International Journal of Engineering Science最新文献_第4页

Impact-governed dynamics of an axially-incompressible bistable continuous metastructure 轴向不可压缩双稳连续元结构的冲击控制动力学

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-12-07 DOI: 10.1016/j.ijengsci.2025.104436

Andrea Nobili , Dipendu Pramanik

We study the dynamics of a bistable Single Degree of Freedom mechanism that bifurcates from the trivial straight configuration when subjected to a critical traction force and it is otherwise incompressible. We show that the appearance of “impacts”, in correspondence with the minimum axial extension of the system, merely reflects the adoption of the axial extension as the dependent variable, as opposed to the angular rotation. Within this description, the structure realizes a perfectly elastic obstacle. Next, we construct the continuous limit for a dense chain of such mechanisms and axial strain naturally emerges as the continuous dependent field. Consequently, an unilateral constraint becomes associated with the system. Most importantly, the corresponding Lagrangian problem needs to be supplemented by energy conservation across the impacts to faithfully represent the underlying microstructure. In doing so, we generalize the established procedure to construct the continuous limit of a dense chain of discrete systems to the presence of unilateral constraints. Remarkably, energy conservation allows to apply Hamilton’s principle in the form of a variational equality, in contrast to the inequality format usually encountered when dealing with non-smooth problems. This important result, which greatly simplifies the mathematics, is available provided that variations are extended to accommodate for discontinuities in the variables. Besides, the system dynamics may be now constructed semi-analytically by joining pairs of d’Alembert’s solutions through the conditions obtained from the extended variational principle at the impact time and location (which are obviously unknown). As a result, waves propagating in the system are obtained and they are checked against global energy conservation.

我们研究了一个双稳态单自由度机构的动力学问题，该机构在受到临界牵引力作用时，从平凡的直线构型中分叉，否则它是不可压缩的。我们表明，“冲击”的出现，与系统的最小轴向延伸相对应，仅仅反映了轴向延伸作为因变量的采用，而不是角旋转。在这个描述中，结构实现了一个完美的弹性障碍。其次，我们构造了此类机构密集链的连续极限，轴向应变自然成为连续相关场。因此，一个单边约束与系统相关联。最重要的是，相应的拉格朗日问题需要通过跨冲击的能量守恒来补充，以忠实地表示潜在的微观结构。在此过程中，我们将已建立的构造离散系统密集链的连续极限的过程推广到单边约束的存在。值得注意的是，能量守恒允许以变分等式的形式应用汉密尔顿原理，而不是在处理非光滑问题时通常遇到的不等式形式。这个重要的结果，极大地简化了数学，提供了变化的扩展，以适应不连续性的变量。此外，通过扩展变分原理在碰撞时间和位置（显然是未知的）得到的条件，将d 'Alembert解对连接起来，现在可以半解析地构造系统动力学。结果，获得了在系统中传播的波，并根据全局能量守恒进行了检查。

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引用次数: 0

A compact anisotropic model for the mechanical response of double network hydrogels 双网状水凝胶力学响应的紧致各向异性模型

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-12-05 DOI: 10.1016/j.ijengsci.2025.104437

Domenico De Tommasi, Francesco Trentadue, Gennaro Vitucci

Double-network (DN) hydrogels combine exceptional toughness with tissue-like softness, making them promising materials for biomedical and soft engineering applications. In this work, we present a novel constitutive model for predicting their mechanical response under general multiaxial loading conditions. At the microscopic scale, the two interlaced polymer networks are represented by effective semiflexible (worm-like) chains, capturing the cooperative behavior of the stiff, brittle first network and the soft, extensible second one. Irreversible damage is modeled as a progressive increase in the effective contour length of these chains, enabling the reproduction of the characteristic softening and Mullins effects observed experimentally. The macroscopic behavior is obtained through affine microsphere-based homogenization, ensuring a thermodynamically consistent formulation with a minimal number of material parameters. Despite its simplicity, the model accurately reproduces uniaxial and biaxial responses reported in the literature and demonstrates predictive capability across different loading paths. Furthermore, the identified parameters exhibit systematic trends with varying crosslinking densities, highlighting the potential of the proposed framework for the rational design of DN hydrogels with tailored mechanical properties.

双网（DN）水凝胶结合了优异的韧性和组织般的柔软性，使其成为生物医学和软工程应用的有前途的材料。在这项工作中，我们提出了一个新的本构模型来预测它们在一般多轴加载条件下的力学响应。在微观尺度上，这两种交错的聚合物网络由有效的半柔性（蠕虫状）链表示，捕获了僵硬、脆性的第一个网络和柔软、可扩展的第二个网络的合作行为。不可逆损伤被建模为这些链的有效轮廓长度的逐渐增加，从而能够再现实验中观察到的特征软化和穆林斯效应。宏观行为是通过仿射微球为基础的均质化，确保热力学一致的公式与材料参数的最少数量。尽管简单，但该模型准确再现了文献中报道的单轴和双轴响应，并展示了跨不同加载路径的预测能力。此外，所识别的参数在不同的交联密度下呈现出系统的趋势，突出了所提出的框架在合理设计具有定制力学性能的DN水凝胶方面的潜力。

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引用次数: 0

Kirsch problem in classical and gradient elasticity. Part I: Anisotropic and homogeneous bodies 经典和梯度弹性中的Kirsch问题。第一部分：各向异性和均质体

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-12-05 DOI: 10.1016/j.ijengsci.2025.104439

Teoman Özer , Martin Kröger

In this first part of our study, we examine the Kirsch problem analytically for a body composed of a homogeneous but anisotropic material from the perspectives of both classical and gradient elasticity theories. As a continuation, the second part will address the Kirsch problem for a body that is isotropic but inhomogeneous. In the model, the plane is assumed anisotropic and, with positive

ϵ_{i j} ≪ 1

characterizing the degree of anisotropy, we consider a weakly anisotropic material for which the six elastic coefficients deviate slightly from their values in the equivalent isotropic material. The Airy stress function is used to obtain analytical solutions for stress fields. Similarly, a gradient Airy stress function notation is employed to solve the Kirsch problem in gradient elasticity theory. The stress and displacement fields for the anisotropic Kirsch problem are determined analytically within both classical and gradient elasticity frameworks. The analytical solutions from isotropic and classical elasticity are obtained and compared with existing literature. In addition to the classical boundary conditions, the higher-order gradient boundary conditions are also included in the stress field calculations. The differences that emerge within the scope of classical and gradient elasticity theories are also examined, along with a comparative analysis of the graphical representations of the analytical solutions obtained and the size effects in the gradient elasticity theory. Furthermore, based on both classical and gradient elasticity theories, the comparative presentation of the influence of anisotropic material qualities on the solutions is provided. In this study, we represent the analytical solutions for the homogeneous but anisotropic Kirsch problem, using both classical elasticity and gradient elasticity theory for the first time in the literature.

在本研究的第一部分中，我们从经典弹性理论和梯度弹性理论的角度分析了由均质但各向异性材料组成的物体的Kirsch问题。作为延续，第二部分将讨论各向同性但非均匀的物体的基尔希问题。在模型中，假定平面是各向异性的，并且以正ϵij≪1表示各向异性的程度，我们考虑一种弱各向异性材料，其六个弹性系数与等效各向同性材料中的值略有偏离。利用Airy应力函数得到应力场的解析解。同样，梯度弹性理论中的Kirsch问题也采用梯度Airy应力函数符号来解决。在经典和梯度弹性框架下，分析确定了各向异性Kirsch问题的应力场和位移场。得到了各向同性和经典弹性力学的解析解，并与已有文献进行了比较。应力场计算除考虑经典边界条件外，还考虑了高阶梯度边界条件。在经典弹性理论和梯度弹性理论范围内出现的差异也进行了检查，并对所获得的解析解的图形表示和梯度弹性理论中的尺寸效应进行了比较分析。在经典弹性理论和梯度弹性理论的基础上，对比分析了材料各向异性对解的影响。在本研究中，我们首次在文献中同时使用经典弹性和梯度弹性理论，给出了齐次但各向异性Kirsch问题的解析解。

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引用次数: 0

Out-of-plane compression and energy absorption performance of twisted auxetic honeycomb tubes 扭转异形蜂窝管的面外压缩和吸能性能

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-12-04 DOI: 10.1016/j.ijengsci.2025.104435

Que Zhou , Zhihui Xu , Youjiang Cui , Kaifa Wang , Baolin Wang

Lightweight structures with exceptional energy absorption properties are essential for the engineering demands. Auxetic honeycombs are promising candidates for dynamic impact protection and high-performance energy absorption devices. Inspired by horsetail stems and helical geometry, this study proposes a novel twisted auxetic honeycomb tube (TAHT), which combines the advantages of auxetic structures, thin-walled tubes, and twisted configurations. The energy absorption performance of the TAHT under out-of-plane compression is investigated through experiments and numerical simulations. The influence of the optimal twist angle, multi-layer configuration, and wall thickness is further analyzed. The results show that the twist angle changes the deformation mode from parallel crushing to a unique twisting-compression mode, delaying densification and significantly enhancing energy absorption. Specifically, the TAHT with an optimal twist angle increased specific energy absorption (SEA) by 41.9 % and crush force efficiency (CFE) from 72.6 % to 78.3 % compared to a non-twisted structure. Furthermore, a multilayer configuration and increased wall thickness both improved energy absorption performance. A theoretical model derived from the super folding element theory, accurately predicts the mean crushing force (F_mean) and validates with experimental and numerical results. These findings confirm the superior energy absorption capabilities of the TAHT, offering new design insights for lightweight and high-strength metamaterials.

具有特殊能量吸收性能的轻质结构是满足工程需求的必要条件。补充蜂窝是动态冲击保护和高性能能量吸收装置的有希望的候选者。受马尾茎和螺旋几何结构的启发，本研究提出了一种新型的扭曲消声蜂窝管（TAHT），它结合了消声结构、薄壁管和扭曲结构的优点。通过实验和数值模拟研究了TAHT在面外压缩下的吸能性能。进一步分析了最优扭角、多层结构和壁厚的影响。结果表明：扭转角的改变使物料的变形模式由平行破碎转变为独特的扭转压缩模式，延缓了致密化，显著提高了能量吸收；具体来说，与非扭曲结构相比，具有最佳扭转角的TAHT比能量吸收（SEA）提高了41.9%，粉碎力效率（CFE）从72.6%提高到78.3%。此外，多层结构和增加的壁厚都提高了能量吸收性能。根据超折叠单元理论建立的理论模型准确地预测了平均破碎力（Fmean），并通过实验和数值结果进行了验证。这些发现证实了TAHT优越的能量吸收能力，为轻量化和高强度超材料的设计提供了新的见解。

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引用次数: 0

A multi-well energy landscape strategy of the rubber-like polymers undergoing intermolecular interactions for exploring rubber elasticity 基于分子间相互作用的类橡胶聚合物多井能量景观策略研究橡胶弹性

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-12-04 DOI: 10.1016/j.ijengsci.2025.104438

Ziyu Xing , Xiaodong Wang , Xiaoling Hu , Rongguo Zhao

Rubber elasticity is considered the cornerstone of understanding the conformation of rubbery polymer chains. This paper presents a multi-well energy landscape strategy to explore the rubber elasticity of rubber-like polymers that undergo intermolecular interactions. Based on the tube model and Langevin statistics, the proposed constitutive formulation explicitly incorporates the intrinsic heterogeneity of cross-linked networks and topological entanglements, while simultaneously accounting for the coupling effects of intermolecular interactions. The model postulates that intermolecular interactions manifest as localized constraints, which amplify the inherent heterogeneity by inducing variations in tube diameter and effective chain length, thereby modulating the entropic contributions to the free energy density. Furthermore, the framework captures the emergence of a multi-well energy landscape arising from the intermolecular interaction-induced heterogeneity in conformations of polymer chains. The model was validated against comprehensive experimental datasets of rubber-like polymers, including inflation of balloons, uniaxial tension/compression, pure shear deformation, and equi-biaxial tension. The results demonstrate that the proposed model can accurately predict the mechanical behavior of rubber-like polymers across various deformation modes and conditions. Compared to other models like the Anssari-Benam model, Yeoh model, and Pucci-Saccomnadi model, the proposed model shows advantages in capturing the complex mechanical responses of rubbers, particularly in multi-axial stress states. The study enhances the understanding of rubber elasticity and provides a robust tool for predicting the mechanical behavior of soft rubbery materials.

橡胶弹性被认为是理解橡胶聚合物链构象的基石。本文提出了一种多井能量景观策略，以探索发生分子间相互作用的类橡胶聚合物的橡胶弹性。基于管模型和朗之万统计，提出的本构公式明确地考虑了交联网络和拓扑纠缠的内在异质性，同时考虑了分子间相互作用的耦合效应。该模型假设分子间相互作用表现为局部约束，通过诱导管径和有效链长度的变化放大了固有的非均质性，从而调节了自由能密度的熵贡献。此外，该框架捕获了由分子间相互作用诱导的聚合物链构象非均质性引起的多井能量景观的出现。该模型在类橡胶聚合物的综合实验数据集上进行了验证，包括气球膨胀、单轴拉伸/压缩、纯剪切变形和等双轴拉伸。结果表明，该模型能够准确预测类橡胶聚合物在各种变形模式和条件下的力学行为。与其他模型如Anssari-Benam模型、Yeoh模型和Pucci-Saccomnadi模型相比，该模型在捕获橡胶的复杂力学响应方面具有优势，特别是在多轴应力状态下。该研究提高了对橡胶弹性的认识，为预测软质橡胶材料的力学行为提供了有力的工具。

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引用次数: 0

Mechanics of re-damage and re-healing in continuum damage and healing mechanics of materials 材料连续损伤中的再损伤与再修复力学

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-11-28 DOI: 10.1016/j.ijengsci.2025.104432

George Z. Voyiadjis, Peter I. Kattan

This work presents a unified thermodynamic framework that incorporates primary and secondary damage and healing variables, enabling the modeling of re-damage and re-healing under cyclic loading. The damage is characterized by the reduction in stiffness of the material and other material properties. A new secondary damage variable is introduced that may account for re-damage of the healed material. This addresses damage and healing after the initial or subsequent damage/healing occurred. It is a consequence of reloading the material or structure. This is then followed by the introduction of a new secondary healing variable that may account for the re-healing of the damaged material. This process may continue indefinitely in a continuous manner. These ideas and new concepts are explored here based on sound mathematical and thermodynamic treatment. It should be noted that the idea of re-damage of the healed material has appeared previously in the literature, but here it is afforded a consistent and systematic mathematical treatment. This allows for the proper physical interpretation that accounts for damage/healing occurring in subsequent unloading/reloading sequences. Both the scalar and tensorial formulations are presented. Finally, as an example, the problem of plane stress, plane damage, and plane healing is illustrated in detail. Two application examples from the aerospace industry are illustrated. Comparisons with experimental observations with two different materials are also shown. In the two materials investigated, plastic deformation is involved and is accounted for in the model as well as in the thermodynamics section.

这项工作提出了一个统一的热力学框架，其中包括初级和次级损伤和愈合变量，使循环加载下的再损伤和再修复建模成为可能。损伤的特征是材料的刚度和其他材料性能的降低。引入了一个新的二次损伤变量，可以解释愈合材料的再损伤。这涉及初始或后续伤害/治疗发生后的伤害和治疗。它是重新加载材料或结构的结果。然后引入一个新的次级愈合变量，可以解释受损材料的再愈合。这个过程可能以连续的方式无限期地继续下去。这些思想和新概念是在完善的数学和热力学处理的基础上探讨的。应该指出的是，愈合材料的再损伤的想法已经出现在以前的文献中，但这里提供了一个一致的和系统的数学处理。这允许适当的物理解释，说明在随后的卸载/重新加载序列中发生的伤害/治疗。给出了标量公式和张量公式。最后，作为一个例子，详细说明了平面应力、平面损伤和平面愈合问题。给出了航空航天工业的两个应用实例。并与两种不同材料的实验结果进行了比较。在研究的两种材料中，塑性变形被涉及，并在模型和热力学部分中被考虑。

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引用次数: 0

Acoustofluidic polymer micropillars for efficient micromixing and nanoparticle synthesis 用于高效微混合和纳米颗粒合成的声流控聚合物微柱

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-11-22 DOI: 10.1016/j.ijengsci.2025.104430

Abdulrahman Agha , Anas Alazzam , Eiyad Abu-Nada

Acoustofluidics has emerged as a promising field for particle manipulation and micromixing in lab-on-a-chip technologies. Among the various materials utilized in microfluidics, cyclic olefin copolymer (COC) is increasingly employed due to its excellent physical and chemical properties, low cost, and versatile fabrication methods. In this work, we demonstrated a unique approach to acoustic mixing by integrating polydimethylsiloxane (PDMS) and COC microchannels with oscillating COC micropillars. These micropillars, fabricated via a COC-hydrocarbon solvent swelling microfabrication process, protrude from the COC surface and oscillate out-of-plane when actuated by a piezoelectric transducer, generating vortices that enhance mixing. A 3D numerical model was employed to optimize micropillar geometry through a parametric study of diameter and height. Both simulation and experimental results showed that smaller diameters and greater heights enhance mixing performance, with the 20 µm diameter and height configuration outperforming other designs. This geometry achieved effective mixing up to 900 µL/h (15 µL/min) and maintained observable effects even at 6000 µL/h (100 µL/min). The numerical model was validated against experimental data, with <5 % error. Finally, the PDMS-COC micropillar microchannel was successfully employed for the synthesis of gold nanoparticles (AuNPs) using acoustically assisted mixing. The innovative system enabled the synthesis of high-concentration AuNPs with average sizes ranging from 15 to 35 nm and polydispersity index (PDI) <0.36. These results demonstrate the effectiveness of the micropillar-based microchannel for nanoparticle synthesis and highlight its potential for broader applications in lab-on-a-chip mixing technologies.

声流体学已经成为芯片实验室技术中粒子操纵和微混合的一个有前途的领域。在微流体中应用的各种材料中，环烯烃共聚物（COC）因其优异的物理化学性能、低廉的成本和多种制备方法而得到越来越多的应用。在这项工作中，我们展示了一种独特的声学混合方法，通过将聚二甲基硅氧烷（PDMS）和COC微通道与振荡COC微柱集成。这些微柱通过COC-碳氢化合物溶剂膨胀微加工工艺制成，在压电传感器的驱动下，从COC表面伸出，并在平面外振荡，产生涡流，增强混合。采用三维数值模型对微柱的直径和高度进行参数化研究，优化微柱的几何形状。仿真和实验结果均表明，直径和高度越小，混合性能越好，其中直径和高度为20 μ m的混合性能越好。这种几何结构实现了高达900 μ L/h （15 μ L/min）的有效混合，即使在6000 μ L/h （100 μ L/min）下也能保持可观察的效果。数值模型与实验数据进行了验证，误差为<； 5%。最后，将PDMS-COC微柱微通道成功用于声辅助混合合成金纳米颗粒（AuNPs）。该创新体系能够合成平均尺寸为15 ~ 35 nm的高浓度aunp，其多分散性指数（PDI）为0.36。这些结果证明了基于微柱的微通道在纳米颗粒合成中的有效性，并突出了其在芯片上实验室混合技术中更广泛应用的潜力。

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引用次数: 0

Predicting thrombus formation and growth in patient-specific models of aortic dissection: a multiphase approach based on porous media theory 预测主动脉夹层患者特异性模型血栓形成和生长：基于多孔介质理论的多阶段方法

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-11-21 DOI: 10.1016/j.ijengsci.2025.104423

Xiaofan Li , Xuehuan Zhang , Yuan Xue , Xuyang Zhang , Linyu Qin , Xiaoyu Yang , Jiang Xiong , Chiyu Xie , Shuaitong Zhang , Duanduan Chen

Aortic dissection represents a life-threatening vascular emergency with significant morbidity and mortality. Traditional models for predicting aortic thrombosis often depend on complex biochemical parameters, lack clearly defined phase interfaces, and require extensive computational time. Existing porous media algorithms are limited in their ability to accurately capture the dynamic processes of thrombus growth and hemodynamic changes, largely due to imprecise physical formulations. This study presents a novel multiphase porous media approach for predicting thrombus formation in various types of aortic dissection, which is innovatively applied to a large number of patient-specific aortic models. By incorporating an extended Darcy–Brinkman–Stokes (DBS) equation to explicitly model the interaction between solid and liquid phases, and introducing a novel porosity equation to simplify platelet transport and deposition, the method achieves substantial improvements in computational efficiency. Applied to computed tomography-based reconstructions, the algorithm demonstrated high predictive accuracy, achieving a correlation coefficient of 0.97 between predicted and actual thrombus volumes in 12 cases of partial false lumen and 9 cases of complete false lumen. The average prediction time per case was reduced to 40 min, representing a 70 % improvement in efficiency. Furthermore, the study investigated mechanical factors underlying enhanced postoperative recovery in patients with complete false lumens and introduced an acceleration factor to align simulation time with actual thrombus progression. By integrating a mechanically grounded thrombus evolution model, this method enables rapid, dynamic predictions, thereby supporting timely clinical decision-making and facilitating the development of personalized treatment strategies for patients with aortic dissection.

主动脉夹层是危及生命的血管急症，具有显著的发病率和死亡率。传统的主动脉血栓预测模型往往依赖于复杂的生化参数，缺乏明确定义的相界面，并且需要大量的计算时间。现有的多孔介质算法在准确捕捉血栓生长和血流动力学变化的动态过程方面受到限制，这主要是由于不精确的物理配方。本研究提出了一种新的多相多孔介质预测各种类型主动脉夹层血栓形成的方法，并创新地应用于大量患者特异性主动脉模型。该方法采用扩展的DBS （Darcy-Brinkman-Stokes）方程来明确地模拟固液相之间的相互作用，并引入新的孔隙度方程来简化血小板的运输和沉积，从而大大提高了计算效率。将该算法应用于基于计算机断层成像的重建中，预测精度较高，在12例部分假腔和9例完全假腔中，预测血栓体积与实际血栓体积的相关系数为0.97。每个病例的平均预测时间减少到40分钟，效率提高了70%。此外，该研究还研究了完全假腔患者术后恢复增强的机械因素，并引入了一个加速因素，使模拟时间与实际血栓进展保持一致。通过集成基于机械的血栓演化模型，该方法可以实现快速、动态的预测，从而支持及时的临床决策，促进主动脉夹层患者个性化治疗策略的制定。

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引用次数: 0

Spatial decay in mixtures of heat conductive rigid solids as an evolutive problem 作为演化问题的导热刚性固体混合物的空间衰减

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-11-20 DOI: 10.1016/j.ijengsci.2025.104422

J.R. Fernández , R. Quintanilla

The objective of this article is to study the spatial behavior of solutions in the case of heat conduction in a static cylinder for a mixture of rigid solids. Although this question is an ill-posed problem in the Hadamard sense, since there is no uniqueness of solutions nor continuous dependence on initial data, we focus on the study of decaying solutions. When we restrict to this class of functions, we obtain a well-posed problem. We will show that we can see the solutions through an analytic semigroup structure, for which the long variable acts as the evolution variable. Therefore, we can apply the properties of these semigroups. Finally, we also consider the case in which a certain type of supply terms is introduced, and the solutions are obtained with the help of semigroups theory. A few comments for alternative boundary conditions are also considered.

本文的目的是研究在刚性固体混合物的静态圆柱体中热传导情况下溶液的空间行为。虽然这个问题是Hadamard意义上的不适定问题，但由于它不存在解的唯一性，也不存在对初始数据的连续依赖，所以我们着重研究了衰减解。当我们限制这类函数时，我们得到一个适定问题。我们将证明我们可以通过解析半群结构看到解，其中长变量作为演化变量。因此，我们可以应用这些半群的性质。最后，我们还考虑了引入某一类供给条件的情况，并利用半群理论得到了其解。还考虑了对可选边界条件的一些评论。

引用次数: 0

The effect of wall thickness on the scattering of electromagnetic waves by open-ended rectangular cavities 壁厚对开放式矩形空腔电磁波散射的影响

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-11-20 DOI: 10.1016/j.ijengsci.2025.104419

Oğuzhan Demiryürek, Filiz Bi̇rbi̇r Ünal

The scattering of electromagnetic waves by an infinitely long rectangular cavity with finite wall thickness is rigorously analyzed for E-polarization by developing a modified Wiener–Hopf formulation that extends the classical procedure to non-canonical geometries. The finite wall thickness introduces additional waveguide sections and coupling interfaces, which break the half-plane geometry underlying the standard Wiener–Hopf procedure. To overcome this challenge, the problem is reformulated as a system of modified Wiener–Hopf equations of the third kind (MWHE-3) by integrating the mode-matching technique within the cavity and wall regions. The resulting formulation accommodates the multiple reflections and modal interactions introduced by thick walls while preserving the mathematical rigor and edge condition satisfaction characteristic of the Wiener–Hopf approach. The solution involves coupled infinite systems of linear algebraic equations, efficiently solved through truncation. The scattered field is then evaluated using the inverse Fourier transform and saddle-point techniques. Numerical examples demonstrate the influence of wall thickness on the diffraction characteristics.

通过建立一个改进的Wiener-Hopf公式，将经典过程扩展到非正则几何，对具有有限壁厚的无限长矩形腔的电磁波散射进行了严格的e极化分析。有限的壁厚引入了额外的波导部分和耦合接口，这打破了标准Wiener-Hopf程序的半平面几何结构。为了克服这一挑战，该问题被重新表述为一个修正的第三类Wiener-Hopf方程（MWHE-3）系统，通过在腔和壁区域内集成模式匹配技术。所得到的公式适应了厚壁引入的多重反射和模态相互作用，同时保留了维纳-霍普夫方法的数学严谨性和边缘条件满足特征。该解决方案涉及线性代数方程的耦合无限系统，通过截断有效地解决。然后使用傅里叶反变换和鞍点技术评估散射场。数值算例验证了壁厚对衍射特性的影响。

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引用次数: 0