双层磁致伸缩压电异质结构中弯曲畴壁的动力学进行了分析研究。该系统包括与厚压电层的上表面完美结合的薄磁致伸缩层。我们考虑了一类横向各向同性的六边形磁致伸缩材料,它具有结构反演不对称性。我们的分析考虑了外部磁场、自旋极化电流、磁弹性相互作用、磁晶各向异性、Rashba自旋轨道场和非线性粘干摩擦耗散机制的耦合效应。采用约化微扰技术,推导出稳态下畴壁运动的速度、迁移率、阈值和击穿条件等关键动力学参数的显式解析表达式。我们的研究结果揭示了平均曲率、Rashba场、磁弹性耦合和非线性耗散之间复杂的相互作用,它们共同控制着磁致伸缩层中畴壁的传播。此外,我们数值说明了在恒定曲率表面(如平面、球体和圆柱体)上获得的弯曲畴壁的分析结果。这里得出的结果与最近的研究有很好的定性一致性。
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引用次数: 0
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