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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
A semi-analytical model for effective conductivity of parallelogram-periodic fibrous composites with circular inclusions 含圆形夹杂物的平行四边形周期纤维复合材料有效导电性的半解析模型
IF 5.7 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2025-12-24 DOI: 10.1016/j.ijengsci.2025.104448
Raúl Guinovart-Díaz , Julián Bravo-Castillero , Manuel E. Cruz , Leslie D. Pérez-Fernández , Federico J. Sabina , David Guinovart
A two-dimensional, three-phase conducting composite with coated circular inclusions, periodically distributed in a parallelogram lattice, is analyzed. The phases are isotropic, with perfect contact at interfaces. The effective behavior is characterized by combining asymptotic homogenization with analytic function theory. Local problems are solved using a series expansion involving Weierstrass elliptic functions and their derivatives, with undetermined complex coefficients. Effective coefficients follow from the residue of this solution, expressed via products of infinite-dimensional vectors and matrices. Unified analytical formulas valid for any parallelogram periodic cell are derived through systematic truncation. Explicit expressions are provided for two-phase fibrous composites with perfect or imperfect interfacial contact. The results allow determination of the critical normalized interfacial thickness and conductivity enhancement in composites with annular cross sections. Gains in the effective conductivity tensor, linked to thermal barriers and parallelogram periodicity, are examined through reiterated homogenization. The model is validated through numerical examples and by comparison to available bounds showing excellent agreement up to percolation. The programs for computation are provided in an open-access repository.
研究了一种具有周期性分布于平行四边形晶格中的包覆圆形夹杂物的二维三相导电复合材料。相是各向同性的,在界面处有完美的接触。将渐近均匀化与解析函数理论相结合,对其有效行为进行了表征。局部问题的求解采用了包含复系数待定的weerstrass椭圆函数及其导数的级数展开式。有效系数来源于这个解的余数,通过无穷维向量和矩阵的乘积来表示。通过系统截断,导出了适用于任何平行四边形周期单元的统一解析公式。给出了界面接触完全或不完全的两相纤维复合材料的显式表达式。结果允许确定临界归一化界面厚度和电导率增强的复合材料与环形截面。有效电导率张量的增益,与热障和平行四边形周期性相联系,通过重复均质化进行检查。通过数值算例和与现有边界的比较,验证了该模型在渗流问题上的一致性。计算程序在一个开放存取的存储库中提供。
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引用次数: 0
Coupled-translation-rotation mechanics model and design for broadband wave energy conversion in anisotropic multiphase metamaterials 各向异性多相超材料宽带波能转换耦合-平移-旋转力学模型与设计
IF 5.7 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2025-12-19 DOI: 10.1016/j.ijengsci.2025.104450
Yuxuan Ma, Zhiwen Ren, Hao-Wen Dong
Elastic metamaterials typically display anisotropic scattering behavior which mainly stems from high-order modes linked to shear and rotation deformations, thus complicating the characterization of the scattering behavior. However, most existing mass-spring models can only describe the coupled in-plane motions of longitudinal and transverse waves, which naturally ignores the essential rotations. Considering the pure translation and coupled-translation-rotation motions, this study proposes two spring-interconnected mass-in-mass models with rotational symmetry, featuring 2-degree-of-freedom (2-DOF) and 3-DOF anisotropic configurations respectively. For an incident longitudinal wave, the scattered transverse wave energy in these models is theoretically demonstrated at a specific rotation angle of spring. The established scattered elastic wave energy theory associating the dynamic response with structural parameters indicates that the higher scattering energy conversion of metamaterials can be achieved if two polarization components of translation and rotation are considered simultaneously. Comparing the scattering energy conversion capabilities of uni-layer and bi-layer models reveals that the bi-layer 3-DOF anisotropic model promotes the higher-efficiency low-frequency scattering energy conversion by reducing the dynamic effective stiffness. Variations in the scattering conversion coefficient with mass and aspect ratio clarify that lightweight components and soft springs are beneficial for efficient scattering energy conversion over a low-frequency broadband range. Furthermore, by investigating damping on energy distribution of 3-DOF anisotropic model, the underlying mechanism for capturing longitudinal wave energy is identified as integrating low-frequency scattering for energy conversion with high-frequency mechanisms for energy dissipation. Consequently, the 3-DOF anisotropic model achieves reflection-free wave energy across a broadband frequency range with a small amount of loss. To validate the proposed theory, model, and the underlying mechanism, anisotropic multiphase metamaterials are inversely designed to simultaneously deliver broadband wave-energy dissipation and high load-bearing capacity. Scattering characteristic analysis indicates that the metamaterials exhibit strong anisotropy and broadband energy conversion capability, with further validation by simulations and experiments. The present study establishes a foundation for high-load-bearing metamaterial-based elastic-wave absorbers and isolators.
弹性超材料通常表现出各向异性散射行为,这种散射行为主要源于与剪切和旋转变形相关的高阶模式,从而使散射行为的表征复杂化。然而,大多数现有的质量弹簧模型只能描述纵波和横波的耦合面内运动,自然忽略了基本的旋转。考虑到纯平移运动和平移-旋转耦合运动,本文提出了两种具有旋转对称性的质量-质量-弹簧连接模型,分别具有2自由度和3自由度各向异性构型。对于入射纵波,这些模型中的散射横波能量在弹簧的特定旋转角度下得到了理论上的证明。建立的将动力响应与结构参数联系起来的散射弹性波能理论表明,如果同时考虑平移和旋转两个极化分量,可以实现更高的超材料散射能量转换。通过对单层和双层模型散射能量转换能力的比较,发现双层三自由度各向异性模型通过降低动态有效刚度促进了低频散射能量转换效率的提高。散射转换系数随质量和长径比的变化表明,轻量化元件和软弹簧有利于低频宽带范围内的有效散射能量转换。此外,通过研究3-DOF各向异性模型能量分布的阻尼,确定了纵波能量捕获的基本机制是将低频散射与高频能量耗散相结合。因此,三自由度各向异性模型在宽带频率范围内以少量损耗实现无反射波能量。为了验证所提出的理论、模型和潜在的机制,各向异性多相超材料被反向设计,同时提供宽带波能耗散和高承载能力。散射特性分析表明,该材料具有较强的各向异性和宽带能量转换能力,并通过模拟和实验得到了进一步的验证。本研究为高承载超材料弹性波吸波和隔波器的研究奠定了基础。
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引用次数: 0
Three-phase particle reinforced composites: Effective fields and the Mori–Tanaka method 三相颗粒增强复合材料:有效场和Mori-Tanaka方法
IF 5.7 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2025-12-16 DOI: 10.1016/j.ijengsci.2025.104449
Helmut J. Böhm
The Mori–Tanaka method is a micromechanical effective-field model that approximates the local fields acting on any inhomogeneity phase by the corresponding matrix field. This assumption is tested in a case study using finite-element-based periodic homogenization for numerically evaluating the effective-field inhomogeneity concentration tensors of the reinforcement phases for a set of simple three-phase particle reinforced composites. The numerical predictions show a clear dependence of the mechanical and thermal effective fields on the material properties of the particulate phases. Even though this behavior deviates from the assumption underlying the Mori–Tanaka method, the latter provides useful approximations for the macroscopic stiffnesses and conductivities for the set of composites covered by the study.
Mori-Tanaka方法是一种微力学有效场模型,它通过相应的矩阵场来近似作用于任何非均匀相的局部场。本文采用基于有限元的周期均匀化方法,对一组简单三相颗粒增强复合材料增强相的有效场非均匀性浓度张量进行了数值计算,验证了这一假设。数值预测表明,颗粒相的材料性能明显依赖于力学和热效应场。尽管这种行为偏离了Mori-Tanaka方法的假设,但后者为研究涵盖的一组复合材料的宏观刚度和电导率提供了有用的近似。
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引用次数: 0
On wave dispersion in nonlocal simplified strain gradient elasticity 非局部简化应变梯度弹性中的波频散
IF 5.7 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2025-12-13 DOI: 10.1016/j.ijengsci.2025.104431
Markus Lazar, Eleni Agiasofitou
In this work, wave dispersion is investigated within the framework of nonlocal simplified strain gradient elasticity theory. This theory represents a unification of Eringen’s nonlocal elasticity theory of Helmholtz type and the simplified first strain gradient elasticity theory. It incorporates two characteristic length scale parameters, namely the characteristic length N of nonlocal elasticity of Helmholtz type and the characteristic length G of simplified first strain gradient elasticity. The dispersion relations as well as the phase and group velocities for longitudinal and transverse acoustic waves are analytically determined. A qualitative analysis of the phase and group velocities is also presented. It is found that nonlocal simplified strain gradient elasticity can exhibit normal or anomalous dispersion depending only on the values of the two characteristic lengths. Normal dispersion occurs when N2>G2, whereas anomalous dispersion arises when G2>N2. It is shown that in the case of normal dispersion, nonlocal simplified strain gradient elasticity yields physically realistic dispersive wave propagation in agreement with lattice dynamics. Moreover, a match between the obtained dispersion relations and those of the Born-von Kármán lattice model is established, leading to an important relation between the two characteristic length scales.
本文在非局部简化应变梯度弹性理论的框架下研究了波的色散。该理论是Eringen的Helmholtz型非局部弹性理论与简化的第一应变梯度弹性理论的统一。它包含两个特征长度尺度参数,即亥姆霍兹型非局部弹性的特征长度N和简化的一阶应变梯度弹性的特征长度G。用解析法确定了纵波和横波的频散关系以及相速度和群速度。本文还对相速度和群速度进行了定性分析。发现非局部简化应变梯度弹性仅依赖于这两个特征长度的值就可以表现出正常或异常的色散。在N2>; N2时出现反常色散,而在N2>; N2时出现反常色散。结果表明,在正常色散的情况下,非局部简化应变梯度弹性产生符合晶格动力学的物理真实色散波传播。此外,将得到的色散关系与Born-von Kármán晶格模型的色散关系进行了匹配,得到了两个特征长度尺度之间的重要关系。
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引用次数: 0
Multiscale bending model of graphene based on asymmetric elasticity: The role of microscopic bond rotation in macroscopic deformation 基于非对称弹性的石墨烯多尺度弯曲模型:微观键旋转在宏观变形中的作用
IF 5.7 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2025-12-13 DOI: 10.1016/j.ijengsci.2025.104434
Yekai Zhou , Xinghua Shi , Yin Zhang
Classical continuum mechanics models fail to capture some critical nanoscale deformation mechanisms, leading to significant deviations/errors in predicting the bending stiffness of two-dimensional (2D) materials. To address this, the model based on the asymmetric elasticity is developed to describe the micro-deformation of the bond rotation as well as the macroscopic bending deformation. The asymmetric elasticity originates from the imbalance between the transverse shear stress and interlayer tractions. The torque generated thereby is balanced by the bending and twisting of the bond. For the hexagonal system, a strain energy function which incorporates asymmetric tensors is derived from cyclic polynomials. By using the Reissner’s mixed variational theorem (RMVT), the Reissner plate model within the framework of asymmetric elasticity is developed. Additional parameters, which correlate with the asymmetric elasticity, are introduced compared with the classical plate theory. Although numerous continuum mechanics models are developed to describe the deformation of these hierarchical materials, the experimental validation of the model with the correspondence between the microscopic deformation mechanisms and the macroscopic continuum deformation mechanisms is quite few. The asymmetric parameters, which are the unknowns in the previous studies, are numerically extracted by the experimental data of the blister test. The governing equations are numerically solved and the comparison with the experiments demonstrates the capability of the model to accurately predict the bending behaviors of 2D materials. A multiscale asymmetric elasticity model is developed and it bridges the atomic-scale deformation mechanisms with the macroscopic bending behavior in 2D materials, which provides an insight in the mechanical modeling of 2D materials.
经典的连续介质力学模型未能捕捉到一些关键的纳米尺度变形机制,导致在预测二维(2D)材料的弯曲刚度时存在显著偏差/误差。为了解决这一问题,建立了基于非对称弹性的模型来描述键旋转的微观变形和宏观弯曲变形。不对称弹性源于横向剪应力与层间牵引力之间的不平衡。由此产生的扭矩由键的弯曲和扭转来平衡。对于六边形系统,利用循环多项式导出了包含非对称张量的应变能函数。利用Reissner混合变分定理(RMVT),建立了非对称弹性框架下的Reissner板模型。与经典板理论相比,引入了与非对称弹性有关的附加参数。虽然已经建立了许多连续介质力学模型来描述这些分层材料的变形,但对微观变形机制与宏观连续介质变形机制之间对应关系的模型进行实验验证的却很少。利用水疱试验的实验数据,对以往研究中未知的非对称参数进行了数值提取。对控制方程进行了数值求解,并与实验结果进行了比较,验证了该模型能够准确预测二维材料的弯曲行为。建立了一种多尺度非对称弹性模型,它将二维材料的原子尺度变形机制与宏观弯曲行为联系起来,为二维材料的力学建模提供了新的思路。
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引用次数: 0
On the use of effective mass in modeling undamped mass-in-mass metamaterials 有效质量在无阻尼质量中超材料建模中的应用
IF 5.7 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2025-12-10 DOI: 10.1016/j.ijengsci.2025.104447
Raffaele Capuano , Walter Lacarbonara , Muhammad R. Hajj
The theoretical foundations of the effective mass concept in undamped mass-in-mass metamaterials are revisited to reassess its validity and physical interpretation. Within a dynamical systems framework, analytical derivations reveal that the effective mass is not an intrinsic property but a dynamic quantity linking the motion of the internal mass to the observable response of the primary mass under specific initial conditions. An infinite family of periodic orbits is identified using Poincaré maps, each characterized by an identical initial potential energy, elucidating the mathematical source of ambiguity in defining a unique effective mass. The analysis is extended to a discrete lattice of internal resonators, where a single periodic solution satisfies the periodicity constraints, confirming that the effective mass concept holds only under specific dynamic conditions.
本文重新审视了无阻尼质量中有效质量概念的理论基础,以重新评估其有效性和物理解释。在动力系统框架内,解析推导表明,有效质量不是一个内在性质,而是一个动态量,将内部质量的运动与特定初始条件下主质量的可观测响应联系起来。使用庞加莱图确定了无限的周期轨道族,每个轨道都具有相同的初始势能,阐明了定义唯一有效质量时模糊的数学来源。将分析扩展到内部谐振器的离散晶格,其中单个周期解满足周期性约束,确认有效质量概念仅在特定的动态条件下成立。
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引用次数: 0
Effects of hematocrit levels on hemodynamics and atherosclerosis risk in the left main coronary artery: a comparative computational mechanobiological study 红细胞压积水平对左冠状动脉主干血流动力学和动脉粥样硬化风险的影响:一项比较计算力学生物学研究
IF 5.7 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2025-12-08 DOI: 10.1016/j.ijengsci.2025.104446
Seyedmajid Hosseini, Mohammadhossein Abdolmohammadi, Bahar Firoozabadi
Coronary artery disease is the leading cause of cardiovascular mortality worldwide, yet the role of altered hematocrit (Hct) in atherosclerotic plaque formation remains unclear. This study uses a mechanobiological model to computationally investigate the effect of non-Newtonian blood behavior and varying Hct on plaque formation in a three-dimensional left main coronary artery. Hct levels of 25 % (low), 45 % (normal), and 65 % (high) are investigated. The Navier–Stokes and Darcy equations are solved to model fluid flow. Coupled convection–diffusion–reaction equations for low-density lipoprotein (LDL), oxidized LDL, monocytes, macrophages, and foam cells (FC) are solved to simulate a 10-year inflammatory evolution within the arterial wall. The results reveal that as Hct increases in the non-Newtonian model, peak FC concentration within the wall decreases. After 5 years, low Hct leads to a maximum concentration that is 1.6- and 4.7-fold higher than normal and high Hct concentration respectively, and 1.2-fold higher than that in the Newtonian model. Therefore, low Hct results in maximal plaque growth. Additionally, low Hct expands the areas of high FC concentration, thereby increasing plaque burden. Moreover, in the non-Newtonian model, the ratio of peak FC concentration at 10 years to that at 5 years rises with Hct. High Hct shows a ratio that is 1.17- and 1.43-fold greater than normal and low Hct, respectively, and 1.24-fold higher than that in the Newtonian model. Therefore, high Hct accelerates plaque formation during the second half of the 10-year inflammatory process. In addition, with increasing Hct, regions of high FC concentration in the left anterior descending artery (LAD) shift from the myocardial side to the carina. These findings deepen our understanding of atherosclerosis.
冠状动脉疾病是全球心血管疾病死亡的主要原因,然而红细胞压积(Hct)改变在动脉粥样硬化斑块形成中的作用尚不清楚。本研究使用机械生物学模型来计算研究非牛顿血液行为和不同Hct对三维左冠状动脉主动脉斑块形成的影响。Hct水平分别为25%(低)、45%(正常)和65%(高)。求解了Navier-Stokes方程和Darcy方程来模拟流体的流动。通过求解低密度脂蛋白(LDL)、氧化LDL、单核细胞、巨噬细胞和泡沫细胞(FC)的耦合对流-扩散-反应方程,模拟动脉壁内10年的炎症演变。结果表明,在非牛顿模型中,随着Hct的增加,壁内FC峰浓度降低。5年后,低Hct导致的最大浓度分别是正常Hct和高Hct的1.6倍和4.7倍,比牛顿模型高1.2倍。因此,低Hct导致最大的斑块生长。此外,低Hct扩大了高FC浓度的区域,从而增加了斑块负担。此外,在非牛顿模型中,随着Hct的增加,10年的FC峰值浓度与5年的FC峰值浓度之比增大。高Hct比正常Hct和低Hct分别高1.17倍和1.43倍,比牛顿模型高1.24倍。因此,在10年炎症过程的后半段,高Hct加速了斑块的形成。此外,随着Hct的增加,左前降支(LAD)的高FC浓度区域从心肌侧转移到隆突。这些发现加深了我们对动脉粥样硬化的理解。
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引用次数: 0
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 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
期刊
International Journal of Engineering Science
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