多孔硅橡胶有限变形的粘弹性行为

针对孔隙度较大（孔隙度大于50％）的硅橡胶材料在有限变形时的粘弹性行为，从建立描述材料粘弹性特征的松驰函数和变形特征的应变能函数出发，提出了适合多孔隙、可压硅橡胶材料的非线性粘弹性力学行为的本构关系，松驰函数和应变能函数可解耦为等容和体积变形两部分，并引入了拟时间的概念来反映变形对材料特征时间的影响，利用硅橡胶材料的单轴压缩松驰实验与材料模型进行了对比，讨论了多孔硅橡胶的等容变形和体积变形对应力松驰的影响。     

一种变温非线性粘弹性理论

实验表明,在高温下,某些金属材料呈非线性粘弹性：对不同的应变增量,材料有不同的瞬时弹性模量,所产生的应力沿不同的松弛曲线松弛。该了表述材料这一力学行为的变温非线性粘弹性本构方程,它可用于在高温和变温下工作的构件（如模具）的变形计算。     

粘弹性材料的变形动力学模型

粘弹性材料的变形动力学模型周建平（长沙国防科技大学，４１００７３）关键词粘弹性，本构关系，内变量，老化１引言许多工程材料，特别是聚合物材料的应力应变关系具有粘弹性特征，使得材料或结构在受力过程中发生蠕变或应力松弛现象．从微观上讲，这种粘弹性变形是由于...     

纤维加强复合材料的总体粘弹性响应

在某些纤维增强复合材料(FRC)中使用金属或高分子聚合物作为基体材料。在高温等情况下,这类材料具有明显的粘弹性特性。本文采用Riemann—Liouville形式的分数阶导数模型描述基体的粘弹性特性。通过渐近均匀化方法给出了预测FRC整体三维本构关系的解析表达式。给出了应用于基体具有Makris粘弹性关系的具体形式。以圆截面纤维正方形排列的情形为例,给出了等效模量随纤维体积比的变化曲线。结果说明,这类复合材料仍具有粘弹性特性,其整体粘弹性本构关系的弹性部分综合了纤维弹性和基体弹性的贡献,粘性部分来自基体粘性的贡献,复合材料具有和基体相同的粘性系数和分数阶。为分析微结构特征对整体特性的贡献,须求解两类局部问题。可以看出,在整体的等效模量中包含了局部变形的贡献,局部变形增加了复合材料的耦合刚度。     

非线性粘弹性平面问题的数学模型及其失记效应

本文以位移为基本未知量,利用非线性粘弹性力学中的Leaderman本构关系和线性几何假设,建立了非线性粘弹性平面问题的数学模型;在粘弹性泊松比为常数的情况下,利用Titchmarsh定理和Laplace变换法证明了非线性粘弹性平面问题与非线性弹性平面问题之间存在着某些对应关系,对应关系为粘弹性问题的求解提供了一种新的思路,利用这些关系可直接从相应弹性问题获得粘弹性平面问题的部分响应,与传统的时域有限差分法相比,计算时间明显缩短,另外,对应关系也揭示了粘弹性结构的失记效应,即结构的部分响应仅与外部输入的现时值有关,而与其历史无关。     

丁基橡胶粘弹性材料的非线性蠕变本构描述

对丁基橡胶ZN-17粘弹性材料进行了不同温度、不同应力水平下的蠕变实验,揭示了该材料的非线性蠕变特性。基于蠕变实验结果,对标准线性固体模型描述该材料蠕变行为的预言能力进行了评估,提出了新的非线性蠕变本构模型。通过与实验结果比较,表明新模型能较好地描述该材料的非线性蠕变特性。     

具有广义力场损伤粘弹性梁-柱的广义变分原理及应用

本文从考虑损伤的粘弹性材料的卷积型本构关系出发,建立了在小变形下损伤粘弹性梁-柱的控制方程。提出了以卷积形式表示的梁-柱弯曲问题的泛函,并给出了损伤粘弹性梁-柱的广义变分原理。应用这个广义变分原理,可分别给出梁-柱位移和损伤满足的基本方程,以及相应的初始条件和边界条件。应用Galerkin截断和非线性动力学的数值分析方法,分析了两端简支损伤粘弹性梁柱的动力学行为,给出了不同的材料参数对系统响应的影响。     

非线性粘弹性板的失稳条件

研究了给定面内周期激励作用下简支各向同性均匀粘弹性板平衡失稀问题,板的材料特性由Leaderman非线性本构关系描述,将板的动力学方程进行（Galerkin截断得到简化数学模型为弱非线性系统,采用平均法得到系统的平均化方程,对平均化方程进行稳定性分析得到了板平衡失稳的解析条件,对原系统用数值仿真进行研究,数值结果表明,随着激励幅值的增加或粘弹性材料系数的减少,系统平衡点推失稳,激励幅值和粘弹性材料系数的临界值均与解析结果接近。     

在有限变形条件下损伤粘弹性梁的动力学行为

本文在有限变形条件下，根据损伤粘弹性材料的一种卷积型本构关系和温克列假设，建立了粘弹性基础上损伤粘弹性Timoshenko梁的控制方程。这是一组非线性积分——偏微分方程。为了便于分析，首先利用Galerkin方法对该方程组进行简化，得到一组非线性积分一常微分方程。然后应用非线性动力学中的数值方法，分析了粘弹性地基上损伤粘弹性Timoshenko梁的非线性动力学行为，得到了简化系统的相平面图、Poincare截面和分叉图等。考察了材料参数和载荷参数等对梁的动力学行为的影响。特别，考察了基础和损伤对粘弹性梁的动力学行为的影响。     

有机玻璃在高应变率下的损伤型非线性粘弹性本构关系及破坏准则

对两种有机玻璃高应变率下的大变形和破坏行为进行了实验研究,通过改进文献[2]本构关系的非线性弹性项并引入损伤参量,建立了一个适用于更大变形范围、能描述“应力平台”及“本构失稳”的损伤型非线性粘弹性本构方程。相应地,从临界损伤量概念出发,提出以应变和应变率为控制变量的破坏准则。不论是本构关系还是破坏准则,理论计算均与试验结果吻合良好。     

Nonlinear Fractional Order Viscoelasticity at Large Strains

In this paper, we formulate a fractional order viscoelastic model for large deformations and develop an algorithm for the integration of the constitutive response. The model is based on the multiplicative split of the deformation gradient into elastic and viscous parts. Further, the stress response is considered to be composed of a nonequilibrium part and an equilibrium part. The viscous part of the deformation gradient (here regarded as an internal variable) is governed by a nonlinear rate equation of fractional order. To solve the rate equation the finite element method in time is used in combination with Newton iterations. The method can handle nonuniform time meshes and uses sparse quadrature for the calculations of the fractional order integral. Moreover, the proposed model is compared to another large deformation viscoelastic model with a linear rate equation of fractional order. This is done by computing constitutive responses as well as structural dynamic responses of fictitious rubber materials.     

Nonlinear Fractional Order Viscoelasticity at Large Strains

In this paper, we formulate a fractional order viscoelastic model for large deformations and develop an algorithm for the integration of the constitutive response. The model is based on the multiplicative split of the deformation gradient into elastic and viscous parts. Further, the stress response is considered to be composed of a nonequilibrium part and an equilibrium part. The viscous part of the deformation gradient (here regarded as an internal variable) is governed by a nonlinear rate equation of fractional order. To solve the rate equation the finite element method in time is used in combination with Newton iterations. The method can handle nonuniform time meshes and uses sparse quadrature for the calculations of the fractional order integral. Moreover, the proposed model is compared to another large deformation viscoelastic model with a linear rate equation of fractional order. This is done by computing constitutive responses as well as structural dynamic responses of fictitious rubber materials.     

A viscoelastic constitutive model of rubber under small oscillatory load superimposed on large static deformation

Summary  A viscoelastic constitutive equation of rubber that is under small oscillatory load superimposed on large static deformation is proposed. The model is derived through linearization of Simo's nonlinear viscoelastic constitutive model and reference configuration transformation. Most importantly, in this model, static deformation correction factor is introduced to consider the influence of pre-strain on the relaxation function. Natural statically pre-deformed state is served as reference configuration. The proposed constitutive equation is extended to a generalized viscoelastic constitutive equation that includes widely used Morman's model as a special case using objective stress increment. The proposed constitutive model is tested for dynamic behavior of rubber specimens with different carbon black content. It is concluded from the test that the assumption that the effects of static deformation can be separated from time effects, which is the basis of Morman's model, is only applicable to unfilled rubber. The viscoelastic constitutive equation for filled rubber must include, therefore, the influence of the static deformation on the time effects. The suggested constitutive equation with static deformation correction factor shows good agreement with test values. Received 4 January 2001; accepted for publication 13 June 2001     

An Approach to Constructing a Rheological Model of a Strain-Hardening Medium

The one-dimensional constitutive equations of strain-hardening materials subject to nonlinear creep are derived. The solution is found using the hypothesis of unified deformation curve based on the similarity of the tensile and isochronic creep curves. A generalized rheological model is constructed which accounts for the instantaneous strain rate, loading rate, and the mode of strain hardening. This model is used to derive one-dimensional constitutive equations for linear viscoelastic, nonlinear viscoelastic, and linear- and nonlinear-hardening viscoelastoplastic materials. It is shown that the creep of linear viscoelastic and linear-hardening viscoelastoplastic materials is transient. For nonlinear viscoelastic and nonlinear-hardening viscoelastoplastic materials, all the characteristic stages of creep are present     

含黏弹性夹芯FG-GRC后屈曲梁的低速冲击响应

研究了含黏弹性夹芯的功能梯度石墨烯增强复合材料(functionally graded graphene reinforced composite, FG-GRC)后屈曲梁在低速跌落冲击下的跳跃振荡行为.采用修正Halpin-Tsai细观模型预测FG-GRC的材料宏观属性.使用赫兹点接触模型确定冲击器和梁之间的接触力.提出了考虑轴向预应力的复合材料层本构关系和阻尼层的Kelvin型黏弹性本构.通过一种广义高阶剪切变形锯齿梁模型建立夹芯梁的非线性位移场. 基于Hamilton 能量变分原理, 推导了动力学控制方程组. 通过两步分析,首先获得弹性后屈曲平衡路径作为冲击问题的初始状态. 随后, 结合四阶龙格库塔法,拓展了两步摄动-伽辽金法计算接触力的时程曲线以及后屈曲梁的位移时程曲线.研究了后屈曲梁在单次和两次撞击下双稳态大幅振荡过程的动力学特征.讨论了轴向载荷、冲击速度、黏弹性阻尼特性、冲击器材料等因素对于碰撞接触力以及后屈曲梁动力响应的影响规律.结果表明, 接触力仅对冲击速度较为敏感,一定的结构碰撞参数设计可以在接触力变化不大的情况下,使得后屈曲梁由单势能阱运动转变为双阱大幅振荡.      

高应变率下航空透明聚氨酯的动态本构模型

采用低阻抗分离式霍普金森压杆对航空透明聚氨酯进行了高应变率下的动态力学性能测试,得到的应力应变曲线表现出了显著的非线性黏弹性特征。基于本构理论和实验数据,构建了航空透明聚氨酯的松弛时间应变相关的超黏弹性本构形式。该本构模型由2部分组成:一部分表征准静态下的超弹性行为,另一部分描述非线性应变率的相关特性。利用超黏弹性本构模型对不同应变率下航空透明聚氨酯的动态应力应变曲线进行拟合,拟合曲线与实验曲线一致性良好。     

聚氯乙烯弹性体静动态力学性能及本构模型

为揭示聚氯乙烯弹性体在静、动态载荷下的力学性能，采用万能材料试验机和改进的分离式霍普金森压杆实验装置获得了材料在应变率为0.001、0.01、0.1、1 510、2 260和3 000 s?1下的应力应变曲线，并以屈服强度为整形器优选参数，对比了紫铜、铜版纸和铅等3种整形器材料的整形效果。使用修正的ZWT非线性黏弹性本构模型描述聚氯乙烯弹性体在静、动态载荷下的力学性能。结果表明:聚氯乙烯弹性体在静态载荷下具有应变率效应和显著的超弹性特性，动态载荷下表现出较明显的应变率效应和较强的抗变形能力，且静动态载荷下的力学行为受应变历史影响较大。3种整形器材料中铜版纸的整形效果最好。修正后的ZWT非线性黏弹性本构模型能够得到统一参数的本构表达式，且各应变率下的拟合结果与实验结果具有较好的一致性。     

心肌细胞大变形黏弹性模型及在实验中的应用

在衡量单个细胞力学行为的研究中,越来越多地采用结合实验的数值模拟方法. 在连续介质力学框架下,发展了一种新的心肌细胞本构模型,并与微管吮吸实验结合,探讨了心肌细胞的力学特性. 本构模型是对普遍使用的仅能用于小变形分析的标准线性固体模型的一种扩展,它将超弹性性能引入到黏弹性模型中,用以描述细胞的大变形黏弹性效应. 基于改进的本构模型,对心肌细胞微管吮吸实验过程进行了有限元模拟,并将计算结果与实验结果以及经典理论解进行了对比. 结果显示发展的本构模型适合细胞大变形问题的有限元数值模拟.      

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.     

STATE OF THE ART OF CONSTITUTIVE RELATIONS OF HYPERELASTIC MATERIALS 1)

超弹性材料是工程实际中的常用材料, 具有在外力作用下经历非常大变形、在外力撤去后完全恢复至初始状态的特征. 超弹性材料是典型的非线性弹性材料, 其性能可通过材料的应变能函数予以表征. 近几十年来, 围绕应变能函数形式的构造, 已提出许多超弹性材料本构关系研究的数学模型和物理模型, 但适用于多种变形模式和全变形范围的完全本构关系仍是该领域期待解决的重要问题. 本文从3个不同角度, 对超弹性材料本构关系研究的最新进展进行了总结和分析: (1)不同体积变化模式, 包含不可压与可压两种; (2)多变形模式, 包含单轴拉伸、剪切、等双轴以及复合拉剪等多个种类; (3)全范围变形程度, 包含小变形、中等变形到较大变形范围. 超弹性材料本构关系研究的最新进展表明, 为了全面描述具体材料的实验数据并在实际问题中应用超弹性材料, 需要建立适合于多种变形模式和全变形范围的可压超弹性材料的完全本构关系. 对实际超弹性材料完全本构关系的建立及可压超弹性材料应变能函数的构造, 笔者还提出了相应的实施步骤和研究方法.