基于横观各向同性超弹性理论的短纤维增强橡胶本构模型的建立与应用Establishment and application of short fiber reinforced rubber constitutive model based on transversely isotropic hyperelastic theory

提出了一种能够表征短纤维增强橡胶的横观各向同性超弹性本构模型,并结合试验体系,对其在数值分析中的应用方法和效果进行了研究。基于连续介质力学理论,建立了横观各向同性材料的应变能函数,推导得到不同变形形式下的应力应变关系,给出材料参数辨识试验方法,并成功应用于某短纤维增强橡胶测试中,得到表征其超弹性特性的相关材料参数。利用有限元软件ANSYS对不同纤维排布方向的单轴拉伸和平行纤维方向的平面拉伸进行仿真计算,并对比相应试验数据,以验证材料参数的可靠性。最后基于已验证的本构模型,建立了某铣槽装备减振环仿真模型,并对其进行了校核计算。研究结果表明,本文提出的本构模型能够有效表征短纤维增强橡胶的静态力学特性并且方便嵌入现有的有限元软件中,具有材料参数少、测试简便和结果准确等特点,工程实用性强。     

一种考虑剪切作用的各向异性超弹性本构模型

基于纤维增强复合材料连续介质力学理论,提出了一种轮胎帘线/橡胶复合材料的各向异性超弹性本构模型. 应变能被分解为分别代表橡胶、帘线、帘线/橡胶之间的角剪切和正剪切应变能4个部分. 给出了模型参数的简单确定方法,通过拟合文献中的实验数据,得到了本构模型参数,并用该模型预测了其他变形条件下的力学行为,得到了和实验数据较一致的结果,验证了该模型的有效性,为整体轮胎的有限元分析打下了基础.     

橡胶复合材料结构大变形有限元分析

建立了一个橡胶复合材料结构有限元分析模型。在该模型中 ,考虑了轮胎变形的几何非线性、轮胎与地面和轮胎与轮辋的大变形非线性接触、轮胎材料的非均匀性和物理非线性及橡胶基复合材料的各向异性。此外 ,本文还利用该模型研制的有限元分析软件对全钢丝子午胎的变形轮廓进行了详细的分析。     

载重子午线轮胎三维非线性有限元分析

建立了一个轮胎结构有限元分析模型，考虑了轮胎变形的几何非线性，轮胎与地面和轮胎与轮辋的大变形非线性接触，轮胎材料的非均匀性，橡胶材料的不可压缩性和物理非线性及橡胶基复合材料的各向异性。结果表明，该模型有效可靠。     

Finite element simulation of deformation behaviour of cellular rubber components

This paper presents a new prospect of investigating the mechanical behaviour of cellular rubber using a porous hyperelastic material model within the framework of homogenisation method to consider pore volume fraction. There are number of hyperelastic material models to describe the behaviour of homogeneous elastomer, but very few to characterise the complex properties of cellular rubber. The analysis of dependence of material behaviour on pore density using the new material model is supported with experiments to characterise the actual material behaviour. The finite element simulations are then followed by compression load tests to validate the material model.     

滑轮绳索系统中动态节点绳索单元

解除了传统有限元方法中单元节点与物质点固结的假设, 建立了空间点的速度和加速度与相应物质点的速度和加速度之间的数学关系, 强调了虚功率原理中出现的速度和加速度皆为物质速度和物质加速度. 在此基础上构造了单元节点既不与空间坐标固定也不与物质坐标固定的动态节点绳索单元. 根据滑轮绳索系统的特点, 选取绳索出入绳点的弧长坐标、出入绳角、面外摆角以及拉伸应变等空间参数描述了滑轮绳索系统的运动. 将绳索与滑轮以及绳索与卷筒之间的相互作用合理简化为物质速度间的约束条件, 避免了传统方法中接触力计算不收敛、效率低等缺点. 所提方法可精细求解绳索与滑轮间接触边界点位置和卷筒入绳点在卷筒上的运动、滑轮的中心和其连体基的运动、绳索出入滑轮和卷筒时空间方位的变化以及绳索上任意点的拉力变化等细节. 可为含绳索机械系统的力学分析提供新的理论基础. 所用的解除单元节点与物质点绑定的理论具有一定的普适性, 可为有限元方法的理论和应用提供参考.      

轮胎有限元分析技术及其在轮胎结构优选中的应用

建立了一个轮胎结构有限元分析模型,考虑了轮胎变形的几何非线性、轮胎与地面和轮胎与轮辋的大变形非线性接触、轮胎的非均匀性、橡胶材料的不可压缩性和物理非线性及橡胶基复合材料的各向异性,此外,还探讨了这种轮胎有限分析模型在轮胎结构优选中的应用。     

帘线/橡胶复合材料各向异性黏-超弹性本构模型

帘线/橡胶复合材料广泛应用于轮胎等重要工程领域,为了描述其在服役条件下的大变形、非线性、各向异性和高应变率等材料力学行为,基于纤维增强复合材料连续介质力学理论,提出了一种考虑应变率效应的帘线/橡胶复合材料各向异性黏-超弹性本构模型. 该模型中单位体积的应变能被解耦为便于参数识别的基体等容变形能、帘线拉伸变形能、剪切应变能和黏性应变能四部分. 给出了模型参数的确定方法,并通过拟合文献中单轴拉伸、偏轴拉伸实验数据,得到了模型参数. 利用该模型预测了不同加载和变形条件下的力学行为,并将预测结果与实验结果对比分析. 结果表明, 考虑黏性模型和不考虑黏性模型对不同应变率变形条件下的预测结果相差很大,且考虑黏性模型的预测结果与实验结果吻合很好. 因此,与不考虑黏性模型相比,所提出的各向异性黏-超弹性本构模型能更好地表征帘线/橡胶复合材料在大变形、高应变率条件下的力学特性.      

Nanoindentation of hyperelastic polymer layers at finite deformation and parameter re-identification

Thin polymer layers on substrates have a wide range of application in important areas. However, it is impossible to measure the mechanical properties with the traditional testing methods. Recently, nanoindentation became a new but primary testing technique of thin layers. In the present work, based on a finite element model of contact mechanics and hyperelastic materials, nanoindentation of polymer layers is simulated with the finite element code ABAQUS^?. Three often used hyperelastic models, that is, the neo-Hookean, Mooney–Rivlin and Yeoh models are investigated. The behaviour of these three models is compared to each other in different boundary value problems of nanoindentation in order to get some feeling of the different behaviour of various hyperelastic models under nanoindentation. In contrast to the traditional analytical method, the penetration depth is not restrained to avoid the influence of the substrate. A parameter re-identification strategy is employed to extract the parameters of the material models at small and finite deformation based on the principle of biological evolution. Furthermore, it is investigated how large the penetration depth has to be chosen in order to distinguish different models in reference to the load–displacement curves. Finally, the possibility is discussed of describing the data obtained by a non-linear complex model using the relatively simple approach based on the neo-Hookean model.     

短纤维增强三元乙丙橡胶横观各向同性黏-超弹性本构模型

短纤维增强三元乙丙橡胶包覆薄膜,是一种应用于固体火箭发动机缠绕包覆装药的新型复合材料.为了描述其在工作过程中受振动、冲击等载荷作用时的力学行为,基于黏弹性理论和纤维增强连续介质力学理论,提出了一种考虑应变率强化效应的横观各向同性黏-超弹本构模型.模型中应变能函数被分解为超弹性应变能和黏性应变能,其中超弹性应变能包括表征各向同性的橡胶基体应变能和表征各向异性的纤维拉伸应变能,黏性应变能采用表征橡胶和纤维黏性响应的宏观唯象模型.选取表征各应变能的函数形式,经过数学变换、替代、叠加,求解确定最终的应力应变形式,明确模型参数获取的具体步骤,将预测结果与实验结果对比分析,准确性较高.研究表明:该模型能有效预测材料在低应变率下纤维方向为0?～45?的非线性率相关力学特性;模型形式易于实现有限元开发,对固体火箭发动机装药结构完整性分析具有参考价值.     

HIA: A Hybrid Integral Approach to model incompressible isotropic hyperelastic materials – Part 2: Finite element analysis

The present paper is devoted to the modeling of finite deformations of hyperelastic bodies by using the Hybrid Integral Approach (HIA) model introduced by the Authors. This model combines the affine behavior of chains included in the molecular 8-chains density, the interleaving constraint part and an original phenomenological integral density which allows to balance the mismatch between model and experimental data. A total Lagrangian formulation is adopted to describe the geometrical and material non-linearities and a finite element implementation is performed in the FER software. Four test examples, including homogeneous and non-homogeneous deformations, as well as complex computation involving dynamic contact and impact are proposed to show the applicability of the developed approach and the efficiency of the model.     

Finite element modeling of interfacial forces and contact stresses of pneumatic tire on fresh snow for combined longitudinal and lateral slips

Significant challenges exist in the prediction of interaction forces generated from the interface between pneumatic tires and snow-covered terrains due to the highly non-linear nature of the properties of flexible tires, deformable snow cover and the contact mechanics at the interface of tire and snow. Operational conditions of tire-snow interaction are affected by many factors, especially interfacial slips, including longitudinal slip during braking or driving, lateral slip (slip angle) due to turning, and combined slip (longitudinal and lateral slips) due to brake-and-turn and drive-and-turn maneuvers, normal load applied on the wheel, friction coefficient at the interface and snow depth. This paper presents comprehensive three-dimensional finite element simulations of tire-snow interaction for low-strength snow under the full-range of controlled longitudinal and lateral slips for three vertical loads to gain significant mechanistic insight. The pneumatic tire was modeled using elastic, viscoelastic and hyperelastic material models; the snow was modeled using the modified Drucker-Prager Cap material model (MDPC). The traction, motion resistance, drawbar pull, tire sinkage, tire deflection, snow density, contact pressure and contact shear stresses were obtained as a function of longitudinal slip and lateral slip. Wheel states - braked, towed, driven, self-propelled, and driving - have been identified and serve as key classifiers of discernable patterns in tire-snow interaction such as zones of contact shear stresses. The predicted results can be applied to analytical deterministic and stochastic modeling of tire-snow interaction.     

各向同性超弹性本构模型数值计算及验证

现有多种形式的橡胶本构模型试图预测橡胶力学性质,其中部分模型已写入有限元软件中用于仿真计算,还存在较多拟合性较好的模型无法在有限元材料库中直接获得。本文详述了由不变量和主伸长率描写的各向同性超弹性本构模型的数值实现方法,并结合最新的本构模型开发了UHYPER和UMAT子程序。将UHYPER用于有限元实现对多孔橡胶板的拉伸仿真,对比仿真和试验结果,验证子程序的正确性以及评估本构模型预测复杂应变场的准确性;将UMAT用于单轴、等双轴和剪切拉伸的有限元仿真,对比仿真和本构模型理论结果,验证子程序的可靠性。结果表明,有限元仿真结果与理论结果拟合较好,子程序能够契合本构模型的力学描述,所述方法可以用于超弹性材料的数值计算。     

缆索吊装系统有限元分析中的滑轮单元

为精确模拟结构中的滑轮，建立了滑轮支承一段索的单元，它考虑了滑轮的半径. 该``滑轮单元'的中间节点在滑轮的中心，另两个节点为索段位于滑轮两侧的端点. 新单元通过自动调整索在滑轮两侧的长度，使单元达到平衡状态. 单元算法的推导基于有限元分析的基本原理，并利用了处于平衡状态时单元内力之间的关系. 介绍新单元的推导过程，算例验证了它的正确性，并显示了其在含有滑轮索结构有限元分析中的高效性和方便性.     

单峰接触研究及其在分形表面接触中的应用

基于有限元方法,建立了弹塑性单峰的接触模型.粗糙峰为理想的弹塑性材料,为了考虑不同的材料特性对微凸体变形的影响,分别对9种不同的材料进行了分析.根据有限元计算结果,分析了接触面积,平均接触压力和接触力与变形干涉量之间的关系,并进行了经验公式的拟合.单峰接触所经历的4个不同的阶段,以及不同阶段之间的转化点均作了明确的表达.然后,根据分形理论,将单峰接触模型扩展到了三维的粗糙表面的接触,并提出了一个计算接触表面法向刚度的模型.通过与实验数据和以往模型的结果对比,证明本文中所提出的模型具有较高的精度.     

A new nonlinear multibody/finite element formulation for knee joint ligaments

The focus of this investigation is to study the mechanics of the human knee using a new method that integrates multibody system and large deformation finite element algorithms. The major bones in the knee joint consisting of the femur, tibia, and fibula are modeled as rigid bodies. The ligaments structures are modeled using the large displacement finite element absolute nodal coordinate formulation (ANCF) with an implementation of a Neo-Hookean constitutive model that allows for large change in the configuration as experienced in knee flexion, extension, and rotation. The Neo-Hookean strain energy function used in this study takes into consideration the near incompressibility of the ligaments. The ANCF is used in the formulation of the algebraic equations that define the ligament/bone rigid connection. A unique feature of the ANCF model developed in this investigation is that it captures the deformation of the ligament cross section using structural finite elements such as beams. At the ligament/bone insertion site, the ANCF is used to define a fully constrained joint. This model will reflect the fact that the geometry, placement and attachment of the two collateral ligaments (the LCL and MCL), are significantly different from what has been used in most knee models developed in previous investigations. The approach described in this paper will provide a more realistic model of the knee and thus more applicable to future research studies on ligaments, muscles and soft tissues (LMST). Current finite element models are limited due to simplified assumptions for the spatial and time dependent material properties inherent in the anisotropic and anatomic constraints associated with joint stability, and the static conditions inherent in the analysis. The ANCF analysis is not limited to static conditions and results in a fully dynamic model that accounts for the distributed inertia and elasticity of the ligaments. The results obtained in this investigation show that the ANCF finite elements can be an effective tool for modeling very flexible structures like ligaments subjected to large flexion and extension. In the future, the more realistic ANCF models could assist in examining the mechanics of the knee to study knee injuries and possible prevention means, as well as an improved understanding of the role of each individual ligament in the diagnosis and assessment of disease states, aging and potential therapies.     

Folding of fiber composites with a hyperelastic matrix

This paper presents an experimental and numerical study of the folding behavior of thin composite materials consisting of carbon fibers embedded in a silicone matrix. The soft matrix allows the fibers to microbuckle without breaking and this acts as a stress relief mechanism during folding, which allows the material to reach very high curvatures. The experiments show a highly non-linear moment vs. curvature relationship, as well as strain softening under cyclic loading. A finite element model has been created to study the micromechanics of the problem. The fibers are modeled as linear-elastic solid elements distributed in a hyperelastic matrix according to a random arrangement based on experimental observations. The simulations obtained from this model capture the detailed micromechanics of the problem and the experimentally observed non-linear response. The proposed model is in good quantitative agreement with the experimental results for the case of lower fiber volume fractions but in the case of higher volume fractions the predicted response is overly stiff.     

A model reduction technique for laminated solids of revolution with a curved cross-section

This paper presents an extension of the numerical reduction method, which has been proposed in Lejeunes et al. (Arch Appl Mech, 76:311–326, 2006), for modeling curved laminated structures of revolution such as for instance rubber bearings. This method based on high-order finite elements is developed in the context of nearly incompressible hyperelastic behavior. The displacement is approximated with a sum of independent functions, leading to a separation of variables. Therefore, a one-dimensional finite element can be formulated, which represents a 3-dimensional solid in a general loading case. Comparisons with classical finite element models are provided and show the reliability of this model reduction. An important decrease in the model size and a greatly reduced computing time, compared to standard models, is observed.     

New approach based on continuum damage mechanics with simple parameter identification to fretting fatigue life prediction

A new continuum damage mechanics model for fretting fatigue life prediction is established. In this model, the damage evolution rate is described by two kinds of quantities. One is associated with the cyclic stress characteristics obtained by the finite element(FE) analysis, and the other is associated with the material fatigue property identified from the fatigue test data of standard specimens. The wear is modeled by the energy wear law to simulate the contact geometry evolution. A two-dimensional(2D) plane strain FE implementation of the damage mechanics model and the energy wear model is presented in the platform of ABAQUS to simulate the evolutions of the fatigue damage and the wear scar. The effect of the specimen thickness is also investigated. The predicted results of the crack initiation site and the fretting fatigue life agree well with available experimental data. Comparisons are made with the critical plane SmithWatson-Topper(SWT) method.