International Journal of Non-Linear Mechanics最新文献_第2页

Modeling and analysis of aircraft landing nonlinear dynamics for tire safety assessment 飞机着陆非线性动力学建模与分析，用于轮胎安全评估

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2026-03-01 Epub Date: 2025-12-16 DOI: 10.1016/j.ijnonlinmec.2025.105309

Shuangbao Li , Yapeng Li , Bo Zhang , Zhongmin Jia , Xiangli Gao , Liying Kou

Modeling and analysis of aircraft landing nonlinear dynamics for tire safety assessment is formulated in this paper. Firstly, an aircraft landing process is reviewed to introduce the principle of tire rotation, friction coefficients and random pavement profiles. Secondly, a tire of a main landing gear is simplified to be a rim and a belt ring connected by three spring-damping elements. The traditional 1/4 vehicle model is generalized to construct a new seven-degree-of-freedom single-wheel landing dynamic model in order to describe the vertical, longitudinal and circumferential motions of the tire during different landing phases. The influence of braking force, lift and pavement roughness are considered. Thirdly, numerical analysis of the aircraft landing process is carried out to obtain the variation trend of tire deformation, load and friction at different phases, as well as the movement state of the aircraft fuselage and the tire. Finally, tire safety is evaluated through cumulative tread wear and transient landing load. The former is related with airworthiness requirements on maximum allowable wear depth and replacement cycles, while the latter is compared with structural load limits during touchdown. The results demonstrate that high landing speeds and low-friction surfaces markedly accelerate wear progression, while the overall numerical predictions remain consistent with established physical trends, confirming the validity of the proposed safety assessment method. The proposed methodology addresses a new viewpoint to employ the aircraft landing nonlinear dynamics to carry out tire safety evaluation and maintenance planning in civil aviation.

建立了用于轮胎安全评价的飞机着陆非线性动力学建模与分析方法。首先，回顾了飞机着陆过程，介绍了轮胎旋转、摩擦系数和随机路面轮廓的原理。其次，将主起落架的轮胎简化为由三个弹簧阻尼元件连接的轮辋和带环。将传统的1/4车辆模型进行推广，建立了新的七自由度单轮着陆动力学模型，以描述轮胎在不同着陆阶段的垂直、纵向和周向运动。考虑了制动力、升力和路面平整度的影响。第三，对飞机着陆过程进行数值分析，得到不同阶段轮胎变形、载荷和摩擦力的变化趋势，以及飞机机身和轮胎的运动状态。最后，通过累积胎面磨损和瞬态着陆载荷对轮胎安全性进行评价。前者与最大允许磨损深度和更换周期的适航要求有关，后者与着陆时的结构载荷限值进行比较。结果表明，高着陆速度和低摩擦表面显著加速了磨损进程，而总体数值预测与已建立的物理趋势保持一致，证实了所提出的安全评估方法的有效性。该方法为利用飞机着舰非线性动力学进行民航轮胎安全评价和维修规划提供了新的视角。

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引用次数: 0

Optimal design of a novel SMA assisted yield damper (SMA-YD) under random earthquake for building response control 随机地震作用下新型SMA辅助屈服阻尼器（SMA- yd）的优化设计

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2026-03-01 Epub Date: 2025-12-13 DOI: 10.1016/j.ijnonlinmec.2025.105307

Mohammad Yasir Mohammad Hasan Shaikh, Sourav Gur

This study introduces an optimal design for a novel shape memory alloy-assisted yield damper (SMA-YD) by employing the multi-objective optimisation (MOO) framework and random vibration analysis, under stochastic ground motions (GMs). Two conflicting objectives, namely the root mean square (rms) top floor acceleration (TFA) and top floor displacement (TFD), are utilized as the primary design variables, and optimised to design SMA-YD. Further, stochastic analysis results are verified through the Monte Carlo (MC) simulations results, which shows a good agreement. Study results revealed that the optimised damper strength ratio and fraction of SMA in damper strength are two critical design parameters for SMA-YD. Comparison of Pareto optimal front clearly illustrates the trade-off possibilities among these conflicting responses in the SMA-YD assisted building, and compared with the yield damper (YD) assisted building. Furthermore, the study verifies the variation in optimum responses under recorded GMs. Compare to the YD, the robustness in the optimal design and enhanced performance of SMA-YD are investigated through the parametric variation, adopting various damper and building parameters, along with different seismic loading scenarios. As found, the SMA-YD requires up to 15 % more strength than YD, however provides up to 20 % and 50 % more reduction in the rms TFA and rms TFD, respectively. Finally, nonlinear time history analysis (NLTHA) results aligned with the stochastic response behaviour, as observed in the study.

本文介绍了一种新型形状记忆合金辅助屈服阻尼器（SMA-YD）的优化设计，采用多目标优化（MOO）框架和随机振动分析，在随机地面运动（gm）下。两个相互冲突的目标，即均方根顶楼加速度（TFA）和顶楼位移（TFD），被用作主要设计变量，并优化设计SMA-YD。通过蒙特卡罗（MC）模拟结果对随机分析结果进行了验证，结果显示出较好的一致性。研究结果表明，优化后的阻尼器强度比和SMA占阻尼器强度的比例是SMA- yd的两个关键设计参数。帕累托最优前的比较清楚地说明了SMA-YD辅助建筑中这些冲突响应之间的权衡可能性，并与屈服阻尼器（YD）辅助建筑进行了比较。此外，该研究还验证了在记录的gm下最佳响应的变化。通过参数变化，采用不同的阻尼器和建筑参数，以及不同的地震荷载场景，研究了SMA-YD优化设计的鲁棒性和增强性能。研究发现，SMA-YD需要比YD多15%的强度，但在rms TFA和rms TFD上分别提供了20%和50%的减少。最后，非线性时程分析（NLTHA）结果与研究中观察到的随机响应行为一致。

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引用次数: 0

Unilateral vibration transmission in mechanical systems with bilinear coupling 双线性耦合机械系统的单边振动传递

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2026-02-01 Epub Date: 2025-10-01 DOI: 10.1016/j.ijnonlinmec.2025.105272

Ali Kogani, Behrooz Yousefzadeh

Unilateral vibration transmission refers to a scenario in which the transmitted response of a system is in purely tensile or compressive oscillations, despite the system being driven by a symmetric harmonic input. This intriguing transmission phenomenon can arise in systems that exhibit different effective elasticity in compression and tension; i.e., bilinear elasticity. We present a computational investigation of unilateral transmission in the steady-state response of harmonically driven mechanical systems with bilinear coupling. Starting with two bilinearly coupled oscillators, we find that breaking the mirror symmetry of the system, in either elastic or inertial properties, facilitates unilateral transmission by allowing it to occur near a primary resonance. This asymmetry also enables nonreciprocal transmission to occur. We then investigate the nonreciprocal dynamics of the system, including linear stability analysis, with a focus on unilateral transmission. We also extend our discussion to a bilinear periodic structure, for which we investigate the influence of the number of units and energy dissipation on unilateral transmission. We report on the existence of stable nonreciprocal unilateral transmission near primary and internal resonances of the system, as well as other nonreciprocal features such as period-doubled and quasiperiodic response characteristics.

单侧振动传递是指尽管系统由对称谐波输入驱动，但系统的传递响应是纯拉伸或压缩振动的情况。这种有趣的传输现象可能出现在压缩和拉伸表现出不同有效弹性的系统中；即双线性弹性。本文对双线性耦合谐波驱动机械系统稳态响应中的单边传动进行了计算研究。从两个双线性耦合振荡器开始，我们发现打破系统的镜像对称性，在弹性或惯性特性中，通过允许它发生在主共振附近，促进单边传输。这种不对称也使非互传发生。然后，我们研究了系统的非互易动力学，包括线性稳定性分析，重点是单边传输。我们还将讨论扩展到双线性周期结构，研究了单元数和能量耗散对单侧传输的影响。我们报道了系统在主共振和内部共振附近存在稳定的非互易单侧传输，以及其他非互易特征，如倍周期和准周期响应特征。

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引用次数: 0

Crashworthiness of composite sandwich structures with tailored Poisson's ratios under bird strike 定制泊松比复合材料夹层结构在鸟击下的耐撞性

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2026-02-01 Epub Date: 2025-10-01 DOI: 10.1016/j.ijnonlinmec.2025.105273

Shaochen Ning, Yadong Zhou

Bird strike has emerged as one of the most critical soft-body impact scenarios encountered by modern aircraft during take-off and landing. Among crashworthiness designs, composite sandwich structures have received considerable attention due to their superior energy absorption capacity and design flexibility. This study explores the combined influence of Poisson's ratios and unit cell alignment directions. Finite Element Analysis (FEA) was used to evaluate the non-linear structure responses of five cell designs with tailored positive (PPR), negative (NPR), and zero (ZPR-1, ZPR-2 and ZPR-3) Poisson's ratios under three orthogonal directions, in terms of energy absorptions, deformation modes, and damage degrees. Among all configurations, ZPR-3 demonstrates the most balanced and robust performance, achieving kinetic energy reductions of 7.43 %, 6.91 %, and 11.63 % greater than the conventional PPR structure in three orthogonal directions, respectively. Moreover, ZPR-3 maintains the lowest core equivalent plastic strain (PEEQ), with peak values as low as 0.26, and consistently exhibits wide but slight plastic zones. Its ability to balance elastic recovery, plastic deformation, and resistance to repeated bird strikes highlights its strong potential for crashworthiness sandwich components in aerospace applications.

鸟撞已经成为现代飞机在起飞和降落过程中遇到的最关键的软体撞击场景之一。在抗碰撞设计中，复合材料夹层结构因其优越的吸能能力和设计灵活性而备受关注。本研究探讨了泊松比和单元胞排列方向的综合影响。采用有限元分析（FEA）对正（PPR）、负（NPR）和零（ZPR-1、ZPR-2和ZPR-3）泊松比设计的5种单元格在3个正交方向上的非线性结构响应进行了评价，包括能量吸收、变形模式和损伤程度。在所有构型中，ZPR-3表现出最平衡和稳健的性能，在三个正交方向上分别比传统的PPR结构减少了7.43%、6.91%和11.63%的动能。ZPR-3保持最低的芯等效塑性应变（PEEQ），峰值低至0.26，且始终呈现较宽但较弱的塑性区。其平衡弹性恢复、塑性变形和抵抗反复鸟击的能力突出了其在航空航天应用中作为耐撞夹层组件的强大潜力。

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引用次数: 0

Nonlinear dynamic analysis of rolling element bearings with misalignment defects 滚动轴承偏心缺陷的非线性动力学分析

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2026-02-01 Epub Date: 2025-10-29 DOI: 10.1016/j.ijnonlinmec.2025.105286

Bi Li , Zhinong Li , Deqiang He

Bearings with misalignment defects are comprehensively affected by defect sizes and misalignment parameters, thereby causing more complex motion of rolling elements (REs), which makes existing models struggle to effectively simulate their Nonlinear Dynamic Characteristics (NDCs). Therefore, first, a misalignment defect theory is proposed that fully accounts for defect/rolling element sizes and misalignment parameters (shift distance and skew angle). Various motion scenarios of REs when passing through misalignment defects are thoroughly analyzed, and a new REs' time-varying trajectory conforming to the parabolic motion trend is proposed. Then, a dynamic model of RE bearings with misalignment defects is established, which considers Hertzian contact and thermo-elasto-hydrodynamic lubrication, and the bearing NDCs are studied. The research shows that: (1) Reducing defect width or rotational speed, increasing shift distance, increasing the skew angle β when β ≤ arctan (b_k/l_k), and decreasing it when 90° ≥ β > arctan (b_k/l_k) all contribute to mitigating the impact of local defects on the bearing NDCs. (2) Changes in defect width or shift distance may alter the bearing failure modes. Finally, experiments on bearings with misalignment defects at different speeds verify the validity of the proposed model. This study can provide important references for bearing design optimization and fault diagnosis.

含错中缺陷的轴承受到缺陷尺寸和错中参数的综合影响，从而导致滚动体（REs）运动更为复杂，这使得现有模型难以有效地模拟其非线性动态特性（ndc）。因此，首先，提出了一种充分考虑缺陷/滚动元件尺寸和错位参数（移位距离和倾斜角度）的错位缺陷理论。深入分析了re在通过错位缺陷时的各种运动情况，提出了一种新的符合抛物线运动趋势的re时变运动轨迹。在此基础上，建立了考虑赫兹接触和热弹流体动力润滑的含偏心缺陷稀土轴承动力学模型，并对轴承ndc进行了研究。研究表明：(1)减小缺陷宽度或转速，增大位移距离，在β≤arctan （bk/lk）时增大斜倾角β，在90°≥β >； arctan （bk/lk）时减小斜倾角β，均有助于减轻局部缺陷对轴承ndc的影响。(2)缺陷宽度或移位距离的变化可能会改变轴承的失效模式。最后，对不同转速下存在不对准缺陷的轴承进行了实验，验证了所提模型的有效性。该研究可为轴承设计优化和故障诊断提供重要参考。

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引用次数: 0

Non-linear fluid-structure interaction of sloped wall tuned liquid dampers for mitigating the hysteretic response of multi-degree-of-freedom structures subjected to various categories of near-fault ground motions 斜壁调谐液体阻尼器的非线性流固相互作用，用于减轻多自由度结构在各种近断层地震动下的滞后响应

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2026-02-01 Epub Date: 2025-11-22 DOI: 10.1016/j.ijnonlinmec.2025.105299

Sidhartha Sankar Roy, Kishore Chandra Biswal

To ensure the safety of structures under strong excitations such as near-fault earthquakes with high-amplitude velocity pulses, effective damping mechanisms are crucial to counteract the potential weakening or loss of structural stiffness. This paper presents a numerical study on the effectiveness of sloped wall tuned liquid dampers in mitigating structural vibrations, taking into account the non-linearities in both sloshing dynamics and structural behavior. The hybrid Eulerian-Lagrangian non-linear finite element scheme for the sloshing and the elasto-plastic spring-mass scheme for the structure are combined and utilized for the modeling of the present problem. The dynamic bahavior of the structure with coupled tuned liquid dampers is analyzed at the optimal tuning ratio for different types of near-fault earthquakes (i.e., Directivity effect type and Fling-step effect type). Forward directivity-type earthquakes are found to be more likely to cause potential weakening or loss of structural stiffness compared to fling-step-type earthquakes. The non-linear dynamic response shows better agreement with existing experimental results compared to the linear response, thereby validating the accuracy of the non-linear model. Also, the response reduction capacity of the damper is observed to be overestimated by the linear sloshing model.

为了保证结构在强激励下的安全，如近断层高振幅速度脉冲地震，有效的阻尼机制至关重要，以抵消结构刚度的潜在减弱或损失。本文在考虑结构晃动动力学和结构特性非线性的情况下，对斜壁调谐液体阻尼器的减振效果进行了数值研究。结合欧拉-拉格朗日混合非线性有限元法和弹塑性弹簧-质量法对该问题进行了建模。分析了不同类型近断层地震（即指向性效应型和飞阶效应型）下，耦合调谐液体阻尼器在最佳调谐比下的结构动力性能。研究发现，与飞跃式地震相比，正向指向性地震更有可能导致结构刚度的潜在减弱或丧失。非线性动态响应比线性响应更符合现有实验结果，从而验证了非线性模型的准确性。线性晃动模型对阻尼器的减振能力估计过高。

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引用次数: 0

Nonlinear slipping dynamics of locally faulted bearings considering rolling-sliding-elastic-fluid coupling 考虑滚动-滑动-弹性-流体耦合的局部故障轴承非线性滑动动力学

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2026-02-01 Epub Date: 2025-10-11 DOI: 10.1016/j.ijnonlinmec.2025.105284

Juanjuan Shi, Yifan Huangfu, Yulu Zhang, Xinyin Zhang, Changqing Shen, Zhongkui Zhu

Rolling bearings are key components of transmission systems and their dynamic behaviors are closely related to health conditions during equipment operation. However, the nonlinear slipping behaviors of rolling bearings with local faults currently have not been sufficiently investigated. A novel coupled excitation modeling framework for locally faulted rolling bearings is developed in this work. The rolling-sliding-elastic-fluid contact mechanics is incorporated to accurately characterize the nonlinear slipping dynamics. Distinguished from over-simplified traditional models, the proposed model integrates cage flexibility, hydrodynamic lubrication, roller-raceway rolling-sliding-elastic coupling, and cage-roller collisions to guarantee the accuracy of the dynamic model. An experiment is carried out to verify the proposed dynamic model. Moreover, an in-depth analysis of the slipping characteristics of the faulty bearings are carried out to reveal the underlying mechanism of fault-slipping interaction. Through the nonlinear tribo-dynamic analysis, the slipping characteristics of the rolling bearings are investigated to uncover the key factors of bearing slipping. By comparing the slip rate under various fault severities, the slipping characteristics of rolling elements of locally faulted bearings are analyzed, which fundamentally explains why the local faults aggravate the slipping phenomenon of bearings. These findings provide fundamental insights into the nonlinear dynamic behaviors of faulty bearings, offering a theoretical foundation for model-based fault diagnosis.

滚动轴承是传动系统的关键部件，其动态行为与设备运行过程中的健康状况密切相关。然而，滚动轴承局部故障的非线性滑动行为目前还没有得到充分的研究。本文提出了一种新的局部故障滚动轴承耦合激励建模框架。结合滚动-滑动-弹性-流体接触力学，准确表征了非线性滑动动力学。与过度简化的传统模型不同，该模型集成了保持架柔性、流体动力润滑、滚子-滚道滚动-滑动-弹性耦合以及保持架-滚子碰撞，保证了动态模型的准确性。通过实验验证了所提出的动态模型。此外，对故障轴承的滑动特性进行了深入分析，揭示了断层-滑动相互作用的潜在机制。通过非线性摩擦动力学分析，研究了滚动轴承的滑动特性，揭示了轴承滑动的关键因素。通过比较不同故障严重程度下的滑动率，分析了局部故障轴承滚动体的滑动特性，从根本上解释了局部故障加剧轴承滑动现象的原因。这些发现为故障轴承的非线性动力学行为提供了基本见解，为基于模型的故障诊断提供了理论基础。

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引用次数: 0

Energy-constrained Lagrangian neural networks for data-driven modeling of robotic systems: Method and prosthetic applications 数据驱动机器人系统建模的能量约束拉格朗日神经网络：方法和假肢应用

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2026-02-01 Epub Date: 2025-10-10 DOI: 10.1016/j.ijnonlinmec.2025.105283

Qidi Wu , Wen Zhang , Xingbiao Xie , Shu Zhang , Xiaoxu Zhang , Jian Xu

Dynamic models are crucial for model-based control of multi-degree-of-freedom systems, particularly in robotic applications. While traditional methodologies, including Newtonian and Lagrangian mechanics, have been widely employed, they exhibit limitations in accurately capturing unstructured factors such as joint friction and transmission flexibility. Inspired by the physical interpretability inherent in Lagrangian mechanics and the universal approximation capabilities of neural networks, this paper introduces a novel Energy-constrained Lagrangian Neural Network (EnLNN) modeling framework. The proposed EnLNN decomposes the acceleration field into conservative and nonconservative components, with the former represented by a Lagrangian Neural Network (LNN) and the latter by a feedforward neural network (FNN). A distinctive feature of the EnLNN is its incorporation of energy constraints, which allows the conservative component to preserve energy to the greatest extent, thereby mitigating the misallocation of force fields between conservative and nonconservative components. This approach yields a more precise Lagrangian representation than conventional LNNs. The efficacy of the EnLNN modeling approach was evaluated through numerical simulation of a double pendulum system and experimental validation on a lower limb prosthesis. The results substantiate that the EnLNN framework effectively distinguishes conservative and nonconservative components from empirical data while maintaining high modeling accuracy and demonstrating robust extrapolation capabilities.

动态模型对于多自由度系统的基于模型的控制至关重要，特别是在机器人应用中。虽然包括牛顿力学和拉格朗日力学在内的传统方法已被广泛采用，但它们在准确捕捉关节摩擦和传动灵活性等非结构化因素方面存在局限性。受拉格朗日力学固有的物理可解释性和神经网络的通用逼近能力的启发，提出了一种新的能量约束拉格朗日神经网络（EnLNN）建模框架。提出的EnLNN将加速度场分解为保守和非保守分量，其中保守分量由拉格朗日神经网络（LNN）表示，非保守分量由前馈神经网络（FNN）表示。EnLNN的一个显著特点是它结合了能量约束，这使得保守分量能够最大程度地保留能量，从而减轻了保守和非保守分量之间力场的错配。这种方法产生了比传统LNNs更精确的拉格朗日表示。通过双摆系统的数值模拟和下肢假肢的实验验证，对EnLNN建模方法的有效性进行了评估。结果表明，EnLNN框架有效地从经验数据中区分了保守和非保守成分，同时保持了较高的建模精度，并展示了强大的外推能力。

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引用次数: 0

Axial–torsional dynamic model of a drill-string considering thermal-assisted drilling 考虑热辅助钻井的钻柱轴扭动力学模型

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2026-02-01 Epub Date: 2025-10-10 DOI: 10.1016/j.ijnonlinmec.2025.105279

Yuri B.S. Moralles , Daniel A. Castello , Luiz F. Bez , Thiago G. Ritto

Thermal-assisted drilling, a recent advancement in drilling technology, aims to enhance process efficiency but its effects on drill-string dynamics remain largely unexplored. This paper presents an axial–torsional model with nonlinear bit-rock interaction coupling to investigate these effects. The first contribution is the proposition of a regularization method for a widely used nonlinear bit-rock interaction model. To validate the method, model parameters are calibrated against experimental data, demonstrating strong alignment with observed results. The second contribution is the integration of thermal effects into the bit-rock interaction, using thermal load inputs informed by previous experimental and numerical studies. Results show that under the most critical thermal load, the rate of penetration (ROP) increases by approximately 43%, highlighting the potential of thermal-assisted drilling to enhance drilling efficiency. Additionally, axial and torsional forces at the bit, along with the rotational speed of the bit, exhibit minimal variations under thermal conditions. These results indicate that thermal-assisted drilling can substantially improve ROP without compromising dynamic stability, offering new strategies for efficient and effective drilling operations.

热辅助钻井是钻井技术的最新进展，旨在提高工艺效率，但其对钻柱动力学的影响在很大程度上仍未被探索。本文提出了一个具有非线性钻头-岩石相互作用耦合的轴扭模型来研究这些影响。第一个贡献是提出了一种广泛使用的非线性钻头-岩石相互作用模型的正则化方法。为了验证该方法，根据实验数据校准了模型参数，证明与观测结果有很强的一致性。第二个贡献是将热效应整合到钻头-岩石相互作用中，使用了以前的实验和数值研究提供的热负荷输入。结果表明，在最临界热负荷下，钻速（ROP）提高了约43%，凸显了热辅助钻井提高钻井效率的潜力。此外，在热条件下，钻头的轴向力和扭转力以及钻头的转速变化最小。这些结果表明，热辅助钻井可以在不影响动态稳定性的情况下大幅提高机械钻速，为高效钻井作业提供了新的策略。

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引用次数: 0

An I2-enhanced hyperelastic model to capture secondary strain-stiffening 一个i2增强的超弹性模型来捕捉二次应变硬化

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2026-02-01 Epub Date: 2025-11-05 DOI: 10.1016/j.ijnonlinmec.2025.105285

Subraya Krishna Bhat , Manu Hegde

Soft elastomers, undergoing large deformation, are prevalent in broad class of engineering applications ranging from continuum robotics to artificial skin. Hyperelastic material models are commonly employed to predict the mechanical response of such elastomers. Unstable deformation is often seen when soft elastomer components are subjected to extreme loads. A phenomenological hyperelastic model is formulated in this work to capture one of the experimentally found instabilities in the deformation exhibited by certain class of soft elastomers, namely the secondary strain-stiffening. The issues that restrict the existing invariant based hyperelastic models from reproducing the secondary strain-stiffening are addressed by combining the salient features of Knowles model and the exponent of the second invariant I₂ of the left Cauchy-Green stretch tensor (named Knowles-Exp-Ln model). The capability of the developed model is demonstrated by comparing the model predictions with the results of balloon-inflation experiment. Further, the behavior of the Knowles-Exp-Ln model is analytically explored in the case of other instability-prone homogeneous tests such as the inflation of thin cylindrical shells and the expansion of the spherical cavity. Practical guidelines for the estimation of relevant material parameters are also given, considering Baker-Ericksen inequality. The results obtained in this work suggest that the proposed hyperelastic model captures, apart from usually observed limit-point instabilities, the secondary strain-stiffening accurately. The model can be readily used to solve the boundary value problems involving the particular class of elastomers that experience the secondary strain-stiffening as well as to train surrogate models over a wide range of unstable deformations.

软弹性体，经历大变形，普遍存在于广泛的工程应用，从连续体机器人到人造皮肤。超弹性材料模型通常用于预测这类弹性体的力学响应。当软弹性体部件受到极端载荷时，通常会出现不稳定变形。在这项工作中，一个现象学的超弹性模型被制定，以捕捉实验中发现的变形中的不稳定性之一，即某些软弹性体的二次应变硬化。结合Knowles模型的显著特征和左柯西-格林拉伸张量（Knowles- exp - ln模型）的第二不变量I2的指数，解决了现有基于不变量的超弹性模型无法再现二次应变强化的问题。通过将模型预测结果与气球膨胀实验结果进行比较，验证了模型的有效性。此外，还分析探讨了Knowles-Exp-Ln模型在其他易失稳均质试验（如薄圆柱壳的膨胀和球腔的膨胀）中的行为。考虑到Baker-Ericksen不等式，还给出了估计相关材料参数的实用指南。本研究的结果表明，除了通常观察到的极限点不稳定性外，所提出的超弹性模型准确地捕获了二次应变加劲。该模型可以很容易地用于解决涉及特定类型弹性体的边值问题，这些弹性体经历了二次应变硬化，也可以在大范围的不稳定变形上训练代理模型。

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引用次数: 0