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.     

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.      

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。     

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

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.     

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。     

Kevlar29纱线动态拉伸力学性能与本构方程

为了能够清晰地表征芳纶纱线在不同应变率下的力学行为,进行了Kevlar29纱线的准静态和动态拉伸试验,结合分离式霍普金森拉杆理论和运动目标追踪法,获得了Kevlar29纱线在不同应变率下的应力-应变曲线,分析了纱线动态拉伸的变形与断裂过程,揭示了Kevlar29纱线力学性能的应变率效应;通过最小二乘法拟合得到了基于纱线应变率效应的黏弹性本构方程,分析了三元件和五元件本构模型的差异及适用性。结果表明：随着应变率升高,Kevlar29纱线的断裂应变减小,拉伸强度和韧性先增大后减小,拉伸模量先增大后趋于稳定;五元件黏弹性本构模型能够较好地表征纱线力学性能的应变率效应。     

考虑缠结效应的超弹性本构模型

经典熵弹性模型, 如 Neo-Hookean模型和Arruda-Boyce八链模型, 被广泛应用于预测橡胶等软材料的超弹性力学行为. 然而, 大量实验结果也显示仅采用一套模型参数, 这类模型不能同时准确地描述橡胶在多种加载模式下的应力响应. 为了克服上述模型的不足, 本文在熵弹性的模型基础上引入缠结约束效应. 微观上, 采用Langevin统计模型来表征熵弹性变形自由能, 通过管模型(tube model)引入缠结约束自由能, 并基于仿射假设, 建立微观变形与宏观变形之间的映射关系. 在宏观上, 所建立的超弹性模型的Helmholtz自由能同时包含熵弹性和缠结约束两部分, 其中熵弹性自由能与经典的Arruda-Boyce八链模型一致, 依赖于柯西-格林应变张量的第一不变量, 而缠结约束自由能依赖于柯西-格林应变张量的第二不变量. 与文献中的实验结果对比发现, 该三参数模型能准确地预测实验中所测得的橡胶材料在单轴拉伸、纯剪切和等双轴拉伸变形条件下的应力响应, 也能较好地描述不同预拉伸比条件下双轴拉伸实验结果. 最后, 本文比较了所建立的基于应变不变量的缠结约束模型与文献中相关的缠结约束模型在多种加载模式下自由能的异同. 总的来说, 本文所建立的本构理论能准确模拟橡胶等软材料的大变形力学行为, 对其工程应用有促进作用.      

复合材料层合板面内渐进损伤分析的CDM模型

基于连续介质损伤力学,提出了一个预测复合材料层合板面内渐进损伤分析的模型,它包括损伤表征、损伤判定和损伤演化3 部分. 模型能够区分纤维拉伸断裂、纤维压缩断裂、纤维间拉伸损伤和纤维间压缩损伤4 种损伤模式,定义了与4 个损伤模式对应的损伤状态变量,导出了材料主轴系下损伤前后材料本构之间的关系. 损伤起始采用Puck 准则判定,损伤演化由特征长度内应变能释放密度控制. 假定材料服从线性应变软化行为,建立了损伤状态变量关于断裂面上等效应变的渐进损伤演化法则. 模型涵盖了复合材料面内损伤起始、演化直至最终失效的全过程. 完成了含孔[45/0/-45/90]_2S 层合板在拉伸和压缩载荷下失效分析,结果表明该模型能合理进行层合板的强度预测和损伤失效分析.      

复合材料层合板面内渐进损伤分析的CDM模型简

基于连续介质损伤力学,提出了一个预测复合材料层合板面内渐进损伤分析的模型,它包括损伤表征、损伤判定和损伤演化3 部分. 模型能够区分纤维拉伸断裂、纤维压缩断裂、纤维间拉伸损伤和纤维间压缩损伤4 种损伤模式,定义了与4 个损伤模式对应的损伤状态变量,导出了材料主轴系下损伤前后材料本构之间的关系. 损伤起始采用Puck 准则判定,损伤演化由特征长度内应变能释放密度控制. 假定材料服从线性应变软化行为,建立了损伤状态变量关于断裂面上等效应变的渐进损伤演化法则. 模型涵盖了复合材料面内损伤起始、演化直至最终失效的全过程. 完成了含孔[45/0/-45/90]_2S 层合板在拉伸和压缩载荷下失效分析,结果表明该模型能合理进行层合板的强度预测和损伤失效分析.     

Mechanical response of a short fiber-reinforced thermoplastic: Experimental investigation and continuum mechanical modeling

The present work can be regarded as a first step toward an integrated modeling of mold filling during injection molding process of polymer composites and the resulting material behavior under service loading conditions. More precisely, the emphasis of the present paper is laid on how to account for local fiber orientation in the ground matrix on the prediction of the mechanical response of the composite at its final solid state. To this end, a set of experiments which captures the mechanical behavior of an injection molded short fiber-reinforced thermoplastic under different strain histories is described. It is shown that the material exhibits complex response mainly due to non-linearity, anisotropy, time/rate-dependence, hysteresis and permanent strain. Furthermore, the relaxed state of the material is characterized by the existence of an equilibrium hysteresis independently of the applied strain rate. A three-dimensional phenomenological model to represent experimentally observed response is developed. The microstructure configuration of the material is simplified and assumed to be entirely represented by a distributed fiber orientation in the ground matrix. In order to account for distributed short fiber orientations in a continuum sense, a concept of (symmetric) generalized structural tensor (tensor of orientation) of second order is adopted. The proposed model is based on assumption that the strain energy function of the composite is given by a linear mixture of the strain energy of each constituent: an isotropic part representing Phase 1 which is essentially related to the ground matrix and an anisotropic part describing Phase 2 which is mainly related to the fibers and the interphase as a whole. Hence, taking into account the fiber content and orientation, the efficiency of the model is assessed and perspectives are drawn.     

Finite deformation of a polymer: experiments and modeling

The response of a polymer (polytetrafluoroethylene) to quasi-static and dynamic loading is determined and modeled. The polytetrafluoroethylene is extremely ductile and highly nonlinear in elastic as well as plastic behaviors including elastic unloading. Constitutive model developed earlier by Khan, Huang and Liang (KHL) is extended to include the responses of polymeric materials. The strain rate hardening, creep, and relaxation behaviors of polytetrafluoroethylene were determined through extensive experimental study. Based on the observation that both viscoelastic and viscoplastic deformation of polytetrafluoroethylene are time dependent and nonlinear, a phenomenalogical viscoelasto–plastic constitutive model is presented by a series connection of a viscoelastic deformation module (represented by three elements standard solid spring dashpot model), and a viscoplastic deformation module represented by KHL model. The KHL module is affected only when the stress exceeds the initial yield stress. The comparison between the predictions from the extended model and experimental data for uniaxial static and dynamic compression, creep and relaxation demonstrate that the proposed constitutive model is able to represent the observed time dependent mechanical behavior of polytetrafluoroethylene polytetrafluoroethylene qualitatively and quantitatively.     

Continuous versus discrete (invariant) representations of fibrous structure for modeling non-linear anisotropic soft tissue behavior

The non-linear anisotropic mechanical response of soft tissue is largely dependent on the structure of the underlying collagen network. Collagen structure has been successfully quantified for various tissue types in terms of a locally defined fiber orientation distribution function. The continuous distribution function derived from structural data can be directly incorporated into an integral representation of the strain energy function for modeling tissue behavior. Alternatively, non-integral (often invariant-based) strain energy functions have been developed in which the collagen network structure is approximated using a discrete set of fiber classes. The advantage of such an approach is increased computational efficiency since the values of the strain energy and its derivatives (e.g. stress) can be evaluated without numerical integration. However, because of the structural simplifications such models are presumably unable to predict mechanical data as accurately as the models which incorporate a continuous orientation distribution function. In this work the ability of discrete versus continuous fiber models to capture the non-linear anisotropic response of soft tissue is critically analyzed. Both unimodal and bimodal fiber distributions are considered. A general formulation has been developed in terms of an arbitrary fiber strain energy function, such that the analysis can be performed for any suitable fiber material model. For tissue structures in which a discrete representation is suitable, techniques are presented for establishing the range of loading conditions in which model accuracy is not significantly compromised, thus justifying the use of an invariant-based modeling approach.     

Thermomechanical modeling of the thermo-order-mechanical coupling behaviors in liquid crystal elastomers

Liquid crystal elastomer is a kind of anisotropic polymeric material, with complicated micro-structures and thermo-order-mechanical coupling behaviors. In this paper, we propose a method to systematically model these coupling behaviors. We derive the constitutive model in full tensor structure according to the Clausius-Duhem inequality. Two of the constitutive equations represent the mechanical equilibrium and the other two represent the phase equilibrium. Choosing the total free energy as the combination of the neo-classical free energy and the Landau-de Gennes nematic free energy, we obtain the Cauchy stress-deformation gradient relation and the order-mechanical coupling equations. We find the analytical homogeneous solutions of the deformation for the typical mechanical loadings, such as uniaxial stretch, and simple shear in any directions. We also compare the compression behavior of prolate liquid crystal elastomers with the stretch behavior of oblate liquid crystal elastomers. As a result, the stress, strain, temperature, order parameter, biaxiality and the direction of the director of liquid crystal elastomers couple with each other. When the prolate liquid crystal elastomer sample is stretched in the direction parallel to its director, the deviatoric stress makes the mesogens more order and increase the transition temperature. When the sample is sheared or stretched in the direction non-parallel to the director, the director of the liquid crystal elastomer will rotate, and the biaxiality will be induced. Because of the order-mechanical coupling, under infinitesimal deformation, liquid crystal elastomer has anisotropic Young’s modulus and zero shear modulus in the direction parallel or perpendicular to the director. While for the oblate liquid crystal elastomers, the stretch parallel to the director will cause the rotation of the director and induce the biaxiality.     

Visco-electro-elastic models of fiber-distributed active tissues

We present a constitutive model for stochastically distributed fiber reinforced visco-active tissues, where the behavior of the reinforcement depends on the relative orientation of the electric field. Following our previous works, for the passive behaviors we adopt a second order approximation of the strain energy density associated to the parameters of the fiber distribution. Consistently, we also assume that the active behavior accounts for the stochastic distribution of the fibers. The ensuing mechanical quantities result to be dependent on two average structure tensors. We introduce an extended Helmholtz free energy density characterized by the inclusion of a directional active potential, dependent on a stochastic anisotropic permittivity tensor. The permittivity tensor is expanded in Taylor series up to the second order, allowing to obtain an approximated active potential with the same structure of the passive Helmholtz free energy density. In particular, the explicit expression of active stress and stiffness are dependent on the two average structure tensors that characterize the passive response. Anisotropy follows from the fiber distribution and inherits its stochastic nature through statistics parameters. The active fiber distributed model is extended here to viscous materials by including the contribution of a dual dissipation potential in the variational formulation of the constitutive updates. Additionally, we present a computational example of application of the electro-viscous-mechanical material model by simulating peristaltic contractions on a portion of human intestine.     

A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus

This paper presents a composites-based hyperelastic constitutive model for soft tissue. Well organized soft tissue is treated as a composite in which the matrix material is embedded with a single family of aligned fibers. The fiber is modeled as a generalized neo-Hookean material in which the stiffness depends on fiber stretch. The deformation gradient is decomposed multiplicatively into two parts: a uniaxial deformation along the fiber direction and a subsequent shear deformation. This permits the fiber-matrix interaction caused by inhomogeneous deformation to be estimated by using effective properties from conventional composites theory based on small strain linear elasticity and suitably generalized to the present large deformation case. A transversely isotropic hyperelastic model is proposed to describe the mechanical behavior of fiber-reinforced soft tissue. This model is then applied to the human annulus fibrosus. Because of the layered anatomical structure of the annulus fibrosus, an orthotropic hyperelastic model of the annulus fibrosus is developed. Simulations show that the model reproduces the stress-strain response of the human annulus fibrosus accurately. We also show that the expression for the fiber-matrix shear interaction energy used in a previous phenomenological model is compatible with that derived in the present paper.     

复合材料层板的抗贯穿机理与模拟研究

为了研究树脂基纤维增强复合材料层板的抗侵彻贯穿机理和动态力学行为与抗侵彻毁伤的关系, 通过球形破片模拟弹贯穿实验表征了复合材料层板抗高速侵彻的吸能特性;通过高速摄影技术分析了层板 贯穿过程的瞬态变形失效特点;采用CT扫描成像及SEM 电镜分析等手段研究了复合材料层板的抗贯穿破 坏耗能模式。实验结果显示,高速冲击下层板抗贯穿吸能与入射速度成正比;高速侵彻过程是复合材料层板 高应变率变形的动态过程,高应变率动态力学行为对复合层板抗贯穿吸能特性影响显著;冲击波在层板中的 传播特性决定了不同破坏模式阶段的划分以及损伤区域的范围。基于复合层板高速贯穿下的动力学瞬态分 析,建立了复合层板抗高速侵彻吸能的两阶段动态破坏模型,模型计算值与实验值符合良好。研究结果表明, 应变率效应与惯性效应在复合材料层板抗侵彻性能分析中是不可忽视的2个关键因素。