International Journal of Solids and Structures最新文献

Modeling viscoelasticity–viscoplasticity of high-strain composites for space deployable structures 空间可展开结构高应变复合材料粘弹性-粘塑性建模

IF 3.4 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2024-11-28 DOI: 10.1016/j.ijsolstr.2024.113154

Xiaowei Yue , Ruiwen Guo , Ning An , Jinxiong Zhou

Space deployable structures made of thin-ply fiber-reinforced composite laminates exhibit significant time-dependent mechanical behaviors, including stress relaxation, shape recovery, and permanent residual deformation throughout their service period. Currently, there is a lack of an appropriate composite laminate model that is able to fully describe these phenomena. Here, we address this gap by proposing an anisotropic viscoelastic–viscoplastic continuum constitutive model to capture the mechanical behavior of composite deployable structures during folding, stowage, deployment, and recovery periods. The model adopts a viscoelastic formulation based on the Boltzmann integral, coupled with a Hill-type rate-dependent viscoplastic formulation. A detailed numerical implementation scheme using fully implicit integration with a two-step viscoelastic predictor and viscoplastic corrector strategy is provided. The accuracy and efficiency of the proposed model are validated against experimental results for both unidirectional and woven laminates. Simulations accurately capture the rate-dependent nonlinear stress–strain response, creep response under constant stress, and hysteresis loops in cyclic loading-unloading tests for single-ply lamina under various off-axis loading directions. Importantly, the proposed method is the first to capture the experimentally observed permanent deformation of real-world composite deployable structures, validated through column bending tests. This advanced modeling and simulation capability significantly enhances the simulation and design of space deployable structures.

由薄层纤维增强复合材料层压板制成的空间可展开结构在整个使用期间表现出显著的随时间变化的力学行为，包括应力松弛、形状恢复和永久残余变形。目前，缺乏一种合适的复合材料层压模型，能够充分描述这些现象。在这里，我们通过提出一个各向异性粘弹粘塑性连续本构模型来解决这一差距，以捕捉复合材料可展开结构在折叠、积载、展开和恢复期间的力学行为。该模型采用基于玻尔兹曼积分的粘弹性公式和希尔型速率相关粘塑性公式。给出了一种采用两步粘弹性预测和粘塑性校正策略的全隐式积分的详细数值实现方案。通过对单向板和编织板的实验结果验证了该模型的准确性和有效性。模拟准确捕捉了不同离轴加载方向下单层板循环加卸载试验中速率相关的非线性应力-应变响应、恒应力下的蠕变响应和滞回线。重要的是，所提出的方法是第一个捕获实验观察到的真实复合材料可展开结构的永久变形，并通过柱弯曲试验进行验证。这种先进的建模和仿真能力大大提高了空间可展开结构的仿真和设计。

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引用次数: 0

Mechanics analysis and experimental study of ultra-thin chip peeling from pre-stretching substrates 预拉伸基底超薄切屑剥落的力学分析与实验研究

IF 3.4 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2024-11-26 DOI: 10.1016/j.ijsolstr.2024.113161

Siyu Chen , Kewen Shi , Ziwen Kong , Yinji Ma , Xue Feng

Successful chip peeling from a substrate facilitates the transfer process for obtaining the final functional chips, but remains a challenge in the practical production of ultra-thin chips. Flexible ultra-thin chips are prone to fragmentation during the peeling process, due to their fragility. In this study, a substrate pre-stretching process is introduced to the picking process to achieve a high yield of chip peeling, and this process is explored via modelling and experiments. The chip–adhesive pre-stretched substrate structure is modelled, involving both multi-needle ejection and vacuum suctioning, within the framework of Timoshenko’s beam theory. The theoretical analysis is validated using finite element analysis to compare the surface stress distribution on the chip and tip stress within the adhesive layer. During the peeling process, the competitive fracture behaviour of the chip between cracking and peeling is analysed using a dimensionless peeling health index as a metric to assess the health status of the chip. The effects of substrate pre-stretching on the adhesive layer stress, chip layer stress, and peeling health index are analysed. As substrate pre-stretching is found to improve the peeling health index only in the case of needle ejection, but impairs the peeling health index in the case of vacuum suctioning, needle ejection is considered the sole effective peeling method when a substrate pre-stretching process is introduced. Furthermore, through meticulous experimental verification, it is confirmed that pre-stretching of the substrate can significantly improve the success rate of chip peeling.

成功地从衬底上剥离芯片有利于获得最终功能芯片的转移过程，但在超薄芯片的实际生产中仍然是一个挑战。柔性超薄芯片由于其易碎性，在剥离过程中容易碎裂。本研究将衬底预拉伸工艺引入到采摘过程中，以实现高成品率的切屑剥离，并通过建模和实验对该工艺进行了探索。在Timoshenko的光束理论框架内，对贴片粘合剂预拉伸基板结构进行了建模，包括多针弹射和真空抽吸。通过有限元分析对比了贴片表面应力分布和粘接层内尖端应力分布，验证了理论分析的正确性。在剥离过程中，采用无量纲剥离健康指数作为评估切屑健康状态的指标，分析了切屑在开裂和剥离之间的竞争断裂行为。分析了基材预拉伸对粘接层应力、切屑层应力和剥离健康指数的影响。由于基材预拉伸仅在引针情况下提高了脱皮健康指数，而在真空抽吸情况下降低了脱皮健康指数，因此在引入基材预拉伸工艺时，认为引针是唯一有效的脱皮方法。此外，通过细致的实验验证，证实了基片的预拉伸可以显著提高切屑剥离的成功率。

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引用次数: 0

Analytical and experimental studies on the sequential flaring-buckling behavior of combined bi-tubes in blind bolts 盲螺栓组合双管序贯扩曲行为的分析与实验研究

IF 3.4 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2024-11-26 DOI: 10.1016/j.ijsolstr.2024.113158

Jiaming Feng , Yuyin Sun , Wanjun Jin , Ridong Liao

Combined bi-tubes are innovatively applied in modern composite blind bolts to provide the clamping force. In this study, the sequential flaring-buckling behavior of combined bi-tubes under axial compression on expanding dies was experimentally and analytically investigated. First, axial compression tests were performed on bi-tubes in three different dimension groups. Based on the test results, deformation modes and force–displacement curves were obtained to assess the specific energy absorption (SEA), clamping energy (E_CL), and energy transfer ratio (ETR). The results show that bi-tubes have superior energy-absorbing capacity and clamping efficiency. SEA can reach 21 kJ/kg, and the E_CL accounts for 50 ± 6 % of the total energy dissipated. Afterwards, a theoretical solution for flaring-buckling bi-tubes, which involves the flaring forming force, friction, and critical buckling force, was derived on the basis of an equal-thickness circular tube. A comparison of forces and deformation modes from analytical and experimental approaches leads to the observations that the analytical theory can assess the sequential flaring-buckling bi-tubes within acceptable proximity, the maximum deviations of flaring forming forces and critical buckling forces being 3.3 % and 6.6 %, and that it can effectively predict diverse deformation modes, i.e., a single bell-shaped bulb on the clamped structure, an upper bulb close to the platen, or double bulbs. This study is expected to provide guidance for the optimal design of the clamping structure on aircraft and automobiles.

组合双管创新地应用于现代复合盲螺栓，以提供夹紧力。本文通过实验和分析研究了双管在膨胀模轴压作用下的连续扩口-屈曲行为。首先，在三个不同的维度组中对双管进行轴压试验。根据试验结果，获得了变形模式和力-位移曲线，评估了比能吸收（SEA）、夹紧能（ECL）和能量传递比（ETR）。结果表明，双管具有较好的吸能能力和夹紧效率。SEA可达21 kJ/kg， ECL占总耗散能量的50±6%。然后，以等厚圆管为例，推导了扩口成形力、摩擦力和临界屈曲力的扩口-屈曲双管理论解。通过对分析方法和实验方法的受力和变形模式的比较发现，分析理论可以在可接受的接近范围内评估连续扩口-屈曲双管，扩口成形力和临界屈曲力的最大偏差分别为3.3%和6.6%，并且可以有效地预测多种变形模式，即夹紧结构上的单个钟形球，靠近压板的上部球，或双球。该研究可为飞机和汽车夹紧结构的优化设计提供指导。

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引用次数: 0

Beyond effective stiffness: A modified differential Mori-Tanaka-Voigt homogenization for predicting stresses in individual inclusions 超越有效刚度：用于预测单个夹杂应力的改进的Mori-Tanaka-Voigt微分均质化

IF 3.4 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2024-11-24 DOI: 10.1016/j.ijsolstr.2024.113152

Deepjyoti Dhar, Atul Jain

Mean field homogenization (MFH) methods are widely employed for homogenizing heterogeneous materials. However, they are limited to predicting effective properties and phase-averaged stresses, failing to capture stresses within individual inclusions. This paper introduces a novel homogenization approach, termed MDMT-Voigt, aimed at addressing this lacuna. The proposed model is validated extensively using finite element analysis (FEA), encompassing virtual Representative Volume Elements (RVEs) with a range of aspect ratios, volume fractions, and orientation distributions. Furthermore, validation is conducted using RVEs derived from experimentally determined microstructures via micro-computed tomography. Across all models considered, the FEA results yield a range of stresses for inclusions with same orientation and aspect ratio which is captured well by the proposed MDMT-Voigt model. Prediction of stresses in individual inclusions represents a significant advancement over conventional MFH methods, offering substantial potential for enhanced micromechanics modelling comparable to full finite element approaches, but at a computational efficiency order of magnitude lower. The paper ends with a demonstration confirming improved micromechanics using the Modified Coulomb criteria.

平均场均质（MFH）方法被广泛应用于非均质材料的均质化。然而，它们仅限于预测有效性质和相平均应力，而不能捕获单个夹杂物中的应力。本文介绍了一种新的均质化方法，称为MDMT-Voigt，旨在解决这一空白。该模型采用有限元分析（FEA）进行了广泛的验证，包括具有一系列宽高比、体积分数和方向分布的虚拟代表性体积单元（RVEs）。此外，通过微计算机断层扫描实验确定的微观结构，使用RVEs进行验证。在所有考虑的模型中，FEA结果产生了具有相同取向和纵横比的包裹体的应力范围，这被提出的MDMT-Voigt模型很好地捕获。与传统的MFH方法相比，单个包裹体的应力预测是一项重大进步，为增强微观力学建模提供了巨大的潜力，可与全有限元方法相媲美，但计算效率要低一个数量级。最后，用修正的库仑准则验证了改进的细观力学。

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引用次数: 0

Characterizing and modeling the wide strain rate range behavior of air-filled open-cell polymeric foam 充气开孔聚合物泡沫的宽应变速率范围特性表征与建模

IF 3.4 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2024-11-24 DOI: 10.1016/j.ijsolstr.2024.113155

Xinghao Wang , Zhibo Du , Jiarui Zhang , Yue Kang , Chenxu Liu , Tian Ma , Zhanli Liu

Air-filled open-cell polymeric foams are widely used for absorbing impact energy under various strain rates. Modeling their compression behavior under large deformation across a wide strain rate range remains a challenge, as the air pressure is dominated by viscous effect or inertial effect at different strain rates. In this study, the compression response of air-filled open-cell polyurethane (PU) foam is characterized across a wide strain rate range from 0.0001 s⁻¹ to 5000 s⁻¹. The plateau stress and energy absorption properties of the foam exhibit a power-law dependency on strain rate, showing lower rate sensitivity at quasi-static rates and increased sensitivity at high strain rates. To describe the observed rate sensitivity variation, the effect of airflow resistance is quantitatively modeled and a visco-hyperelastic constitutive model considering air pressure is developed. It shows that at high strain rates, the air pressure can constitute up to 30 % of the energy absorption contribution while it is relatively negligible at quasi-static strain rates, which significantly amplifies the difference in rate sensitivity between quasi-static and high strain rates. Furthermore, a simplified semi-empirical formula is proposed to rapidly estimate the air pressure in open-cell foams at high strain rates. This formula demonstrates the mechanical response transition from open-cell to closed-cell foams with increasing strain rates. This study is meaningful for understanding the dynamic response and the energy absorption capabilities of air or fluid filled open-cell foam.

充气开孔泡沫塑料被广泛用于吸收不同应变速率下的冲击能。由于在不同应变率下，空气压力主要受粘性效应或惯性效应的影响，因此在大变形、宽应变率范围内对其压缩行为进行建模仍然是一个挑战。在本研究中，充气开孔聚氨酯（PU）泡沫的压缩响应特征是在0.0001 s−1到5000 s−1的宽应变速率范围内。泡沫的平台应力和能量吸收性能与应变速率呈幂律关系，在准静态速率下表现出较低的速率敏感性，在高应变速率下表现出较高的灵敏度。为了描述观测到的速率敏感性变化，对气流阻力的影响进行了定量建模，并建立了考虑气压的粘-超弹性本构模型。结果表明，在高应变率下，气压可占能量吸收贡献的30%，而在准静态应变率下，气压相对可以忽略不计，这显著放大了准静态应变率与高应变率之间的速率灵敏度差异。此外，提出了一种简化的半经验公式来快速估计高应变率下开孔泡沫内的空气压力。该公式显示了随应变速率的增加，从开孔泡沫到闭孔泡沫的力学响应转变。本研究对了解空气或流体填充开孔泡沫的动态响应和吸能能力具有重要意义。

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引用次数: 0

Experimental and numerical analysis of geometry on joint strength in GFRP-aluminum alloy adhesive joints 关于 GFRP 铝合金粘接接头几何形状对接头强度影响的实验和数值分析

IF 3.4 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2024-11-22 DOI: 10.1016/j.ijsolstr.2024.113153

Tuqiang Wang , Shuang Yang , Jun Wang , Xi Chen , Chaoqun Wu , Weirong Zhu

Enhancing the bonding strength between composites and metals is one of the urgent challenges that needs to be addressed. One of the methods to improve the strength of adhesive joints is to change the geometry of the joints. In this paper, four different types of aluminum alloy sleeves were developed by designing grooves with varying angles and shapes. Glass fiber reinforced polymer rods were adhesively bonded to these sleeves, resulting in the preparation of five different types of adhesive joints, including a conventional structure. The mechanical performance and failure mechanisms of these joints were analyzed experimentally and numerically. The results indicate that, compared to conventional adhesive joints, the load-bearing capacity of the four designed adhesive joints has been significantly improved, with a maximum increase of 49.6% and a minimum increase of 35.6%. The axial angle of the groove structures designed within the joint is a factor that influences the ultimate load capacity of the joint. Furthermore, the shear stress in the adhesive layer is identified as the primary cause of adhesive layer failure. The designed mechanical interlocking structures can not only increase the interfacial bonding force between the adhesive layer and the substrate but also delay the complete failure of the adhesive layer, thereby improving the load-bearing strength of the joint. This work is expected to provide new insights for the design of composite and metal joints.

提高复合材料与金属之间的粘接强度是亟待解决的难题之一。提高粘合接头强度的方法之一是改变接头的几何形状。本文通过设计不同角度和形状的凹槽，开发了四种不同类型的铝合金套筒。玻璃纤维增强聚合物棒被粘合到这些套筒上，从而制备出包括传统结构在内的五种不同类型的粘合接头。实验和数值分析了这些接头的机械性能和失效机理。结果表明，与传统的粘接接头相比，所设计的四种粘接接头的承载能力有了显著提高，最大提高了 49.6%，最小提高了 35.6%。接头内凹槽结构的轴向角度是影响接头极限承载能力的一个因素。此外，粘合剂层中的剪应力被认为是粘合剂层失效的主要原因。设计的机械联锁结构不仅能增加粘合剂层与基材之间的界面粘合力，还能延缓粘合剂层的完全失效，从而提高接头的承载强度。这项工作有望为复合材料和金属接头的设计提供新的启示。

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引用次数: 0

Modeling the pull-off force of a mushroom-shaped fibrillar adhesive in dynamic detachment 蘑菇状纤维粘合剂动态脱落时的拉脱力建模

IF 3.4 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2024-11-20 DOI: 10.1016/j.ijsolstr.2024.113150

Ru-Guo Ji , Yue-Yu Yuan , Xiao-Feng Liu , Xiao-Long Zhang , Guo-Ping Cai

Fibrillar adhesive, as a novel biomimetic controllable adhesive, holds broad application prospects in the fields of medical devices, aerospace, and robotics. Evaluating the critical detachment force (pull-off force) of such materials, that is, establishing a pull-off force model, is one of the key issues to be addressed in the application process. The experimental results show that preload, dwell time, and retraction velocity are key factors affecting critical detachment force. However, there is no model that can take into account the influence of these three factors. In order to accurately evaluate the adhesion performance of fibrillar adhesive, this study took mushroom-shaped fibrillar adhesive (MFSA) as the object and carried out theoretical and experimental research on the modeling problem of its pull-off force. First, we derived a new pull-off force model based on the Gent & Schultz hypothesis and linear elastic fracture theory. In this model, the relative contact area is introduced to quantify the impact of preload and dwell time on the pull-off force, and the rate-dependent properties of the effective adhesion work are used to describe the impact of retraction velocity on the pull-off force. Then, the validity of the model is experimentally investigated. The experimental results show that this paper’ s model can accurately predict the pull-off force of MFSA after parameter identification, thereby verifying the model’s effectiveness. Finally, we used the pull-off force model to study the effects of model parameters on pull-off force.

纤维粘合剂作为一种新型仿生物可控粘合剂，在医疗器械、航空航天和机器人领域有着广阔的应用前景。评估此类材料的临界分离力（拉脱力），即建立拉脱力模型，是应用过程中需要解决的关键问题之一。实验结果表明，预紧力、停留时间和回缩速度是影响临界脱模力的关键因素。然而，目前还没有一个模型能考虑到这三个因素的影响。为了准确评估纤维状粘合剂的粘合性能，本研究以蘑菇形纤维状粘合剂（MFSA）为对象，对其拉脱力的建模问题进行了理论和实验研究。首先，我们基于 Gent & Schultz 假设和线性弹性断裂理论推导出了一个新的拉拔力模型。在该模型中，引入了相对接触面积来量化预紧力和停留时间对拉拔力的影响，并利用有效粘附功的速率依赖特性来描述回缩速度对拉拔力的影响。然后，对模型的有效性进行了实验研究。实验结果表明，本文的模型在参数识别后可以准确预测 MFSA 的拉脱力，从而验证了模型的有效性。最后，我们利用拉拔力模型研究了模型参数对拉拔力的影响。

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引用次数: 0

Asymptotic Numerical Method for dynamic buckling of shell structures with follower pressure 有随动压力的壳体结构动态屈曲渐近数值法

IF 3.4 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2024-11-20 DOI: 10.1016/j.ijsolstr.2024.113135

Anh-Khoa Chau, Michael Brun, Pascal Ventura, Hamid Zahrouni, Michel Potier-Ferry

Asymptotic Numerical Method (ANM) is applied to non-linear dynamics of thin-shells subjected to conservative and non-conservative loads such as follower pressure. ANM is decomposed into several stages: the finite element discretization of the non-linear equations of motion of the shell dynamics, a homotopy transformation of the semi-discrete non-linear equations, a perturbation technique to expand the quantities into Taylor series according to the homotopy parameter and the time integration scheme to solve the series of linear problems resulting from the perturbation technique. ANM is applied here with the 7-parameter shell elements thanks to the Enhanced Assumed Strain (EAS) concept and implicit Newmark integration. In the case of non-conservative force, follower pressure also requires to be decomposed in either Taylor series or rational Padé approximants. The academic case of the cylindrical roof with dynamic snap-through phenomenon is investigated for the purpose of comparing ANM strategies and the classical Newton–Raphson (NR) method. Two engineering cases including an I-shaped thin-walled beam and a closed thin-shell cylinder under dynamic external follower pressure are also investigated. ANM turns out to be accurate, robust and efficient in terms of computation time, providing an alternative method to the well-established Newton–Raphson method.

渐近数值法（ANM）适用于承受保守和非保守载荷（如随动压力）的薄壳非线性动力学。ANM 分解为几个阶段：壳体动力学非线性运动方程的有限元离散化、半离散非线性方程的同调变换、根据同调参数将量扩展为泰勒级数的扰动技术以及解决由扰动技术产生的一系列线性问题的时间积分方案。由于采用了增强假定应变（EAS）概念和隐式纽马克积分，ANM 在这里被应用于 7 参数壳元素。在非守恒力的情况下，随动压力也需要用泰勒级数或有理 Padé 近似值进行分解。为了比较 ANM 策略和经典的 Newton-Raphson (NR) 方法，研究了具有动态卡穿现象的圆柱形屋顶的学术案例。此外，还研究了两个工程案例，包括承受动态外部随动压力的工字形薄壁梁和封闭薄壳圆柱体。结果表明，ANM 是一种精确、稳健和高效的计算方法，可作为成熟的牛顿-拉斐森方法的替代方法。

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引用次数: 0

Ductile failure by strain localisation: A computational study of materials and structures subjected to highly non-proportional load histories 应变局部化的韧性破坏：高度非比例载荷历史条件下材料和结构的计算研究

IF 3.4 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2024-11-19 DOI: 10.1016/j.ijsolstr.2024.113128

Martin Kristoffersen, David Morin, Tore Børvik, Odd Sture Hopperstad

Ductile failure by the onset of strain localisation after non-proportional load paths is investigated herein by using the imperfection version of the strain localisation theory. A computational framework assuming a planar, porous imperfection band inside a homogeneous solid was used to investigate ductile failure as caused by void nucleation, growth, and coalescence. The localisation analysis framework was calibrated based on a single uniaxial tension test and finite element simulations thereof. Despite the somewhat frugal calibration, the localisation analyses successfully reproduced experimentally measured macroscopic fracture strains from notched tension tests and notched compression–tension tests. The method was subsequently applied to a structural problem involving large deformations and complex load paths, and the results show great promise for future work.

本文利用应变局部化理论的不完善版本，研究了非比例载荷路径后应变局部化的韧性破坏。计算框架假定均质固体内部存在平面多孔缺陷带，用于研究由空洞成核、生长和凝聚引起的韧性破坏。根据单个单轴拉伸试验和有限元模拟对定位分析框架进行了校准。尽管校准略显节俭，但定位分析成功地再现了缺口拉伸试验和缺口压缩拉伸试验中实验测量的宏观断裂应变。随后，该方法被应用于一个涉及大变形和复杂载荷路径的结构问题，其结果显示了未来工作的巨大前景。

引用次数: 0

Hyperelastic model for nonlinear elastic deformations of graphene-based polymer nanocomposites 石墨烯基聚合物纳米复合材料非线性弹性变形的超弹性模型

IF 3.4 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2024-11-19 DOI: 10.1016/j.ijsolstr.2024.113144

Matteo Pelliciari , Stefano Sirotti , Angelo Aloisio , Angelo Marcello Tarantino

Graphene-based polymer nanocomposites (PNCs) are increasingly important in engineering applications involving large deformations. However, the nonlinear behavior of these materials has not been thoroughly studied. Current models do not address the specific nonlinear effects of graphene nanofillers under large strains, lack sufficient comparison with experimental data, and primarily focus on uniaxial behavior without exploring biaxial responses, which are relevant in technological applications. This study investigates PNCs composed of silicone elastomer and graphene nanoplatelets (GNPs). We present experimental tests conducted in both simple tension and biaxial inflation on circular membranes. A homogenized hyperelastic model is developed, incorporating distinct contributions from the matrix and the nanofiller. Specifically, we introduce a novel strain energy function for the nanofiller contribution, tailored to reproduce the observed experimental behavior. The model accurately predicts the nonlinear elastic response of the studied PNCs across varying contents of GNPs. The proposed strain energy function is implemented in MATLAB to obtain an exact numerical solution for the inflation of circular PNC membranes. Finally, to demonstrate its broader applicability, the hyperelastic model is applied to additional experimental data from other PNCs found in the literature. This model contributes to establishing a robust framework for the effective use of PNCs.

石墨烯基聚合物纳米复合材料（PNCs）在涉及大变形的工程应用中越来越重要。然而，这些材料的非线性行为尚未得到深入研究。目前的模型没有涉及石墨烯纳米填料在大应变下的特定非线性效应，缺乏与实验数据的充分比较，而且主要集中在单轴行为上，没有探索与技术应用相关的双轴响应。本研究调查了由硅树脂弹性体和石墨烯纳米颗粒（GNPs）组成的 PNC。我们介绍了在圆形薄膜上进行的简单拉伸和双轴充气实验测试。我们建立了一个均质化超弹性模型，其中包含了基体和纳米填料的不同贡献。具体来说，我们为纳米填料的贡献引入了一个新的应变能函数，以重现观察到的实验行为。该模型能准确预测所研究的 PNC 在不同 GNP 含量下的非线性弹性响应。建议的应变能函数在 MATLAB 中实现，以获得圆形 PNC 膜充气的精确数值解。最后，为了证明该模型具有更广泛的适用性，我们将超弹性模型应用于文献中其他 PNC 的实验数据。该模型有助于建立有效使用 PNC 的稳健框架。

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引用次数: 0