International Journal of Mechanical Sciences最新文献_第3页

Thermohydrodynamic analysis of liquid metal journal bearings in CT tubes CT管液态金属滑动轴承的热流体力学分析

IF 9.4 1区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Mechanical Sciences

Pub Date : 2026-03-15 Epub Date: 2026-02-07 DOI: 10.1016/j.ijmecsci.2026.111365

Yujie Wang, Shuai Huang, JiongGuang Wei, Jian Li, Wenjun Li, Kai Feng

Liquid metal journal bearings (LMJBs), employing liquid metal (LM) as a highly conductive and thermally stable lubricant, are increasingly used in CT tubes to withstand high temperatures and dissipate heat. This work establishes a three-dimensional thermohydrodynamic model of the LMJB, incorporating its distinctive features, including herringbone grooves, extreme operating environment, and thermal input from the CT system. Specifically, it accounts for the groove pumping effect, fluid–solid heat transfer interface, vacuum thermal radiation, and high-temperature input at the end-face. Boundary conditions are assigned according to the local thermal characteristics. An experimental rig was built to validate the model by comparing temperatures at different rotational speeds. The temperature distribution was analyzed, and the effects of bearing parameters and operating conditions were assessed. The results show that the grooves induce fluctuations in the temperature. Groove geometry and bearing structural parameters significantly influence the peak temperature. High-conductivity LM or enhanced convective heat transfer effectively lowers the temperature, with the bush as the primary heat dissipation path. Moreover, the heat input from the end-faces has a decisive influence on the bearing temperature. These findings provide guidance for LMJB design and cooling strategies to ensure reliable operation in high performance CT applications.

液态金属滑动轴承（lmjb）采用液态金属（LM）作为高导电性和热稳定性的润滑剂，越来越多地用于CT管，以承受高温和散热。本文建立了LMJB的三维热流体动力学模型，并结合了其独特的特征，包括人字形凹槽、极端工作环境和CT系统的热输入。具体来说，它考虑了沟槽泵送效应、流固传热界面、真空热辐射和端面高温输入。边界条件是根据局部热特性指定的。建立了一个实验平台，通过比较不同转速下的温度来验证模型。分析了温度分布，评估了轴承参数和运行条件的影响。结果表明，沟槽会引起温度的波动。沟槽几何形状和轴承结构参数对峰值温度有显著影响。高导热LM或增强对流换热有效降低温度，以衬套为主要散热途径。此外，从端面输入的热量对轴承温度有决定性的影响。这些发现为LMJB的设计和冷却策略提供了指导，以确保在高性能CT应用中可靠运行。

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引用次数: 0

Predictive model for cutting forces in ultrasonic-assisted friction drilling of Ti-6Al-4V Ti-6Al-4V超声辅助摩擦钻削切削力预测模型

IF 9.4 1区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Mechanical Sciences

Pub Date : 2026-03-15 Epub Date: 2026-02-11 DOI: 10.1016/j.ijmecsci.2026.111385

Kechuang Zhang, Xian Wu, Shaolong Lin, Yong Zhang, Jianyun Shen, Fuyin Huang

The precision machining of titanium alloy thin-walled components presents significant challenges in aerospace manufacturing due to intricate cutting force variations during friction drilling machining. To address these challenges, this study proposes and comprehensively investigates an ultrasonic-assisted friction drilling (UAFD) process. An equivalent model of a friction drill bit during ultrasound-assisted friction drilling machining is established, simplifying its complex geometry for analytical tractability while preserving the essential physics of force generation. Based on the intermittent machining mechanism of UAFD machining and the friction drilling mechanism of Ti-6Al-4V, a seven-phase drilling cutting force model is innovatively developed to predict the evolution of cutting forces and torque throughout the entire process. Subsequently, the accuracy of the cutting force prediction of this model is verified by ultrasonic-assisted friction drilling machining experiments. Finally, experiments were conducted on conventional drilling and ultrasonic-assisted friction drilling. The results demonstrate that 28.00 kHz ultrasonic vibration reduces the axial force by 4.31% and the torque by 10.01% through the intermittent cutting mechanism and thermal softening effects, while the peak temperature increases by 1.27%. The accuracy of the model predictions was also validated by experimental results. This research provides theoretical foundations and practical guidelines for implementing energy-field assisted machining in aerospace titanium component manufacturing.

由于摩擦钻削过程中切削力的变化复杂，钛合金薄壁零件的精密加工在航空航天制造中面临着巨大的挑战。为了解决这些挑战，本研究提出并全面研究了超声辅助摩擦钻井（UAFD）工艺。建立了超声辅助摩擦钻加工过程中摩擦钻头的等效模型，简化了其复杂的几何形状，便于分析，同时保留了力产生的基本物理特性。基于UAFD加工的间歇加工机理和Ti-6Al-4V的摩擦钻削机理，创新性地建立了七相钻削切削力模型，预测了整个加工过程中切削力和扭矩的演变。随后，通过超声辅助摩擦钻削加工实验验证了该模型切削力预测的准确性。最后进行了常规钻井和超声辅助摩擦钻井试验。结果表明：28.00 kHz超声振动通过间歇切削机制和热软化效应使轴向力降低4.31%，扭矩降低10.01%，峰值温度升高1.27%；实验结果也验证了模型预测的准确性。该研究为实现航空钛部件的能量场辅助加工提供了理论基础和实践指导。

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引用次数: 0

High-velocity perforation of medium-entropy CrCoNi thin plates by spherical projectiles 球形弹丸高速击穿中熵CrCoNi薄板

IF 9.4 1区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Mechanical Sciences

Pub Date : 2026-03-15 Epub Date: 2026-02-06 DOI: 10.1016/j.ijmecsci.2026.111364

J.C. Cheng , T. Yang , L. Wang , J.Y. Hua , J.Y. Huang , L.X. He , W. Feng , Y. Cai , Q.Y. Wang , S.N. Luo

High-speed ballistic impacts are carried out with high-speed photography on 2-mm thick CrCoNi alloy plates with 5-mm spherical stainless steel projectiles within the impact velocity range of 514

-

1436 m s⁻¹. Post-impact samples are characterized by optical imaging, microhardness, electron backscatter diffraction and transmission electron microscopy. With increasing impact velocity, bulging, complete plugging and fragmentation occur sequentially. The ballistic limit velocity for the investigated projectile–target combination is 530 m s⁻¹, significantly higher than that of CrMnFeCoNi plate (495 m s⁻¹). The area of the crater/bullet hole exhibits a linear relationship with projectile kinetic energy loss. Dislocations, stacking faults, Lomer–Cottrell locks, deformation bands and various twin variants, contribute to enhanced strain-hardening capacity and penetration resistance. The bending of the target plate induced by low-velocity impact leads to additional plastic deformation and higher microhardness. Based on the Johnson–Cook constitutive model and the damage criterion, the finite element simulations effectively reproduce the ballistic impact experiments. Molecular dynamics simulations reproduce microstructural evolution at the atomic scale. The

(111) (11 \bar{2})

and

(11 \bar{1}) (112)

twin variants are simultaneously activated, because of the equivalence of the twin planes and twin directions of these two variants relative to the

(\bar{1} 10)

impact direction. This study presents the high-velocity perforation failure behavior of this medium-entropy alloy, elucidates the deformation and damage mechanisms, and provide valuable insights for its safety assessment and material/structural optimization design in extreme loading environments.

在514 ~ 1436 m s−1的冲击速度范围内，采用高速摄影技术对5mm球形不锈钢弹丸在2mm厚CrCoNi合金板上进行高速弹道冲击。通过光学成像、显微硬度、电子背散射衍射和透射电镜对撞击后样品进行表征。随着冲击速度的增加，胀形、完全堵塞和破碎依次发生。弹靶组合的弹道极限速度为530 m s−1，显著高于crmnnfeconi板的极限速度（495 m s−1）。弹坑/弹孔面积与弹丸动能损失呈线性关系。位错、层错、lomo - cottrell锁、变形带和各种孪晶变体有助于增强应变硬化能力和抗渗透能力。低速冲击引起的靶板弯曲导致额外的塑性变形和更高的显微硬度。基于Johnson-Cook本构模型和损伤准则的有限元模拟能够有效地再现弹道冲击实验。分子动力学模拟在原子尺度上再现微观结构的演变。111112和111112双生变体同时被激活，因为这两个变体的双生平面和双生方向相对于1’10撞击方向是等价的。本研究展示了这种中熵合金的高速穿孔破坏行为，阐明了其变形和损伤机制，为其在极端载荷环境下的安全性评估和材料/结构优化设计提供了有价值的见解。

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引用次数: 0

A pretraining-finetuning computational framework for material homogenization 材料均匀化的预训练-微调计算框架

IF 9.4 1区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Mechanical Sciences

Pub Date : 2026-03-15 Epub Date: 2026-02-12 DOI: 10.1016/j.ijmecsci.2026.111388

Yizheng Wang , Xiang Li , Ziming Yan , Shuaifeng Ma , Jinshuai Bai , Bokai Liu , Xiaoying Zhuang , Timon Rabczuk , Yinghua Liu

Homogenization is a fundamental tool for studying multiscale physical phenomena. Traditional numerical homogenization methods, heavily reliant on finite element analysis, demand significant computational resources, especially for complex geometries, materials, and high-resolution problems. To address these challenges, we propose PreFine-Homo, a novel numerical homogenization framework comprising two phases: pretraining and fine-tuning. In the pretraining phase, a Fourier Neural Operator (FNO) is trained on large datasets to learn the mapping from input geometries and material properties to displacement fields. In the fine-tuning phase, the pretrained predictions serve as initial solutions for iterative algorithms, drastically reducing the number of iterations needed for convergence. The pretraining phase of PreFine-Homo delivers homogenization results up to 1000 times faster than conventional methods, while the fine-tuning phase further enhances accuracy. Moreover, the fine-tuning phase grants PreFine-Homo improved generalization capabilities, enabling continuous learning and improvement as data availability increases. We validate PreFine-Homo by predicting the effective elastic tensor for 3D periodic materials, specifically Triply Periodic Minimal Surfaces (TPMS). The results demonstrate that PreFine-Homo achieves high precision, exceptional efficiency, robust learning capabilities, and strong extrapolation ability, establishing it as a powerful tool for multiscale homogenization tasks. The source code is publicly available at: https://github.com/yizheng-wang/HomoGenius.

均匀化是研究多尺度物理现象的基本工具。传统的数值均匀化方法严重依赖于有限元分析，需要大量的计算资源，特别是对于复杂的几何形状，材料和高分辨率问题。为了解决这些挑战，我们提出了PreFine-Homo，这是一个新的数值均匀化框架，包括两个阶段：预训练和微调。在预训练阶段，在大数据集上训练傅里叶神经算子（FNO）来学习从输入几何形状和材料属性到位移场的映射。在微调阶段，预训练的预测作为迭代算法的初始解决方案，大大减少收敛所需的迭代次数。PreFine-Homo的预训练阶段提供的均质结果比传统方法快1000倍，而微调阶段进一步提高了准确性。此外，微调阶段赋予PreFine-Homo改进的泛化能力，使其能够随着数据可用性的增加而持续学习和改进。我们通过预测三维周期材料，特别是三周期最小曲面（TPMS）的有效弹性张量来验证PreFine-Homo。结果表明，PreFine-Homo具有高精度、高效、稳健的学习能力和较强的外推能力，是解决多尺度均匀化问题的有力工具。源代码可以在：https://github.com/yizheng-wang/HomoGenius上公开获得。

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引用次数: 0

Stochastic modeling of short crack fracture in ceramics 陶瓷短裂纹断裂的随机建模

IF 9.4 1区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Mechanical Sciences

Pub Date : 2026-03-15 Epub Date: 2026-02-09 DOI: 10.1016/j.ijmecsci.2026.111370

Shinya Matsuda , Koichi Goda

A stochastic model is proposed to provide a unified description of the nonlinear relationship between fracture strength and crack length, alongside the associated scatter, in ceramics containing short cracks. Although linear elastic fracture mechanics (LEFM) successfully describes fracture in the long-crack regime, short cracks exhibit pronounced nonlinearity and significant scatter, which are not adequately captured by conventional deterministic models. The proposed framework formulates transitions between the discretized effective crack length states as a Markov process combined with a Weibull distribution of fracture strength. This framework characterizes both the nonlinear mean response and the associated scatter. Theoretical analysis reveals that the curvature of the nonlinear behavior in the short-crack regime is governed by the Weibull shape parameter, whereas the finite size of the process zone dictates the magnitude of the scatter without affecting the mean response. The model is validated against experimental data for four ceramic materials, demonstrating its ability to accurately reproduce both the nonlinear behavior and the associated variability. Since the model relies solely on independently measurable material properties—including Weibull parameters, fracture toughness, and the process-zone length—it offers a practical and physically transparent framework for the reliability assessment of ceramic components.

提出了一个随机模型，以提供一个统一的描述断裂强度和裂纹长度之间的非线性关系，以及相关的散射，在陶瓷含有短裂纹。虽然线性弹性断裂力学（LEFM）成功地描述了长裂纹状态下的断裂，但短裂纹表现出明显的非线性和显著的分散，这是传统确定性模型无法充分捕捉的。提出的框架将离散有效裂纹长度状态之间的转换表述为结合断裂强度威布尔分布的马尔可夫过程。该框架描述了非线性平均响应和相关的散射。理论分析表明，短裂纹状态下非线性行为的曲率由威布尔形状参数控制，而过程区的有限大小决定了散射的大小，而不影响平均响应。该模型通过四种陶瓷材料的实验数据进行了验证，证明了它能够准确地再现非线性行为和相关的可变性。由于该模型仅依赖于独立可测量的材料特性，包括威布尔参数、断裂韧性和工艺区长度，因此它为陶瓷部件的可靠性评估提供了一个实用且物理透明的框架。

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引用次数: 0

Strain Monitoring of confined interpenetrating conductive elastomers for isolation bearings 隔震轴承用密闭互穿导电弹性体的应变监测

IF 9.4 1区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Mechanical Sciences

Pub Date : 2026-03-15 Epub Date: 2026-02-10 DOI: 10.1016/j.ijmecsci.2026.111379

Bangwei Wan , Yong Yuan , Yang Yang , Rongxin Guo , Xiaotao Yu , Yong Yan

Conductive elastomer composites (CECMs) hold great promise for structural health monitoring (SHM) of large-scale infrastructure. However, their practical application is often hindered by limitations such as narrow sensing ranges, low sensitivity, and signal instability caused by shoulder-peak effects under large deformation. To overcome these challenges, this study presents a mechanism-guided material design strategy that leverages self-assembled conductive fillers and a confined, interpenetrating polyolefin/silicone rubber (PO/SR) interphase. Multi-walled carbon nanotubes (MWCNTs) functionalized with polyvinylpyrrolidone (PVP) are used to create well-dispersed conductive fillers (CP), while controlled blending of polyolefin (PO) and silicone rubber (SR) forms a compact and constrained interphase, enhancing interfacial coupling continuity and segmental confinement. At an optimized PO:SR ratio of 7:3 (CPP₇–CPS₃), the resulting conductive elastomer exhibits a low percolation threshold of 0.57 wt% and demonstrates a highly stable electromechanical response. Compared to conventional systems, CPP₇–CPS₃ reduces the hysteresis area by 76.71 %, completely suppresses shoulder-peak effects, and improves tensile strength and elongation at break by 81.39 % and 87.88 %, respectively. Additionally, the composite exhibits high strain sensitivity (GF = 352.29), a rapid response time of 329.62 ms, and an ultra-wide sensing range of 560.36 %. Experimental characterization and molecular dynamics simulations reveal that the confined interpenetrating interphase, combined with filler self-assembly, mitigates the mismatch between matrix viscoelastic relaxation and conductive network evolution, thereby preventing cyclic network reconstruction and stabilizing the electromechanical response. Real-time strain monitoring of seismic isolation bearings confirms stable, shoulder-free signal output even under large deformation. This work introduces a confined-interphase-driven design framework for developing robust, large-deformation strain sensors, advancing the long-term SHM of civil infrastructure.

导电弹性体复合材料（cecm）在大型基础设施结构健康监测（SHM）中具有广阔的应用前景。然而，它们的实际应用往往受到传感范围窄、灵敏度低以及大变形下肩峰效应引起的信号不稳定等限制。为了克服这些挑战，本研究提出了一种机制导向的材料设计策略，该策略利用自组装导电填料和受限、互穿的聚烯烃/硅橡胶（PO/SR）界面相。聚乙烯吡咯烷酮（PVP）功能化的多壁碳纳米管（MWCNTs）用于制造分散良好的导电填料（CP），而聚烯烃（PO）和硅橡胶（SR）的可控共混形成致密和受限的界面相，增强了界面耦合的连续性和节段约束。在优化的PO:SR比为7:3 （CPP7-CPS3）时，所得导电弹性体的渗透阈值较低，为0.57 wt%，并表现出高度稳定的机电响应。与传统体系相比，CPP7-CPS3的迟滞面积减小了76.71%，完全抑制了肩峰效应，拉伸强度和断裂伸长率分别提高了81.39%和87.88%。此外，该复合材料具有高应变灵敏度（GF = 352.29），快速响应时间为329.62 ms，超宽传感范围为560.36%。实验表征和分子动力学模拟表明，封闭的互穿界面与填料自组装相结合，减轻了基质粘弹性松弛与导电网络演化之间的不匹配，从而防止了循环网络重构，稳定了机电响应。隔震支座的实时应变监测证实，即使在大变形下，信号输出也稳定，无肩。本工作介绍了一种用于开发鲁棒大变形应变传感器的受限相间驱动设计框架，促进了民用基础设施的长期SHM。

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引用次数: 0

A refined Gibson-Ashby model for functionally graded honeycombs with random irregularities 一个改进的吉布森-阿什比模型，用于随机不规则的功能分级蜂巢

IF 9.4 1区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Mechanical Sciences

Pub Date : 2026-03-15 Epub Date: 2026-01-21 DOI: 10.1016/j.ijmecsci.2026.111297

M.J. Beigrezaee , S.K. Jalali , D. Misseroni , N.M. Pugno

Honeycomb lattices are widely used as lightweight architected materials, and their mechanical behavior is strongly influenced by unit-cell wall thickness and geometric configuration. Inspired by natural cellular structures, predicting the elastic response of honeycombs with wall-thickness grading and geometric irregularities remains challenging. This study refines the Gibson-Ashby equation for predicting the elastic modulus of honeycombs by introducing two correction factors,

κ

and

η

, accounting for functionally graded (FG) wall thickness variations and random irregularities, respectively, i.e., (relative modulus) =

κ η C

(relative density)^{textit {n}}. Analytical expressions based on Timoshenko beam theory are extended to FG architectures, providing a stepwise formulation for relative density and elastic modulus variations along the FG direction. This yields a closed-form expression for the effective relative elastic modulus of FG honeycombs, validated by finite element (FE) simulations. Here,

κ

is calibrated over a broad range of linear and nonlinear wall thickness gradients. Since closed-form formulations for periodic lattices cannot capture random irregularities,

η

is fitted to an extensive set of FE simulations with random designs. These correction factors are presented as design charts covering hexagonal, square, and triangular honeycombs. Additively manufactured samples produced by 3D printing are tested to validate the predictions and quantify real-world imperfections. This framework provides a direct and computationally efficient means to estimate the elastic modulus of graded and irregular 2D lattices without requiring full numerical homogenization or experiments. The study introduces a unified correction-based approach that bridges analytical cellular-material models with the complexity of natural and fabricated honeycombs.

蜂窝格是一种被广泛应用的轻质建筑材料，其力学性能受单元胞壁厚度和几何结构的强烈影响。受自然细胞结构的启发，预测蜂窝的壁厚分级和几何不规则的弹性响应仍然具有挑战性。本研究通过引入考虑功能梯度壁厚变化和随机不规则性的κ和η两个校正因子，对预测蜂窝弹性模量的Gibson-Ashby方程进行了改进，即（相对模量）= κη c（相对密度）textit {n}。将基于Timoshenko梁理论的解析表达式扩展到FG结构，提供了相对密度和弹性模量沿FG方向变化的逐步公式。得到了FG蜂窝有效相对弹性模量的封闭表达式，并通过有限元仿真得到了验证。在这里，κ在广泛的线性和非线性壁厚梯度上进行校准。由于周期格的封闭形式公式不能捕获随机不规则性，η拟合到具有随机设计的广泛的FE模拟集。这些校正因子以设计图表的形式呈现，包括六边形、正方形和三角形的蜂窝。通过3D打印生产的增材制造样品进行了测试，以验证预测并量化现实世界的缺陷。该框架提供了一种直接且计算效率高的方法来估计梯度和不规则二维晶格的弹性模量，而不需要完全的数值均匀化或实验。该研究引入了一种统一的基于校正的方法，将分析细胞材料模型与天然蜂窝和人造蜂窝的复杂性联系起来。

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引用次数: 0

Data-physics-driven system reliability assessment via damage interference theory 基于损伤干扰理论的数据物理驱动系统可靠性评估

IF 9.4 1区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Mechanical Sciences

Pub Date : 2026-03-15 Epub Date: 2026-02-08 DOI: 10.1016/j.ijmecsci.2026.111369

Jian-Peng Chen , Li-Yang Xie , Zhi-Yong Hu , Bing-Feng Zhao , Jia-Xin Song , Xing-Yuan Xu , Hang-Hang Gu , Yan-Ding Guo

Reliability assessment of complex mechanical system under multi-source uncertain load environment remains a critical challenge in engineering practice. This study proposes a data-physics-driven system-level reliability assessment framework based on cumulative damage-critical damage interference (CDCDI) theory. A system-level cumulative damage-critical damage interference (SL-CDCDI) model is developed to unify the dual probabilistic characterization of cumulative damage and critical damage with failure correlation mechanisms. Physical models ensure mechanistic fidelity in probabilistic damage evolution and failure correlation, while data-driven techniques leverage surrogate models to address high-dimensional loads uncertainty quantification and failure correlation mapping. A 300MW steam turbine rotor case study demonstrates the implementation of the proposed framework, demonstrating its capability to balance mechanistic interpretability and data tractability. Comparative analysis with independent system model (ISM) and hot spot model (HSM) demonstrates that the proposed method effectively avoids the over-conservatism of ISM and the risk underestimation of HSM. Mechanistic analysis indicates that load uncertainty is the root cause of the failure correlation, whose effect is amplified under high load dispersion. This work provides a novel paradigm for system reliability assessment under coupled damage evolution and failure correlation, offering practical guidance for reliability design and maintenance of complex mechanical system under flexible operational demands.

多源不确定载荷环境下复杂机械系统的可靠性评估一直是工程实践中的重要课题。提出了一种基于累积损伤-临界损伤干扰（CDCDI）理论的数据物理驱动的系统级可靠性评估框架。建立了系统级累积损伤-临界损伤干扰（SL-CDCDI）模型，将累积损伤和临界损伤的双概率特征与失效关联机制统一起来。物理模型确保了概率损伤演化和失效关联的机制保真度，而数据驱动技术利用替代模型来解决高维载荷不确定性量化和失效关联映射。一个300MW汽轮机转子案例研究演示了所提出框架的实施，证明了其平衡机制可解释性和数据可追溯性的能力。与独立系统模型（ISM）和热点模型（HSM）的对比分析表明，该方法有效地避免了独立系统模型（ISM）的过保守性和热点模型（HSM）的风险低估。力学分析表明，荷载不确定性是破坏相关性的根本原因，在荷载弥散较大的情况下，其影响被放大。该研究为损伤演化与失效关联耦合下的系统可靠性评估提供了一种新的范式，为复杂机械系统在灵活运行需求下的可靠性设计与维护提供了实用指导。

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引用次数: 0

Stabilized HEPM for large-deformation hydro-mechanics in saturated porous media 饱和多孔介质中大变形流体力学的稳定HEPM

IF 9.4 1区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Mechanical Sciences

Pub Date : 2026-03-15 Epub Date: 2026-02-03 DOI: 10.1016/j.ijmecsci.2026.111343

Yuanyi Qiu, Zhen-Yu Yin, Huangcheng Fang

The accurate prediction of hydro-mechanical interactions in saturated soils is essential for assessing the stability of critical geotechnical infrastructure. However, modeling the coupled hydro-mechanical response of saturated soils involving large deformations presents a significant computational challenge, primarily due to the limitations of traditional grid-based methods in handling severe mesh distortion. The core of the proposed HEPM lies in its dual spatial discretization, which decouples the material motion from the numerical mesh. The physical continuum is discretized by a collection of particles that store all state variables, along with an auxiliary mesh used to construct the particle interpolation. Formulated within an Updated Lagrangian (UL) framework based on Biot’s theory, the method incorporates a particle-based Finite Increment Calculus (FIC) stabilization technique. This ensures the suppression of spurious pressure oscillations, thereby enabling the use of efficient equal-order interpolations for both solid displacement and pore pressure. The accuracy and robustness of the proposed method are validated through a series of benchmark tests, showing excellent agreement with analytical solutions for consolidation problems and highlighting its versatility in handling complex material nonlinearities, including nonlinear hydraulic behaviors. Ultimately, the results demonstrate the capability of the proposed framework to reliably solve complex failure problems in computational geomechanics, offering a robust numerical strategy that effectively overcomes mesh distortion and numerical instability in large-deformation hydro-mechanical analysis.

饱和土中水-力相互作用的准确预测对于评价关键岩土基础设施的稳定性至关重要。然而，由于传统的基于网格的方法在处理严重网格畸变时的局限性，对涉及大变形的饱和土的耦合水-力学响应进行建模提出了重大的计算挑战。该方法的核心在于它的双空间离散化，将材料运动与数值网格解耦。物理连续体由存储所有状态变量的粒子集合离散，以及用于构建粒子插值的辅助网格。该方法在基于Biot理论的更新拉格朗日（UL）框架内制定，结合了基于粒子的有限增量微积分（FIC）稳定技术。这确保了对虚假压力振荡的抑制，从而能够对固体位移和孔隙压力使用有效的等阶插值。通过一系列基准测试验证了该方法的准确性和鲁棒性，与固结问题的解析解非常吻合，并突出了其在处理复杂材料非线性（包括非线性水力行为）方面的通用性。最后，结果证明了所提出的框架能够可靠地解决计算地质力学中复杂的破坏问题，提供了一个强大的数值策略，有效地克服了大变形水力学分析中的网格畸变和数值不稳定性。

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引用次数: 0

Nonlinear warpage modeling of dielectric-controlled carrier wafers 介电控制载流子晶圆的非线性翘曲建模

IF 9.4 1区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Mechanical Sciences

Pub Date : 2026-03-15 Epub Date: 2026-02-06 DOI: 10.1016/j.ijmecsci.2026.111361

Chang-Yeon Gu , Min Hyeok Choi , Min Sang Ju , Dohun Kim , Sung Woo Ma , Tae-Ik Lee , Taek-Soo Kim

Warpage control of carrier wafers is a critical challenge in advanced semiconductor packaging processes, as wafer-level deformation impacts not only subsequent processing steps but also the quality of the final chip package, which typically requires high-precision assembly. Therefore, understanding the wafer bending behavior is necessary to accurately predict and control the warpage. In this study, nonlinear warpage models were first developed for carrier wafers controlled by dielectric layer deposition to suggest an extended Stoney formula that accounts for elastic anisotropy, including material properties and curvature, and large deformation behavior. Finite element analysis (FEA) simulations were conducted to investigate warpage behavior according to dielectric film thickness and residual stress. Nonlinear warpage models were established for different thickness ratios of film and substrate systems, which were then integrated into a single master curve that enables rapid estimation of the required dielectric layer thickness or residual stress for effective warpage control. Quantitative analysis revealed that incorporating both anisotropic Young’s modulus and anisotropic curvature of carrier wafers improves warpage prediction accuracy by up to 45.1 % for the onset of nonlinearity and 15.2 % for the resulting nonlinearity magnitude. Furthermore, the universal master curve reveals that nonlinear warpage behavior emerges when the edge deflection-to-wafer thickness ratio exceeds 0.85. Based on this framework, a pre-bow treatment strategy is proposed and validated through numerical analysis, demonstrating up to a 97.9 % reduction in warpage. The presented methodology offers a systematic and physically grounded approach to warpage control, enabling improved process reliability while reducing development time and cost in advanced semiconductor packaging.

在先进的半导体封装工艺中，载体晶圆的翘曲控制是一个关键的挑战，因为晶圆级的变形不仅会影响后续的加工步骤，还会影响最终芯片封装的质量，这通常需要高精度的组装。因此，了解晶圆片的弯曲行为是准确预测和控制翘曲的必要条件。在这项研究中，首先针对介电层沉积控制的载流子晶圆建立了非线性翘曲模型，提出了一个扩展的Stoney公式，该公式考虑了弹性各向异性，包括材料性能和曲率，以及大变形行为。通过有限元模拟研究了介质膜厚度和残余应力对材料翘曲行为的影响。针对薄膜和衬底系统的不同厚度比建立了非线性翘曲模型，然后将其集成到单个主曲线中，从而能够快速估计所需的介电层厚度或残余应力，从而有效地控制翘曲。定量分析表明，结合各向异性杨氏模量和载流子晶圆的各向异性曲率，对非线性开始的翘曲预测精度提高了45.1%，对非线性大小的翘曲预测精度提高了15.2%。此外，通用主曲线显示，当边缘挠度与晶圆厚度之比超过0.85时，出现非线性翘曲行为。基于这一框架，提出了一种预弯曲处理策略，并通过数值分析验证了这一策略，结果表明翘曲减少了97.9%。提出的方法提供了一个系统的和物理接地的方法来翘曲控制，使提高工艺可靠性，同时减少开发时间和成本在先进的半导体封装。

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